{"id":388,"date":"2021-05-19T17:07:31","date_gmt":"2021-05-19T17:07:31","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/basicreview\/chapter\/properties-of-real-numbers\/"},"modified":"2023-08-09T22:44:08","modified_gmt":"2023-08-09T22:44:08","slug":"properties-of-real-numbers","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/basicreview\/chapter\/properties-of-real-numbers\/","title":{"raw":"2.5 Properties of Real Numbers","rendered":"2.5 Properties of Real Numbers"},"content":{"raw":"[latexpage]\r\n<div class=\"textbox textbox--learning-objectives\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Learning Objectives<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nBy the end of this section, you will be able to:\r\n<ul>\r\n \t<li>Use the commutative and associative properties<\/li>\r\n \t<li>Use the identity and inverse properties of addition and multiplication<\/li>\r\n \t<li>Use the properties of zero<\/li>\r\n \t<li>Simplify expressions using the distributive property<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<h1>Use the Commutative and Associative Properties<\/h1>\r\n<p id=\"fs-id1170654026828\">Think about adding two numbers, say 5 and 3. The order we add them doesn\u2019t affect the result, does it?<\/p>\r\n\\(\\begin{array}{cccc}\\hfill 5+3\\hfill &amp; &amp; &amp; \\hfill 3+5\\hfill \\\\ \\hfill 8\\hfill &amp; &amp; &amp; \\hfill 8\\hfill \\end{array}\\)\r\n<div id=\"fs-id1166426267603\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(5+3=3+5\\)<\/div>\r\n<p id=\"fs-id1170653891144\">The results are the same.<\/p>\r\n<p id=\"fs-id1170654031116\">As we can see, the order in which we add does not matter!<\/p>\r\n<p id=\"fs-id1170653884964\">What about multiplying \\(5\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}3?\\)<\/p>\r\n\r\n<div id=\"fs-id1170654014649\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\begin{array}{cccc}\\hfill 5\\cdot3\\hfill &amp; &amp; &amp; \\hfill 3\\cdot5\\hfill \\\\ \\hfill 15\\hfill &amp; &amp; &amp; \\hfill 15\\hfill \\end{array}\\)<\/div>\r\n<div id=\"fs-id1166424005906\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(5\\cdot3=3\\cdot5\\)<\/div>\r\n<p id=\"fs-id1170653771564\">Again, the results are the same!<\/p>\r\n<p id=\"fs-id1170654027262\">The order in which we multiply does not matter!<\/p>\r\n<p id=\"fs-id1170654013661\">These examples illustrate the commutative property. When adding or multiplying, changing the <em data-effect=\"italics\">order<\/em> gives the same result.<\/p>\r\n\r\n<div id=\"fs-id1170653917425\" data-type=\"note\">\r\n<div data-type=\"title\">\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Commutative Property<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n\\(\\begin{array}{ccccccccc}\\mathbf{\\text{of Addition}}\\hfill &amp; &amp; &amp; \\text{If}\\phantom{\\rule{0.2em}{0ex}}a,b\\phantom{\\rule{0.2em}{0ex}}\\text{are real numbers, then}\\hfill &amp; &amp; &amp; \\hfill a+b&amp; =\\hfill &amp; b+a\\hfill \\\\ \\mathbf{\\text{of Multiplication}}\\hfill &amp; &amp; &amp; \\text{If}\\phantom{\\rule{0.2em}{0ex}}a,b\\phantom{\\rule{0.2em}{0ex}}\\text{are real numbers, then}\\hfill &amp; &amp; &amp; \\hfill a\\cdot b&amp; =\\hfill &amp; b\\cdot a\\hfill \\end{array}\\)\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1170653751940\">When adding or multiplying, changing the <em data-effect=\"italics\">order<\/em> gives the same result.<\/p>\r\n\r\n<\/div>\r\n<p id=\"fs-id1170654011373\">The commutative property has to do with order. If you change the order of the numbers when adding or multiplying, the result is the same.<\/p>\r\n<p id=\"fs-id1170653758644\">What about subtraction? Does order matter when we subtract numbers? Does \\(7-3\\) give the same result as \\(3-7?\\)<\/p>\r\n\r\n<div id=\"fs-id1170654027324\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\begin{array}{c}\\hfill \\begin{array}{cc}\\hfill 7-3\\hfill &amp; \\hfill \\phantom{\\rule{1em}{0ex}}3-7\\hfill \\\\ \\hfill 4\\hfill &amp; \\hfill \\phantom{\\rule{1em}{0ex}}-4\\hfill \\end{array}\\hfill \\\\ \\\\ \\\\ \\hfill \\phantom{\\rule{0.5em}{0ex}}4\\ne -4\\hfill \\\\ \\hfill 7-3\\ne 3-7\\hfill \\end{array}\\)<\/div>\r\n<p id=\"fs-id1170654013324\">The results are not the same.<\/p>\r\n<p id=\"fs-id1170653892774\">Since changing the order of the subtraction did not give the same result, we know that <em data-effect=\"italics\">subtraction is not commutative<\/em>.<\/p>\r\nLet\u2019s see what happens when we divide two numbers. Is <span class=\"no-emphasis\" data-type=\"term\">division<\/span> commutative?\r\n<div id=\"fs-id1170654031695\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\begin{array}{c}\\\\ \\hfill \\begin{array}{cc}\\hfill 12\\div 4\\hfill &amp; \\hfill \\phantom{\\rule{1em}{0ex}}4\\div 12\\hfill \\\\ \\hfill \\frac{12}{4}\\hfill &amp; \\hfill \\phantom{\\rule{1em}{0ex}}\\frac{4}{12}\\hfill \\\\ \\hfill 3\\hfill &amp; \\hfill \\phantom{\\rule{1em}{0ex}}\\frac{1}{3}\\hfill \\end{array}\\hfill \\\\ \\hfill 3\\ne \\frac{1}{3}\\hfill \\\\ \\hfill 12\\div 4\\ne 4\\div 12\\hfill \\end{array}\\)<\/div>\r\n<p id=\"fs-id1170653797051\">The results are not the same.<\/p>\r\n<p id=\"fs-id1170653742804\">Since changing the order of the division did not give the same result, <em data-effect=\"italics\">division is not commutative<\/em>. The commutative properties only apply to addition and multiplication!<\/p>\r\n\r\n<ul id=\"fs-id1166426095775\" data-bullet-style=\"bullet\">\r\n \t<li>Addition and multiplication <em data-effect=\"italics\">are<\/em> commutative.<\/li>\r\n \t<li>Subtraction and Division <em data-effect=\"italics\">are not<\/em> commutative.<\/li>\r\n<\/ul>\r\n<p id=\"fs-id1170653898679\">If you were asked to simplify this expression, how would you do it and what would your answer be?<\/p>\r\n\\(7+8+2\\)\r\n\r\nSome people would think \\(7+8\\phantom{\\rule{0.2em}{0ex}}\\text{is}\\phantom{\\rule{0.2em}{0ex}}15\\) and then \\(15+2\\phantom{\\rule{0.2em}{0ex}}\\text{is}\\phantom{\\rule{0.2em}{0ex}}17\\). Others might start with \\(8+2\\phantom{\\rule{0.2em}{0ex}}\\text{makes}\\phantom{\\rule{0.2em}{0ex}}10\\) and then \\(7+10\\phantom{\\rule{0.2em}{0ex}}\\text{makes}\\phantom{\\rule{0.2em}{0ex}}17\\).\r\n<p id=\"fs-id1170653887975\">Either way gives the same result. Remember, we use parentheses as grouping symbols to indicate which operation should be done first.<\/p>\r\n\r\n<table id=\"eip-252\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>Add \\(7+8\\).\r\nAdd.<\/td>\r\n<td>\\(\\begin{array}{c}\\left(7+8\\right)+2\\\\ 15+2\\\\ 17\\end{array}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add \\(8+2\\).\r\nAdd.<\/td>\r\n<td>\\(\\begin{array}{c}7+\\left(8+2\\right)\\\\ 7+10\\\\ 17\\end{array}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>\\(\\left(7+8\\right)+2=7+\\left(8+2\\right)\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p id=\"fs-id1170654015259\">When adding three numbers, changing the grouping of the numbers gives the same result.<\/p>\r\n<p id=\"fs-id1170654073631\">This is true for multiplication, too.<\/p>\r\n\r\n<table id=\"eip-989\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>Multiply. \\(5\\cdot\\frac{1}{3}\\)\r\nMultiply.<\/td>\r\n<td>\\(\\begin{array}{c}\\phantom{\\rule{2em}{0ex}}\\left(5\\cdot\\frac{1}{3}\\right)\\cdot3\\\\ \\frac{5}{3}\\cdot3\\\\ 5\\end{array}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply. \\(\\frac{1}{3}\\cdot3\\).\r\nMultiply.<\/td>\r\n<td>\\(\\begin{array}{c}5\\cdot\\left(\\frac{1}{3}\\cdot3\\right)\\\\ 5\\cdot1\\\\ 5\\end{array}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>\\(\\left(5\\cdot\\frac{1}{3}\\right)\\cdot3=5\\cdot\\left(\\frac{1}{3}\\cdot3\\right)\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p id=\"fs-id1170653774811\">When multiplying three numbers, changing the grouping of the numbers gives the same result.<\/p>\r\n<p id=\"fs-id1170653916060\">You probably know this, but the terminology may be new to you. These examples illustrate the associative property.<\/p>\r\n\r\n<div id=\"fs-id1170653849240\" data-type=\"note\">\r\n<div data-type=\"title\">\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Associative Property<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n\\(\\begin{array}{cccc}\\mathbf{\\text{of Addition}}\\hfill &amp; &amp; &amp; \\text{If}\\phantom{\\rule{0.2em}{0ex}}a,b,c\\phantom{\\rule{0.2em}{0ex}}\\text{are real numbers, then}\\phantom{\\rule{0.2em}{0ex}}\\left(a+b\\right)+c=a+\\left(b+c\\right)\\hfill \\\\ \\mathbf{\\text{of Multiplication}}\\hfill &amp; &amp; &amp; \\text{If}\\phantom{\\rule{0.2em}{0ex}}a,b,c\\phantom{\\rule{0.2em}{0ex}}\\text{are real numbers, then}\\phantom{\\rule{0.2em}{0ex}}\\left(a\\cdot b\\right)\\cdot c=a\\cdot \\left(b\\cdot c\\right)\\hfill \\end{array}\\)\r\n\r\nWhen adding or multiplying, changing the <em data-effect=\"italics\">grouping<\/em> gives the same result.\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1170653894784\">Let\u2019s think again about multiplying \\(5\\cdot \\frac{1}{3}\\cdot 3\\). We got the same result both ways, but which way was easier? Multiplying \\(\\frac{1}{3}\\) and \\(3\\) first, as shown above on the right side, eliminates the fraction in the first step. Using the associative property can make the math easier!<\/p>\r\nThe <span class=\"no-emphasis\" data-type=\"term\">associative property<\/span> has to do with grouping. If we change how the numbers are grouped, the result will be the same. Notice it is the same three numbers in the same order\u2014the only difference is the grouping.\r\n<p id=\"fs-id1170653894135\">We saw that subtraction and division were not commutative. They are not associative either.<\/p>\r\n<p id=\"fs-id1170653807341\">When simplifying an expression, it is always a good idea to plan what the steps will be. In order to combine like terms in the next example, we will use the commutative property of addition to write the like terms together.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654077092\" data-type=\"problem\">\r\n<p id=\"fs-id1170653907474\">Simplify: \\(18p+6q+15p+5q\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170653909769\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-193\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>\\(18p+6q+15p+5q\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Use the commutative property of addition to re-order so that like terms are together.<\/td>\r\n<td>\\(18p+15p+6q+5q\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add like terms.<\/td>\r\n<td>\\(33p+11q\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 1.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654076917\" data-type=\"problem\">\r\n<p id=\"fs-id1170653915616\">Simplify: \\(23r+14s+9r+15s\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170653906988\" data-type=\"solution\"><details><summary>Answer<\/summary>\r\n<p id=\"fs-id1170654009182\">\\(32r+29s\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 1.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170653795554\" data-type=\"problem\">\r\n<p id=\"fs-id1170653775684\">Simplify: \\(37m+21n+4m-15n\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654014491\" data-type=\"solution\"><details><summary>Answer<\/summary>\r\n<p id=\"fs-id1170654030751\">\\(41m+6n\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\nWhen we have to simplify algebraic <span class=\"no-emphasis\" data-type=\"term\">expression<\/span>s, we can often make the work easier by applying the commutative or associative property first, instead of automatically following the order of operations. When adding or subtracting fractions, combine those with a common denominator first.\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170653890205\" data-type=\"problem\">\r\n<p id=\"fs-id1170653748931\">Simplify: \\(\\left(\\frac{5}{13}+\\frac{3}{4}\\right)+\\frac{1}{4}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170653984832\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<table id=\"eip-8\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>\\(\\left(\\frac{5}{13}+\\frac{3}{4}\\right)+\\frac{1}{4}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Notice that the last 2 terms have a common denominator, so change the grouping.<\/td>\r\n<td>\\(\\frac{5}{13}+\\left(\\frac{3}{4}+\\frac{1}{4}\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add in parentheses first.<\/td>\r\n<td>\\(\\frac{5}{13}+\\left(\\frac{4}{4}\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify the fraction.<\/td>\r\n<td>\\(\\frac{5}{13}+1\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add.<\/td>\r\n<td>\\(1\\frac{5}{13}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Convert to an improper fraction.<\/td>\r\n<td>\\(\\frac{18}{13}\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 2.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654044584\" data-type=\"problem\">\r\n<p id=\"fs-id1170654044586\">Simplify: \\(\\left(\\frac{7}{15}+\\frac{5}{8}\\right)+\\frac{3}{8}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170653901181\" data-type=\"solution\"><details><summary>Answer<\/summary>\r\n<p id=\"fs-id1170653901183\">\\(1\\frac{7}{15}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 2.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654077704\" data-type=\"problem\">\r\n<p id=\"fs-id1170654077707\">Simplify: \\(\\left(\\frac{2}{9}+\\frac{7}{12}\\right)+\\frac{5}{12}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170653901148\" data-type=\"solution\"><details><summary>Answer<\/summary>\r\n<p id=\"fs-id1170653901150\">\\(1\\frac{2}{9}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1170654044578\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1170654044582\" data-type=\"exercise\">\r\n<div id=\"fs-id1170654044584\" data-type=\"problem\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 3<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654014667\" data-type=\"problem\">\r\n<p id=\"fs-id1170654014669\">Use the associative property to simplify \\(6\\left(3x\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170653901248\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-519\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>\\(6\\left(3x\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Change the grouping.<\/td>\r\n<td>\\(\\left(6 \\cdot 3\\right)x\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply in the parentheses.<\/td>\r\n<td>\\(18x\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p id=\"fs-id1170654059651\">Notice that we can multiply \\(6\\cdot 3\\) but we could not multiply 3<em data-effect=\"italics\">x<\/em> without having a value for <em data-effect=\"italics\">x<\/em>.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY 3.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654077036\" data-type=\"problem\">\r\n<p id=\"fs-id1170654077038\">Use the associative property to simplify 8(4<em data-effect=\"italics\">x<\/em>).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654077047\" data-type=\"solution\"><details><summary>Answer<\/summary>\r\n<p id=\"fs-id1170654077049\">32<em data-effect=\"italics\">x<\/em><\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1170654079038\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1170654079042\" data-type=\"exercise\">\r\n<div id=\"fs-id1170654079044\" data-type=\"problem\">\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 3.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654079044\" data-type=\"problem\">\r\n<p id=\"fs-id1170654079046\">Use the associative property to simplify \\(-9\\left(7y\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654077742\" data-type=\"solution\"><details><summary>Answer<\/summary>\r\n<p id=\"fs-id1170654077744\">\\(-63y\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<h1>Use the Identity and Inverse Properties of Addition and Multiplication<\/h1>\r\n<p id=\"fs-id1170654077762\">What happens when we add 0 to any number? Adding 0 doesn\u2019t change the value. For this reason, we call 0 the additive identity.<\/p>\r\n<p id=\"fs-id1170654084972\">For example,<\/p>\r\n\\(\\begin{array}{ccccccc}\\hfill 13+0\\hfill &amp; &amp; &amp; \\hfill -14+0\\hfill &amp; &amp; &amp; \\hfill 0+\\left(-8\\right)\\hfill \\\\ \\hfill 13\\hfill &amp; &amp; &amp; \\hfill -14\\hfill &amp; &amp; &amp; \\hfill -8\\hfill \\end{array}\\)\r\n<p id=\"fs-id1170654073759\">These examples illustrate the Identity Property of Addition that states that for any real number \\(a\\), \\(a+0=a\\) and \\(0+a=a\\).<\/p>\r\n<p id=\"fs-id1170654078244\">What happens when we multiply any number by one? Multiplying by 1 doesn\u2019t change the value. So we call 1 the multiplicative identity.<\/p>\r\n<p id=\"fs-id1170654078252\">For example,<\/p>\r\n\\(\\begin{array}{ccccccc}\\hfill 43\\cdot1\\hfill &amp; &amp; &amp; \\hfill -27\\cdot1\\hfill &amp; &amp; &amp; \\hfill 1\\cdot\\frac{3}{5}\\hfill \\\\ \\hfill 43\\hfill &amp; &amp; &amp; \\hfill -27\\hfill &amp; &amp; &amp; \\hfill \\frac{3}{5}\\hfill \\end{array}\\)\r\n<p id=\"fs-id1170654014513\">These examples illustrate the Identity Property of Multiplication that states that for any real number \\(a\\), \\(a\\cdot1=a\\) and \\(1\\cdot a=a\\).<\/p>\r\n<p id=\"fs-id1170653990233\">We summarize the Identity Properties below.<\/p>\r\n\r\n<div id=\"fs-id1170653990236\" data-type=\"note\">\r\n<div data-type=\"title\">\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Identity Property<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n\\(\\begin{array}{ccccc}\\text{of addition}\\phantom{\\rule{0.2em}{0ex}}\\text{For any real number}\\phantom{\\rule{0.2em}{0ex}}a\\text{:}\\hfill &amp; &amp; \\hfill a+0=a&amp; &amp; \\hfill 0+a=a\\\\ \\hfill 0\\phantom{\\rule{0.2em}{0ex}}\\text{is the}\\phantom{\\rule{0.2em}{0ex}}\\text{additive identity}\\hfill &amp; &amp; &amp; &amp; \\\\ \\\\ \\\\ \\text{of multiplication}\\phantom{\\rule{0.2em}{0ex}}\\text{For any real number}\\phantom{\\rule{0.2em}{0ex}}a\\text{:}\\hfill &amp; &amp; \\hfill a\\cdot 1=a&amp; &amp; \\hfill 1\\cdot a=a\\\\ \\hfill 1\\phantom{\\rule{0.2em}{0ex}}\\text{is the}\\phantom{\\rule{0.2em}{0ex}}\\text{multiplicative identity}\\hfill \\end{array}\\)\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<span id=\"fs-id1170654036108\" data-type=\"media\" data-alt=\"In the top line of this figure, we have the question \u201cWhat number added to 5 gives the additive identity, 0?\u201d On the following line, we have 5 plus a blank space equals 0. Then it is stated that \u201cWe know 5 plus negative 5 equals 0.\u201d On the following line, we have the question \u201cWhat number added to negative 6 gives the additive identity, 0?\u201d On the following line, we have negative 6 plus a blank space equals 0. Then it is stated that \u201cWe know negative 6 plus 6 equals 0.\u201d\"><img class=\"aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/05\/CNX_ElemAlg_Figure_01_09_003_img_new.jpg\" alt=\"In the top line of this figure, we have the question \u201cWhat number added to 5 gives the additive identity, 0?\u201d On the following line, we have 5 plus a blank space equals 0. Then it is stated that \u201cWe know 5 plus negative 5 equals 0.\u201d On the following line, we have the question \u201cWhat number added to negative 6 gives the additive identity, 0?\u201d On the following line, we have negative 6 plus a blank space equals 0. Then it is stated that \u201cWe know negative 6 plus 6 equals 0.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n<p id=\"fs-id1170654036114\">Notice that in each case, the missing number was the opposite of the number!<\/p>\r\n<p id=\"fs-id1170654036118\">We call \\(-a\\). the additive inverse of <em data-effect=\"italics\">a<\/em>. <em data-effect=\"italics\">The opposite of a number is its additive inverse.<\/em> A number and its opposite add to zero, which is the additive identity. This leads to the Inverse Property of Addition that states for any real number \\(a,a+\\left(-a\\right)=0\\). Remember, a number and its opposite add to zero.<\/p>\r\n<p id=\"fs-id1170654014737\">What number multiplied by \\(\\frac{2}{3}\\) gives the multiplicative identity, 1? In other words, \\(\\frac{2}{3}\\) times what results in 1?<\/p>\r\n<span id=\"fs-id1170653797753\" data-type=\"media\" data-alt=\"We have the statement that 2\/3 times a blank space equals 1. Then it is stated that \u201cWe know 2\/3 times 3\/2 equals 1.\u201d\"><img class=\"aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_09_004_img_new.jpg\" alt=\"We have the statement that 2\/3 times a blank space equals 1. Then it is stated that \u201cWe know 2\/3 times 3\/2 equals 1.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n<p id=\"fs-id1170653797762\">What number multiplied by 2 gives the multiplicative identity, 1? In other words 2 times what results in 1?<\/p>\r\n<span id=\"fs-id1170653797768\" data-type=\"media\" data-alt=\"We have the statement that 2 times a blank space equals 1. Then it is stated that \u201cWe know 2 times 1\/2 equals 1.\u201d\"><img class=\"aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_09_005_img_new.jpg\" alt=\"We have the statement that 2 times a blank space equals 1. Then it is stated that \u201cWe know 2 times 1\/2 equals 1.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n<p id=\"fs-id1170653797777\">Notice that in each case, the missing number was the <span class=\"no-emphasis\" data-type=\"term\">reciprocal<\/span> of the number!<\/p>\r\n<p id=\"fs-id1170654030286\">We call \\(\\frac{1}{a}\\) the multiplicative inverse of <em data-effect=\"italics\">a<\/em>. <em data-effect=\"italics\">The reciprocal of \\(a\\) number is its multiplicative inverse.<\/em> A number and its reciprocal multiply to one, which is the multiplicative identity. This leads to the Inverse Property of Multiplication that states that for any real number \\(a,a\\ne 0,a\\cdot \\frac{1}{a}=1\\).<\/p>\r\n<p id=\"fs-id1170654012966\">We\u2019ll formally state the inverse properties here:<\/p>\r\n\r\n<div id=\"fs-id1170654012970\" data-type=\"note\">\r\n<div data-type=\"title\">\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Inverse Property<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<table id=\"eip-73\" class=\"grid\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><strong>of addition<\/strong><\/td>\r\n<td>For any real number \\(a\\),\r\n\\(-a\\) is the <strong>additive inverse<\/strong> of \\(a\\).\r\nA number and its opposite add to zero.<\/td>\r\n<td>\\(a+\\left(-a\\right)=0\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><strong>of multiplication<\/strong><\/td>\r\n<td>For any real number \\(a\\),\r\n\\(\\frac{1}{a}\\) is the <strong>multiplicative inverse<\/strong> of \\(a\\).\r\nA number and its reciprocal multiply to one.<\/td>\r\n<td>\\(a \\cdot \\frac{1}{a}=1\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 4<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654075038\" data-type=\"problem\">\r\n<p id=\"fs-id1170654075040\">Find the additive inverse of a) \\(\\frac{5}{8}\\) b) \\(0.6\\) c) \\(-8\\) d) \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{4}{3}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654084880\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<p id=\"fs-id1170654084886\">To find the additive inverse, we find the opposite.<\/p>\r\n\r\n<ol id=\"fs-id1166423979092\" class=\"circled\" type=\"a\">\r\n \t<li>The additive inverse of \\(\\frac{5}{8}\\) is the opposite of \\(\\frac{5}{8}\\). The additive inverse of \\(\\frac{5}{8}\\) is \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{5}{8}\\).<\/li>\r\n \t<li>The additive inverse of 0.6 is the opposite of 0.6. The additive inverse of 0.6 is \\(-0.6\\).<\/li>\r\n \t<li>The additive inverse of \\(-8\\) is the opposite of \\(-8\\). We write the opposite of \\(-8\\) as \\(-\\left(-8\\right)\\), and then simplify it to 8. Therefore, the additive inverse of \\(-8\\) is 8.<\/li>\r\n \t<li>The additive inverse of \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{4}{3}\\) is the opposite of \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{4}{3}\\). We write this as \\(-\\left(-\\phantom{\\rule{0.2em}{0ex}}\\frac{4}{3}\\right)\\), and then simplify to \\(\\frac{4}{3}\\). Thus, the additive inverse of \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{4}{3}\\) is \\(\\frac{4}{3}\\).<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 4.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170653800547\" data-type=\"problem\">\r\n<p id=\"fs-id1170653800549\">Find the additive inverse of: a) \\(\\frac{7}{9}\\) b) \\(1.2\\) c) \\(-14\\) d) \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{9}{4}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170653800585\" data-type=\"solution\"><details><summary>Answer<\/summary>\r\n<p id=\"fs-id1170653800587\">a) \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{7}{9}\\) b) \\(-1.2\\) c)\\(14\\) d) \\(\\frac{9}{4}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercises<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654073186\" data-type=\"problem\">\r\n<p id=\"fs-id1170654073188\">Find the additive inverse of: a) \\(\\frac{7}{13}\\) b) \\(8.4\\) c) \\(-46\\) d) \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{5}{2}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654078943\" data-type=\"solution\"><details><summary>Answer<\/summary>\r\n<p id=\"fs-id1170654078945\">a) \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{7}{13}\\) b) \\(-8.4\\) c) \\(46\\) d) \\(\\frac{5}{2}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 5<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654073241\" data-type=\"problem\">\r\n<p id=\"fs-id1170654073243\">Find the multiplicative inverse of a) \\(9\\) b) \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{9}\\) c) \\(0.9\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654073268\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<p id=\"fs-id1170654073274\">To find the multiplicative inverse, we find the reciprocal.<\/p>\r\n\r\n<ol id=\"fs-id1166426176898\" class=\"circled\" type=\"a\">\r\n \t<li>The multiplicative inverse of 9 is the reciprocal of 9, which is \\(\\frac{1}{9}\\). Therefore, the multiplicative inverse of 9 is \\(\\frac{1}{9}\\).<\/li>\r\n \t<li>The multiplicative inverse of \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{9}\\) is the reciprocal of \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{9}\\), which is \\(-9\\). Thus, the multiplicative inverse of \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{9}\\) is \\(-9\\).<\/li>\r\n \t<li>To find the multiplicative inverse of 0.9, we first convert 0.9 to a fraction, \\(\\frac{9}{10}\\). Then we find the reciprocal of the fraction. The reciprocal of \\(\\frac{9}{10}\\) is \\(\\frac{10}{9}\\). So the multiplicative inverse of 0.9 is \\(\\frac{10}{9}\\).<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 5.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170653991352\" data-type=\"problem\">\r\n<p id=\"fs-id1170653991354\">Find the multiplicative inverse of a) \\(4\\) b) \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{7}\\) c) \\(0.3\\)<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654073682\" data-type=\"solution\"><details><summary>Answer<\/summary>\r\n<p id=\"fs-id1170654073684\">a) \\(\\frac{1}{4}\\) b) \\(-7\\) c) \\(\\frac{10}{3}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 5.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654073719\" data-type=\"problem\">\r\n<p id=\"fs-id1170654073721\">Find the multiplicative inverse of a) \\(18\\) b) \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{4}{5}\\) c) \\(0.6\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654036171\" data-type=\"solution\"><details><summary>Answer<\/summary>\r\n<p id=\"fs-id1170654036173\">a) \\(\\frac{1}{18}\\) b) \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{5}{4}\\) c) \\(\\frac{5}{3}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<h1>Use the Properties of Zero<\/h1>\r\n<p id=\"fs-id1170653800723\">The identity property of addition says that when we add 0 to any number, the result is that same number. What happens when we multiply a number by 0? Multiplying by 0 makes the <span class=\"no-emphasis\" data-type=\"term\">product<\/span> equal zero.<\/p>\r\n\r\n<div id=\"fs-id1170653800728\" data-type=\"note\">\r\n<div data-type=\"title\">\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Multiplication by Zero<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<p id=\"fs-id1170653800734\">For any real number <em data-effect=\"italics\">a<\/em>.<\/p>\r\n\\(a\\cdot 0=0\\phantom{\\rule{6em}{0ex}}0\\cdot a=0\\)\r\n<p id=\"fs-id1170653800771\">The product of any real number and 0 is 0.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\nWhat about division involving zero? What is \\(0\\div 3?\\) Think about a real example: If there are no cookies in the cookie jar and 3 people are to share them, how many cookies does each person get? There are no cookies to share, so each person gets 0 cookies. So,\r\n\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1170654014380\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(0\\div 3=0\\)<\/div>\r\n<p id=\"fs-id1170654014398\">We can check division with the related multiplication fact.<\/p>\r\n\r\n<div id=\"fs-id1166426254494\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(12\\div 6=2\\phantom{\\rule{0.2em}{0ex}}\\text{because}\\phantom{\\rule{0.2em}{0ex}}2\\cdot 6=12\\).<\/div>\r\n<p id=\"fs-id1170654014427\">So we know \\(0\\div 3=0\\) because \\(0\\cdot 3=0\\).<\/p>\r\n\r\n<div id=\"fs-id1170654076119\" data-type=\"note\">\r\n<div data-type=\"title\">\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Division of Zero<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nFor any real number <em data-effect=\"italics\">a<\/em>, except \\(0\\), \\(\\frac{0}{a}=0\\) and \\(0\\div a=0\\).\r\n\r\nZero divided by any real number except zero is zero.\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1170654076171\">Now think about dividing <em data-effect=\"italics\">by<\/em> zero. What is the result of dividing 4 by 0? Think about the related multiplication fact: \\(4\\div 0=?\\) means \\(?\\cdot 0=4\\). Is there a number that multiplied by 0 gives 4? Since any real number multiplied by 0 gives 0, there is no real number that can be multiplied by 0 to obtain 4<\/p>\r\n<p id=\"fs-id1170653991470\">We conclude that there is no answer to \\(4\\div 0\\) and so we say that division by 0 is undefined.<\/p>\r\n\r\n<div id=\"fs-id1170653991484\" data-type=\"note\">\r\n<div data-type=\"title\">\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Division by Zero<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<p id=\"fs-id1170653991489\">For any real number <em data-effect=\"italics\">a<\/em>, except 0, \\(\\frac{a}{0}\\) and \\(a\\div 0\\) are undefined.<\/p>\r\n<p id=\"fs-id1170653991514\">Division by zero is undefined.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1170653991519\">We summarize the properties of zero below.<\/p>\r\n\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Properties of Zero<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<p id=\"fs-id1170653991528\"><strong data-effect=\"bold\">Multiplication by Zero:<\/strong> For any real number <em data-effect=\"italics\">a<\/em>,<\/p>\r\n\r\n<table id=\"eip-18\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>\\(a\\cdot 0=0\\phantom{\\rule{1em}{0ex}}0\\cdot a=0\\)<\/td>\r\n<td>The product of any number and 0 is 0.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p id=\"fs-id1170654014590\"><strong data-effect=\"bold\">Division of Zero, Division by Zero:<\/strong> For any real number \\(a,a\\ne 0\\)<\/p>\r\n\r\n<table id=\"eip-866\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>\\(\\frac{0}{a}=0\\)<\/td>\r\n<td>Zero divided by any real number except itself is zero.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>\\(\\frac{a}{0}\\phantom{\\rule{0.2em}{0ex}}\\text{is undefined}\\)<\/td>\r\n<td>Division by zero is undefined.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 6<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654012883\" data-type=\"problem\">\r\n<p id=\"fs-id1170654012885\">Simplify: a) \\(-8\\cdot 0\\) b) \\(\\frac{0}{-2}\\) c) \\(\\frac{-32}{0}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654012915\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-223\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>a)\r\nThe product of any real number and 0 is 0.<\/td>\r\n<td>\\(\\begin{array}{c}-8\\cdot 0\\\\ 0\\end{array}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>b)\r\nZero divided by any real number except itself is zero.<\/td>\r\n<td>\\(\\begin{array}{c}\\frac{0}{-2}\\\\ 0\\end{array}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>c)\r\nDivision by 0 is undefined.<\/td>\r\n<td>\\(\\begin{array}{c}\\frac{-32}{0}\\\\ \\text{Undefined}\\end{array}\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 6.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654077664\" data-type=\"problem\">\r\n<p id=\"fs-id1170654077666\">Simplify: a) \\(-14\\cdot 0\\) b) \\(\\frac{0}{-6}\\) c) \\(\\frac{-2}{0}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654035978\" data-type=\"solution\"><details><summary>Answer<\/summary>\r\n<p id=\"fs-id1170654035980\">a) 0 b) 0 c) undefined<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 6.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654035992\" data-type=\"problem\">\r\n<p id=\"fs-id1170654035994\">Simplify: a) \\(0\\left(-17\\right)\\) b) \\(\\frac{0}{-10}\\) c) \\(\\frac{-5}{0}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654036032\" data-type=\"solution\"><details><summary>Answer<\/summary>\r\n<p id=\"fs-id1170654036035\">a) 0 b) 0 c) undefined<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1170654036041\">We will now practice using the properties of identities, inverses, and zero to simplify expressions.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 7<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654014354\" data-type=\"problem\">\r\n<p id=\"fs-id1170654014356\">Simplify: a) \\(\\frac{0}{n+5}\\), where \\(n\\ne -5\\) b) \\(\\frac{10-3p}{0}\\), where \\(10-3p\\ne 0\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654075609\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<table id=\"eip-851\" summary=\"\/\">\r\n<tbody>\r\n<tr>\r\n<td>a)\r\nZero divided by any real number except itself is 0.<\/td>\r\n<td>\\(\\begin{array}{c}\\frac{0}{n+5}\\\\ 0\\end{array}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>b)\r\nDivision by 0 is undefined.<\/td>\r\n<td>\\(\\begin{array}{c}\\frac{10-3p}{0}\\\\ \\text{Undefined}\\end{array}\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 7.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654069194\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1170654069198\" data-type=\"exercise\">\r\n<div id=\"fs-id1170654069200\" data-type=\"problem\">\r\n<p id=\"fs-id1170654069203\">Simplify: a) \\(\\frac{0}{m+7}\\), where \\(m\\ne -7\\) b) \\(\\frac{18-6c}{0}\\), where \\(18-6c\\ne 0\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654069270\" data-type=\"solution\"><details><summary>Answer<\/summary>\r\n<p id=\"fs-id1170654069272\">a) 0 b) undefined<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 7.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654069285\" data-type=\"problem\">\r\n<p id=\"fs-id1170654069287\">Simplify: a) \\(\\frac{0}{d-4},\\text{where}\\phantom{\\rule{0.2em}{0ex}}d\\ne 4\\) b) \\(\\frac{15-4q}{0},\\text{where}\\phantom{\\rule{0.2em}{0ex}}15-4q\\ne 0\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654034465\" data-type=\"solution\"><details><summary>Answer<\/summary>\r\n<p id=\"fs-id1170654034468\">a) 0 b) undefined<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 8<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654036048\" data-type=\"problem\">\r\n<p id=\"fs-id1170654036051\">Simplify: \\(-84n+\\left(-73n\\right)+84n\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654075181\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-616\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>\\(-84n+\\left(-73n\\right)+84n\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Notice that the first and third terms are opposites; use the\r\ncommutative property of addition to re-order the terms.<\/td>\r\n<td>\\(-84n+84n+\\left(-73n\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add left to right.<\/td>\r\n<td>\\(0+\\left(-73\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add.<\/td>\r\n<td>\\(-73n\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1170653800644\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1170653800647\" data-type=\"exercise\">\r\n<div id=\"fs-id1170653800649\" data-type=\"problem\">\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 8.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170653800649\" data-type=\"problem\">\r\n<p id=\"fs-id1170653800651\">Simplify: \\(-27a+\\left(-48a\\right)+27a\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170653800683\" data-type=\"solution\"><details><summary>Answer<\/summary>\r\n<p id=\"fs-id1170653800685\">\\(-48a\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 8.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170653800702\" data-type=\"problem\">\r\n<p id=\"fs-id1170653800704\">Simplify: \\(39x+\\left(-92x\\right)+\\left(-39x\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654059538\" data-type=\"solution\"><details><summary>Answer<\/summary>\r\n<p id=\"fs-id1170654059540\">\\(-92x\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1170654059552\">Now we will see how recognizing reciprocals is helpful. Before multiplying left to right, look for reciprocals\u2014their product is 1<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 9<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654059561\" data-type=\"problem\">\r\n<p id=\"fs-id1170654059563\">Simplify: \\(\\frac{7}{15}\\cdot \\frac{8}{23}\\cdot \\frac{15}{7}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654059595\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<table id=\"eip-950\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>\\(\\frac{7}{15}\\cdot \\frac{8}{23}\\cdot \\frac{15}{7}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Notice that the first and third terms are reciprocals, so use the\r\ncommutative property of multiplication to re-order the factors.<\/td>\r\n<td>\\(\\frac{7}{15}\\cdot \\frac{15}{7}\\cdot \\frac{8}{23}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply left to right.<\/td>\r\n<td>\\(1\\cdot \\frac{8}{23}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>\\(\\frac{8}{23}\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 9.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654069484\" data-type=\"problem\">\r\n<p id=\"fs-id1170654069486\">Simplify: \\(\\frac{9}{16}\\cdot \\frac{5}{49}\\cdot \\frac{16}{9}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654014276\" data-type=\"solution\"><details><summary>Answer<\/summary>\r\n<p id=\"fs-id1170654014278\">\\(\\frac{5}{49}\\)<\/p>\r\n\r\n<\/details>\r\n<div id=\"fs-id1170654014298\" data-type=\"problem\"><\/div>\r\n<div id=\"fs-id1170654014333\" data-type=\"solution\">\r\n<p id=\"fs-id1170654014335\"><\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 9.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654014298\" data-type=\"problem\">\r\n<p id=\"fs-id1170654014300\">Simplify: \\(\\frac{6}{17}\\cdot \\frac{11}{25}\\cdot \\frac{17}{6}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654014333\" data-type=\"solution\"><details><summary>Answer<\/summary>\r\n<p id=\"fs-id1170654014335\">\\(\\frac{11}{25}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1170654069479\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1170654069482\" data-type=\"exercise\">\r\n<div id=\"fs-id1170654069484\" data-type=\"problem\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 10<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654034479\" data-type=\"problem\">\r\n<p id=\"fs-id1170654034481\">Simplify: \\(\\frac{3}{4}\\cdot \\frac{4}{3}\\left(6x+12\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654034517\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<table id=\"eip-386\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>\\(\\frac{3}{4}\\cdot \\frac{4}{3}\\left(6x+12\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>There is nothing to do in the parentheses, so multiply the\r\ntwo fractions first\u2014notice, they are reciprocals.<\/td>\r\n<td>\\(1\\left(6x+12\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify by recognizing the multiplicative identity.<\/td>\r\n<td>\\(6x+12\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 10.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654073889\" data-type=\"problem\">\r\n<p id=\"fs-id1170654073891\">Simplify: \\(\\frac{2}{5}\\cdot \\frac{5}{2}\\left(20y+50\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654073928\" data-type=\"solution\"><details><summary>Answer<\/summary>\r\n<p id=\"fs-id1170654073930\">\\(20y+50\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 10.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654073952\" data-type=\"problem\">\r\n<p id=\"fs-id1170654073954\">Simplify: \\(\\frac{3}{8}\\cdot \\frac{8}{3}\\left(12z+16\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654073990\" data-type=\"solution\"><details><summary>Answer<\/summary>\r\n<p id=\"fs-id1170654073993\">\\(12z+16\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<h1>Simplify Expressions Using the Distributive Property<\/h1>\r\n<p id=\"fs-id1170654074015\">Suppose that three friends are going to the movies. They each need \\$9.25\u2014that\u2019s 9 dollars and 1 quarter\u2014to pay for their tickets. How much money do they need all together?<\/p>\r\n<p id=\"fs-id1170654074022\">You can think about the dollars separately from the quarters. They need 3 times \\$9 so \\$27, and 3 times 1 quarter, so 75 cents. In total, they need \\$27.75. If you think about doing the math in this way, you are using the <strong data-effect=\"bold\">distributive property<\/strong>.<\/p>\r\n\r\n<div id=\"fs-id1170654074032\" data-type=\"note\">\r\n<div data-type=\"title\">\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Distributive Property<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\n\\(\\begin{array}{cccc}\\text{If}\\phantom{\\rule{0.2em}{0ex}}a,b,c\\phantom{\\rule{0.2em}{0ex}}\\text{are real numbers, then}\\hfill &amp; &amp; &amp; a\\left(b+c\\right)=ab+ac\\hfill \\\\ \\\\ \\\\ \\hfill \\text{Also,}&amp; &amp; &amp; \\left(b+c\\right)a=ba+ca\\hfill \\\\ &amp; &amp; &amp; a\\left(b-c\\right)=ab-ac\\hfill \\\\ &amp; &amp; &amp; \\left(b-c\\right)a=ba-ca\\hfill \\end{array}\\)\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1170654077873\">Back to our friends at the movies, we could find the total amount of money they need like this:<\/p>\r\n\r\n<table style=\"border-collapse: collapse;width: 100%\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 100%;text-align: center\">3(9.25)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 100%;text-align: center\">3(9 + 0.25)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 100%;text-align: center\">3(9) + 3(0.25)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 100%;text-align: center\">27 + 0.75<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 100%;text-align: center\">27.75<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p id=\"fs-id1170654077971\">In algebra, we use the distributive property to remove parentheses as we simplify expressions.<\/p>\r\n<p id=\"fs-id1170654077977\">For example, if we are asked to simplify the expression \\(3\\left(x+4\\right)\\), the order of operations says to work in the parentheses first. But we cannot add <em data-effect=\"italics\">x<\/em> and 4, since they are not like terms. So we use the distributive property, as shown in <a class=\"autogenerated-content\" href=\"#fs-id1170654078015\">(Example 11)<\/a>.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 11<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654078015\" data-type=\"problem\">\r\n<p id=\"fs-id1170654078018\">Simplify: \\(3\\left(x+4\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654078041\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-922\" style=\"height: 42px\" summary=\".\">\r\n<tbody>\r\n<tr style=\"height: 14px\">\r\n<td style=\"height: 14px;width: 225.406px\"><\/td>\r\n<td style=\"height: 14px;width: 384.406px\">\\(3\\left(x+4\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"height: 14px;width: 225.406px\">Distribute.<\/td>\r\n<td style=\"height: 14px;width: 384.406px\">\\(3\\cdot x+3\\cdot 4\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"height: 14px;width: 225.406px\">Multiply.<\/td>\r\n<td style=\"height: 14px;width: 384.406px\">\\(3x+12\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 11.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654078131\" data-type=\"problem\">\r\n<p id=\"fs-id1170654078133\">Simplify: \\(4\\left(x+2\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654078156\" data-type=\"solution\"><details open=\"open\"><summary>Answer<\/summary>\r\n<p id=\"fs-id1170654078158\">\\(4x+8\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 11.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654078181\" data-type=\"problem\">\r\n<p id=\"fs-id1170654078183\">Simplify: \\(6\\left(x+7\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654078206\" data-type=\"solution\"><details open=\"open\"><summary>Answer<\/summary>\r\n<p id=\"fs-id1170654078208\">\\(6x+42\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1170654075701\">Some students find it helpful to draw in arrows to remind them how to use the distributive property. Then the first step in <a class=\"autogenerated-content\" href=\"#fs-id1170654078015\">(Example 11)<\/a> would look like this:<\/p>\r\n<span id=\"fs-id1170654075709\" data-type=\"media\" data-alt=\"We have the expression 3 times (x plus 4) with two arrows coming from the 3. One arrow points to the x, and the other arrow points to the 4.\"><img class=\"aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_09_006_img_new.jpg\" alt=\"We have the expression 3 times (x plus 4) with two arrows coming from the 3. One arrow points to the x, and the other arrow points to the 4.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 12<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654075726\" data-type=\"problem\">\r\n<p id=\"fs-id1170654075729\">Simplify: \\(8\\left(\\frac{3}{8}x+\\frac{1}{4}\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654075761\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-id1169750566181\" class=\"unnumbered unstyled\" summary=\"We have a table with directions on the left side and mathematical steps on the right. The first step says \u201cDistribute.\u201d To the right of this, we have the expression 8 times ((3\/8) times x plus 1\/4) with two arrows coming from the 8. One arrow points to the (3\/8) times x, and the other arrow points to the 1\/4. The next line says \u201cMultiply.\u201d To the right of this we have an equals sign and then 8 times ((3\/8) times x) plus 8 times 1\/4. On the following line, we have another equals sign followed by 3x plus 2.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td><span id=\"eip-id1169750566196\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_09_007a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Distribute.<\/td>\r\n<td><span id=\"eip-id1169750566213\" data-type=\"media\" data-alt=\".\">[latex]8 \\cdot \\frac{3}{8} x+8 \\cdot \\frac{1}{4}[\/latex]<\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]3x+2[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 12.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654075789\" data-type=\"problem\">\r\n<p id=\"fs-id1170654075791\">Simplify: \\(6\\left(\\frac{5}{6}y+\\frac{1}{2}\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654075823\" data-type=\"solution\"><details open=\"open\"><summary>Answer<\/summary>\r\n<p id=\"fs-id1170654075825\">\\(5y+3\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 12.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654075848\" data-type=\"problem\">\r\n<p id=\"fs-id1170654075850\">Simplify: \\(12\\left(\\frac{1}{3}n+\\frac{3}{4}\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654075882\" data-type=\"solution\"><details open=\"open\"><summary>Answer<\/summary>\r\n<p id=\"fs-id1170654075884\">\\(4n+9\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1170654075900\">Using the distributive property as shown in <a class=\"autogenerated-content\" href=\"#fs-id1170654075912\">(Example 13)<\/a> will be very useful when we solve money applications in later chapters.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 13<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654075912\" data-type=\"problem\">\r\n<p id=\"fs-id1170654075915\">Simplify: \\(100\\left(0.3+0.25q\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654075940\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-id1169751856555\" class=\"unnumbered unstyled\" summary=\"We have a table with directions on the left side and mathematical steps on the right. The first step says \u201cDistribute.\u201d To the right of this, we have the expression 100 times (0.3 plus 0.25 times q) with two arrows coming from the 100. One arrow points to the 0.3, and the other arrow points to the 0.25 times q. The next line says \u201cMultiply.\u201d To the right of this we have an equals sign and then 100 times 0.3 plus 100 times the quantity (0.25 times q). On the following line, we have another equals sign followed by 30 plus 25q.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td><span id=\"eip-id1169751856571\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_09_008a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Distribute.<\/td>\r\n<td><span id=\"eip-id1169751856588\" data-type=\"media\" data-alt=\".\">[latex]100(0.3)+100(0.25 q)[\/latex]<\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td><span id=\"eip-id1169751856604\" data-type=\"media\" data-alt=\".\">[latex]30+25q[\/latex]<\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 13.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654075969\" data-type=\"problem\">\r\n<p id=\"fs-id1170654075971\">Simplify: \\(100\\left(0.7+0.15p\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654075999\" data-type=\"solution\"><details open=\"open\"><summary>Answer<\/summary>\r\n<p id=\"fs-id1170654076001\">\\(70+15p\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 13.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654076023\" data-type=\"problem\">\r\n<p id=\"fs-id1170654076025\">Simplify: \\(100\\left(0.04+0.35d\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654076051\" data-type=\"solution\"><details open=\"open\"><summary>Answer<\/summary>\r\n<p id=\"fs-id1170654076053\">\\(4+35d\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1170654076069\">When we distribute a negative number, we need to be extra careful to get the signs correct!<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 14<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654076078\" data-type=\"problem\">\r\n<p id=\"fs-id1170654076080\">Simplify: \\(-2\\left(4y+1\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654076105\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-id1169750823178\" class=\"unnumbered unstyled\" summary=\"We have a table with directions on the left side and mathematical steps on the right. The first step says \u201cDistribute.\u201d To the right of this, we have the expression negative 2 times (4y plus 1) with two arrows coming from the negative 2. One arrow points to the 4y, and the other arrow points to the 1. The next line gives negative 2 times 4y plus negative 2 times 1. On the following line, we have the command \u201cSimplify.\u201d To the right of this, we have negative 8y minus 2.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td><span id=\"eip-id1169750823194\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_09_009a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Distribute.<\/td>\r\n<td>[latex]-2 \\cdot 4 y+(-2) \\cdot (1)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td><span id=\"eip-id1169750823228\" data-type=\"media\" data-alt=\".\">[latex]-8y-2[\/latex]<\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 14.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654067335\" data-type=\"problem\">\r\n<p id=\"fs-id1170654067337\">Simplify: \\(-3\\left(6m+5\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654067363\" data-type=\"solution\"><details open=\"open\"><summary>Answer<\/summary>\r\n<p id=\"fs-id1170654067365\">\\(-18m-15\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 14.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654067387\" data-type=\"problem\">\r\n<p id=\"fs-id1170654067389\">Simplify: \\(-6\\left(8n+11\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654067415\" data-type=\"solution\"><details open=\"open\"><summary>Answer<\/summary>\r\n<p id=\"fs-id1170654067417\">\\(-48n-66\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1170654067381\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1170654067385\" data-type=\"exercise\">\r\n<div id=\"fs-id1170654067415\" data-type=\"solution\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 15<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654067437\" data-type=\"problem\">\r\n<p id=\"fs-id1170654067440\">Simplify: \\(-11\\left(4-3a\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654067465\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<table id=\"eip-id1169751973914\" class=\"unnumbered unstyled\" summary=\"We have a table with directions on the left side and mathematical steps on the right. The first step says \u201cDistribute.\u201d To the right of this, we have the expression negative 11 times (4 minus 3a) with two arrows coming from the negative 11. One arrow points to the 4, and the other arrow points to the 3a. On the next line, we have the command \u201cMultiply.\u201d To the right of this, we have negative 11 times 4 minus negative 11 times 3a. Below this, we have negative 44 minus negative 33a. On the following line, we have the command \u201cSimplify.\u201d To the right of this, we have negative 44 plus 33a.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td>Distribute.<\/td>\r\n<td><span id=\"eip-id1169751973931\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_09_010a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]\\begin{aligned} &amp;-11 \\cdot 4 -(-11)\\cdot (3a) \\\\ &amp;=-44-(-33a) \\end{aligned}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td><span id=\"eip-id1169754247268\" data-type=\"media\" data-alt=\".\">[latex]-44+33a[\/latex]<\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p id=\"fs-id1170654067485\">Notice that you could also write the result as \\(33a-44\\). Do you know why?<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 15.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654067512\" data-type=\"problem\">\r\n<p id=\"fs-id1170654067514\">Simplify: \\(-5\\left(2-3a\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654067540\" data-type=\"solution\"><details open=\"open\"><summary>Answer<\/summary>\r\n<p id=\"fs-id1170654067542\">\\(-10+15a\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 15.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654067564\" data-type=\"problem\">\r\n<p id=\"fs-id1170654067566\">Simplify: \\(-7\\left(8-15y\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654067592\" data-type=\"solution\"><details open=\"open\"><summary>Answer<\/summary>\r\n<p id=\"fs-id1170654067594\">\\(-56+105y\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1170654067610\"><a class=\"autogenerated-content\" href=\"#fs-id1170654067621\">(Example 16)<\/a> will show how to use the distributive property to find the opposite of an expression.<\/p>\r\n\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 16<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654067621\" data-type=\"problem\">\r\n<p id=\"fs-id1170654067623\">Simplify: \\(-\\left(y+5\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654067647\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<table id=\"eip-636\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>\\(\\left(y+5\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiplying by \u22121 results in the opposite.<\/td>\r\n<td>\\(-1\\left(y+5\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Distribute.<\/td>\r\n<td>\\(-1\\cdot y+\\left(-1\\right)\\cdot 5\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>\\(-y+\\left(-5\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>\\(-y-5\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 16.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654067804\" data-type=\"problem\">\r\n<p id=\"fs-id1170654067806\">Simplify: \\(-\\left(z-11\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654067830\" data-type=\"solution\"><details open=\"open\"><summary>Answer<\/summary>\r\n<p id=\"fs-id1170654067832\">\\(-z+11\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 16.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654067854\" data-type=\"problem\">\r\n<p id=\"fs-id1170654067856\">Simplify: \\(-\\left(x-4\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654067880\" data-type=\"solution\"><details open=\"open\"><summary>Answer<\/summary>\r\n<p id=\"fs-id1170654067882\">\\(-x+4\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1170654067848\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1170654067852\" data-type=\"exercise\">\r\n<div id=\"fs-id1170654067880\" data-type=\"solution\">\r\n<p id=\"fs-id1170654067882\">There will be times when we\u2019ll need to use the distributive property as part of the order of operations. Start by looking at the parentheses. If the expression inside the parentheses cannot be simplified, the next step would be multiply using the distributive property, which removes the parentheses. The next two examples will illustrate this.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 17<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654067912\" data-type=\"problem\">\r\n<p id=\"fs-id1170654067914\">Simplify: \\(8-2\\left(x+3\\right)\\).<\/p>\r\n<p id=\"fs-id1170654067941\">Be sure to follow the order of operations. Multiplication comes before subtraction, so we will distribute the 2 first and then subtract.<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654067946\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<table id=\"eip-501\" summary=\"\/\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>\\(8-2\\left(x+3\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Distribute.<\/td>\r\n<td>\\(8-2\\cdot x-2\\cdot 3\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>\\(8-2x-6\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Combine like terms.<\/td>\r\n<td>\\(-2x+2\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 17.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654068319\" data-type=\"problem\">\r\n<p id=\"fs-id1170654068322\">Simplify: \\(9-3\\left(x+2\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654068349\" data-type=\"solution\"><details open=\"open\"><summary>Answer<\/summary>\r\n<p id=\"fs-id1170654068351\">\\(3-3x\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 17.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654068374\" data-type=\"problem\">\r\n<p id=\"fs-id1170654068376\">Simplify: \\(7x-5\\left(x+4\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654068406\" data-type=\"solution\"><details open=\"open\"><summary>Answer<\/summary>\r\n<p id=\"fs-id1170654068408\">\\(2x-20\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1170654068367\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1170654068372\" data-type=\"exercise\">\r\n<div id=\"fs-id1170654068406\" data-type=\"solution\">\r\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">EXAMPLE 18<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654068428\" data-type=\"problem\">\r\n<p id=\"fs-id1170654068430\">Simplify: \\(4\\left(x-8\\right)-\\left(x+3\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654068469\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<table id=\"eip-496\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>\\(4\\left(x-8\\right)-\\left(x+3\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Distribute.<\/td>\r\n<td>\\(4x-32-x-3\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Combine like terms.<\/td>\r\n<td>\\(3x-35\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1170654068573\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1170654068578\" data-type=\"exercise\">\r\n<div id=\"fs-id1170654068580\" data-type=\"problem\">\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 18.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654068580\" data-type=\"problem\">\r\n<p id=\"fs-id1170654068582\">Simplify: \\(6\\left(x-9\\right)-\\left(x+12\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654068620\" data-type=\"solution\"><details open=\"open\"><summary>Answer<\/summary>\r\n<p id=\"fs-id1170654068622\">\\(5x-66\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">TRY IT 18.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654068645\" data-type=\"problem\">\r\n<p id=\"fs-id1170654068647\">Simplify: \\(8\\left(x-1\\right)-\\left(x+5\\right)\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654068685\" data-type=\"solution\"><details open=\"open\"><summary>Answer<\/summary>\r\n<p id=\"fs-id1170654068687\">\\(7x-13\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1170654068703\">All the properties of real numbers we have used in this chapter are summarized in the table below.<\/p>\r\n\r\n<table style=\"border-collapse: collapse;width: 100%\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 33.3333%\" rowspan=\"2\">Commutative Property<\/td>\r\n<td style=\"width: 33.3333%\"><strong data-effect=\"bold\">of addition<\/strong>\u2003If \\(a,b\\) are real numbers, then<\/td>\r\n<td style=\"width: 33.3333%\">\\(a+b=b+a\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3333%\"><strong data-effect=\"bold\">of multiplication<\/strong>\u2003If \\(a,b\\) are real numbers, then<\/td>\r\n<td style=\"width: 33.3333%\">\\(a\\cdot b=b\\cdot a\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3333%\" rowspan=\"2\">Associative Property<\/td>\r\n<td style=\"width: 33.3333%\"><strong data-effect=\"bold\">of addition<\/strong>\u2003If \\(a,b,c\\) are real numbers, then<\/td>\r\n<td style=\"width: 33.3333%\">\\(\\left(a+b\\right)+c=a+\\left(b+c\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3333%\"><strong data-effect=\"bold\">of multiplication<\/strong>\u2003If \\(a,b,c\\) are real numbers, then<\/td>\r\n<td style=\"width: 33.3333%\">\\(\\left(a\\cdot b\\right)\\cdot c=a\\cdot \\left(b\\cdot c\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3333%\">Distributive Property<\/td>\r\n<td style=\"width: 33.3333%\">If \\(a,b,c\\) are real numbers, then<\/td>\r\n<td style=\"width: 33.3333%\">\\(a\\left(b+c\\right)=ab+ac\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3333%\" rowspan=\"2\">Identity Property<\/td>\r\n<td style=\"width: 33.3333%\"><strong data-effect=\"bold\">of addition<\/strong>\u2003For any real number \\(a\\text{:}\\)\r\n0 is the <strong data-effect=\"bold\">additive identity<\/strong><\/td>\r\n<td style=\"width: 33.3333%\">\\(\\begin{array}{c}\\\\ \\hfill a+0=a\\hfill \\\\ \\hfill 0+a=a\\hfill \\end{array}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3333%\"><strong data-effect=\"bold\">of multiplication<\/strong>\u2003For any real number \\(a\\text{:}\\)\r\n\\(1\\) is the <strong data-effect=\"bold\">multiplicative identity<\/strong><\/td>\r\n<td style=\"width: 33.3333%\">\\(\\begin{array}{c}\\hfill a\\cdot 1=a\\hfill \\\\ \\hfill 1\\cdot a=a\\hfill \\end{array}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3333%\" rowspan=\"2\">Inverse Property<\/td>\r\n<td style=\"width: 33.3333%\"><strong data-effect=\"bold\">of addition<\/strong>\u2003For any real number \\(a\\),\r\n\\(-a\\) is the <strong data-effect=\"bold\">additive inverse<\/strong> of \\(a\\)<\/td>\r\n<td style=\"width: 33.3333%\">\\(a+\\left(-a\\right)=0\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3333%\"><strong data-effect=\"bold\">of multiplication<\/strong>\u2003For any real number \\(a,a\\ne 0\\)\r\n\\(\\frac{1}{a}\\) is the <strong data-effect=\"bold\">multiplicative inverse<\/strong> of \\(a\\).<\/td>\r\n<td style=\"width: 33.3333%\">\\(a\\cdot \\frac{1}{a}=1\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3333%\">Properties of Zero<\/td>\r\n<td style=\"width: 33.3333%\">For any real number <em data-effect=\"italics\">a<\/em>,\r\n\r\nFor any real number \\(a,a\\ne 0\\)\r\n\r\nFor any real number \\(a,a\\ne 0\\)<\/td>\r\n<td style=\"width: 33.3333%\">\\(\\begin{array}{c}\\\\ \\hfill a\\cdot 0=0\\hfill \\\\ \\hfill 0\\cdot a=0\\hfill \\end{array}\\)\r\n\r\n\\(\\frac{0}{a}=0\\)\r\n\r\n\\(\\frac{a}{0}\\) is undefined<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h1>Key Concepts<\/h1>\r\n<ul id=\"fs-id1170654053692\" data-bullet-style=\"bullet\">\r\n \t<li><strong data-effect=\"bold\">Commutative Property of<\/strong>\r\n<ul id=\"fs-id1170654053705\" data-bullet-style=\"open-circle\">\r\n \t<li><strong data-effect=\"bold\">Addition:<\/strong> If \\(a,b\\) are real numbers, then \\(a+b=b+a\\).<\/li>\r\n \t<li><strong data-effect=\"bold\">Multiplication:<\/strong> If \\(a,b\\) are real numbers, then \\(a\\cdot b=b\\cdot a\\). When adding or multiplying, changing the <em data-effect=\"italics\">order<\/em> gives the same result.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong data-effect=\"bold\">Associative Property of<\/strong>\r\n<ul id=\"fs-id1170654053796\" data-bullet-style=\"open-circle\">\r\n \t<li><strong data-effect=\"bold\">Addition:<\/strong> If \\(a,b,c\\) are real numbers, then \\(\\left(a+b\\right)+c=a+\\left(b+c\\right)\\).<\/li>\r\n \t<li><strong data-effect=\"bold\">Multiplication:<\/strong> If \\(a,b,c\\) are real numbers, then \\(\\left(a\\cdot b\\right)\\cdot c=a\\cdot \\left(b\\cdot c\\right)\\).\r\nWhen adding or multiplying, changing the <em data-effect=\"italics\">grouping<\/em> gives the same result.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong data-effect=\"bold\">Distributive Property:<\/strong> If \\(a,b,c\\) are real numbers, then\r\n<ul id=\"fs-id1170654071317\" data-bullet-style=\"open-circle\">\r\n \t<li>\\(a\\left(b+c\\right)=ab+ac\\)<\/li>\r\n \t<li>\\(\\left(b+c\\right)a=ba+ca\\)<\/li>\r\n \t<li>\\(a\\left(b-c\\right)=ab-ac\\)<\/li>\r\n \t<li>\\(\\left(b-c\\right)a=ba-ca\\)<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong data-effect=\"bold\">Identity Property<\/strong>\r\n<ul id=\"fs-id1170654071460\" data-bullet-style=\"open-circle\">\r\n \t<li><strong data-effect=\"bold\">of Addition:<\/strong> For any real number \\(a\\text{:}\\phantom{\\rule{0.2em}{0ex}}a+0=a\\phantom{\\rule{0.6em}{0ex}}0+a=a\\)\r\n<strong data-effect=\"bold\">0<\/strong> is the <strong data-effect=\"bold\">additive identity<\/strong><\/li>\r\n \t<li><strong data-effect=\"bold\">of Multiplication:<\/strong> For any real number \\(a\\text{:}\\phantom{\\rule{0.2em}{0ex}}a\\cdot 1=a\\phantom{\\rule{0.6em}{0ex}}1\\cdot a=a\\)\r\n\\(1\\) is the <strong data-effect=\"bold\">multiplicative identity<\/strong><\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong data-effect=\"bold\">Inverse Property<\/strong>\r\n<ul id=\"fs-id1170654071587\" data-bullet-style=\"open-circle\">\r\n \t<li><strong data-effect=\"bold\">of Addition:<\/strong> For any real number \\(a,a+\\left(-a\\right)=0\\). A number and its <em data-effect=\"italics\">opposite<\/em> add to zero. \\(-a\\) is the <strong data-effect=\"bold\">additive inverse<\/strong> of \\(a\\).<\/li>\r\n \t<li><strong data-effect=\"bold\">of Multiplication:<\/strong> For any real number \\(a,\\left(a\\ne 0\\right)\\phantom{\\rule{0.2em}{0ex}}a\\cdot \\frac{1}{a}=1\\). A number and its <em data-effect=\"italics\">reciprocal<\/em> multiply to one. \\(\\frac{1}{a}\\) is the <strong data-effect=\"bold\">multiplicative inverse<\/strong> of \\(a\\).<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong data-effect=\"bold\">Properties of Zero<\/strong>\r\n<ul id=\"fs-id1170654071732\" data-bullet-style=\"open-circle\">\r\n \t<li>For any real number \\(a\\),\r\n\\(a\\cdot 0=0\\phantom{\\rule{0.5em}{0ex}}0\\cdot a=0\\) \u2013 The product of any real number and 0 is 0.<\/li>\r\n \t<li>\\(\\frac{0}{a}=0\\) for \\(a\\ne 0\\) \u2013 Zero divided by any real number except zero is zero.<\/li>\r\n \t<li>\\(\\frac{a}{0}\\) is undefined \u2013 Division by zero is undefined.<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<h1>Glossary<\/h1>\r\n<div class=\"textbox shaded\">\r\n<dl id=\"fs-id1166426340719\">\r\n \t<dt>additive identity<\/dt>\r\n \t<dd id=\"fs-id1166426340725\">The additive identity is the number 0; adding 0 to any number does not change its value.<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1166426272008\">\r\n \t<dt>additive inverse<\/dt>\r\n \t<dd id=\"fs-id1166426272014\">The opposite of a number is its additive inverse. A number and it additive inverse add to 0.<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1166426274404\">\r\n \t<dt>multiplicative identity<\/dt>\r\n \t<dd id=\"fs-id1166426274410\">The multiplicative identity is the number 1; multiplying 1 by any number does not change the value of the number.<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-id1166426154985\">\r\n \t<dt>multiplicative inverse<\/dt>\r\n \t<dd id=\"fs-id1166426154990\">The reciprocal of a number is its multiplicative inverse. A number and its multiplicative inverse multiply to one.<\/dd>\r\n<\/dl>\r\n<\/div>\r\n<h1>Practice Makes Perfect<\/h1>\r\n<h2>Use the Commutative and Associative Properties<\/h2>\r\n<p id=\"fs-id1166423746090\">In the following exercises, use the associative property to simplify.<\/p>\r\n\r\n<table style=\"border-collapse: collapse;width: 100%;height: 28px\" border=\"0\">\r\n<tbody>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">1. 3(4<em data-effect=\"italics\">x<\/em>)<\/td>\r\n<td style=\"width: 50%;height: 14px\">2. 4(7<em data-effect=\"italics\">m<\/em>)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">3. \\(\\left(y+12\\right)+28\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">4. \\(\\left(n+17\\right)+33\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div id=\"fs-id1170654071839\" data-type=\"exercise\">\r\n<div id=\"fs-id1170654071842\" data-type=\"problem\">In the following exercises, simplify.<\/div>\r\n<\/div>\r\n<table style=\"border-collapse: collapse;width: 100%;height: 112px\" border=\"0\">\r\n<tbody>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">5. \\(\\frac{1}{2}+\\frac{7}{8}+\\left(-\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{2}\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">6. \\(\\frac{2}{5}+\\frac{5}{12}+\\left(-\\phantom{\\rule{0.2em}{0ex}}\\frac{2}{5}\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">7. \\(\\frac{3}{20}\\cdot\\frac{49}{11}\\cdot\\frac{20}{3}\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">8. \\(\\frac{13}{18}\\cdot\\frac{25}{7}\\cdot\\frac{18}{13}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">9. \\(-24\\cdot 7 \\cdot\\frac{3}{8}\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">10. \\(-36\\cdot 11\\cdot\\frac{4}{9}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">11. \\(\\left(\\frac{5}{6}+\\frac{8}{15}\\right)+\\frac{7}{15}\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">12. \\(\\left(\\frac{11}{12}+\\frac{4}{9}\\right)+\\frac{5}{9}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">13. 17(0.25)(4)<\/td>\r\n<td style=\"width: 50%;height: 14px\">14. 36(0.2)(5)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">15. [2.48(12)](0.5)<\/td>\r\n<td style=\"width: 50%;height: 14px\">16. [9.731(4)](0.75)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">17. 7(4<em data-effect=\"italics\">a<\/em>)<\/td>\r\n<td style=\"width: 50%;height: 14px\">18. 9(8<em data-effect=\"italics\">w<\/em>)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">19. \\(-15\\left(5m\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">20. \\(-23\\left(2n\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">21. \\(12\\left(\\frac{5}{6}p\\right)\\)<\/td>\r\n<td style=\"width: 50%\">22. \\(20\\left(\\frac{3}{5}q\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">23. \\(43m+\\left(-12n\\right)+\\left(-16m\\right)+\\left(-9n\\right)\\)<\/td>\r\n<td style=\"width: 50%\">24. \\(-22p+17q+\\left(-35p\\right)+\\left(-27q\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">25. \\(\\frac{3}{8}g+\\frac{1}{12}h+\\frac{7}{8}g+\\frac{5}{12}h\\)<\/td>\r\n<td style=\"width: 50%\">26. \\(\\frac{5}{6}a+\\frac{3}{10}b+\\frac{1}{6}a+\\frac{9}{10}b\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">27. \\(6.8p+9.14q+\\left(-4.37p\\right)+\\left(-0.88q\\right)\\)<\/td>\r\n<td style=\"width: 50%\">28. \\(9.6m+7.22n+\\left(-2.19m\\right)+\\left(-0.65n\\right)\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div id=\"fs-id1170654071977\" data-type=\"exercise\">\r\n<h2>Use the Identity and Inverse Properties of Addition and Multiplication<\/h2>\r\n<\/div>\r\n<p id=\"fs-id1166414478758\">In the following exercises, find the additive inverse of each number.<\/p>\r\n\r\n<table style=\"border-collapse: collapse;width: 100%\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 50%\">29.\r\na) \\(\\frac{2}{5}\\)\r\nb) 4.3\r\nc) \\(-8\\)\r\nd) \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{10}{3}\\)<\/td>\r\n<td style=\"width: 50%\">30.\r\na) \\(\\frac{5}{9}\\)\r\nb) 2.1\r\nc) \\(-3\\)\r\nd) \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{9}{5}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">31.\r\na) \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{7}{6}\\)\r\nb) \\(-0.075\\)\r\nc) 23\r\nd) \\(\\frac{1}{4}\\)<\/td>\r\n<td style=\"width: 50%\">32.\r\na) \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{8}{3}\\)\r\nb) \\(-0.019\\)\r\nc) 52\r\nd) \\(\\frac{5}{6}\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div id=\"fs-id1170653990564\" data-type=\"exercise\">\r\n<div id=\"fs-id1170653990566\" data-type=\"problem\">In the following exercises, find the multiplicative inverse of each number.<\/div>\r\n<\/div>\r\n<table style=\"border-collapse: collapse;width: 100%\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 50%\">33. a) 6 b) \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{3}{4}\\) c) 0.7<\/td>\r\n<td style=\"width: 50%\">34. a) 12 b) \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{9}{2}\\) c) 0.13<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">35. a) \\(\\frac{11}{12}\\) b) \\(-1.1\\) c) \\(-4\\)<\/td>\r\n<td style=\"width: 50%\">36. a) \\(\\frac{17}{20}\\) b) \\(-1.5\\) c) \\(-3\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h2>Use the Properties of Zero<\/h2>\r\n<p id=\"fs-id1166425983092\">In the following exercises, simplify.<\/p>\r\n\r\n<table style=\"border-collapse: collapse;width: 100%\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 50%\">37. \\(\\frac{0}{6}\\)<\/td>\r\n<td style=\"width: 50%\">38. \\(\\frac{3}{0}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">39. \\(0\\div \\frac{11}{12}\\)<\/td>\r\n<td style=\"width: 50%\">40. \\(\\frac{6}{0}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">41. \\(\\frac{0}{3}\\)<\/td>\r\n<td style=\"width: 50%\">42. \\(0\\cdot \\frac{8}{15}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">43. \\(\\left(-3.14\\right)\\left(0\\right)\\)<\/td>\r\n<td style=\"width: 50%\">44. \\(\\frac{\\frac{1}{10}}{0}\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h2>Mixed Practice<\/h2>\r\n<p id=\"fs-id1166426154959\">In the following exercises, simplify.<\/p>\r\n\r\n<table style=\"border-collapse: collapse;width: 100%;height: 126px\" border=\"0\">\r\n<tbody>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">45. \\(19a+44-19a\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">46. \\(27c+16-27c\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">47. \\(10\\left(0.1d\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">48. \\(100\\left(0.01p\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">49. \\(\\frac{0}{u-4.99}\\), where \\(u\\ne 4.99\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">50. \\(\\frac{0}{v-65.1}\\), where \\(v\\ne 65.1\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">51. \\(0\\div\\left(x-\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{2}\\right)\\), where \\(x\\ne \\frac{1}{2}\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">52. \\(0\\div\\left(y-\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{6}\\right)\\), where \\(x\\ne \\frac{1}{6}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">53. \\(\\frac{32-5a}{0}\\), where \\(32-5a\\ne 0\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">54. \\(\\frac{28-9b}{0}\\), where \\(28-9b\\ne 0\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">55. \\(\\left(\\frac{3}{4}+\\frac{9}{10}m\\right)\\div 0\\) where \\(\\frac{3}{4}+\\frac{9}{10}m\\ne 0\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">56. \\(\\left(\\frac{5}{16}n-\\phantom{\\rule{0.2em}{0ex}}\\frac{3}{7}\\right)\\div 0\\) where \\(\\frac{5}{16}n-\\phantom{\\rule{0.2em}{0ex}}\\frac{3}{7}\\ne 0\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">57. \\(15\\cdot\\frac{3}{5}\\left(4d+10\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">58. \\(18\\cdot\\frac{5}{6}\\left(15h+24\\right)\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h2>Simplify Expressions Using the Distributive Property<\/h2>\r\n<p id=\"fs-id1166423978166\">In the following exercises, simplify using the distributive property.<\/p>\r\n\r\n<table style=\"border-collapse: collapse;width: 100%;height: 266px\" border=\"0\">\r\n<tbody>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">59. \\(8\\left(4y+9\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">60. \\(9\\left(3w+7\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">61. \\(6\\left(c-13\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">62. \\(7\\left(y-13\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">63. \\(\\frac{1}{4}\\left(3q+12\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">64. \\(\\frac{1}{5}\\left(4m+20\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">65. \\(9\\left(\\frac{5}{9}y-\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{3}\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">66. \\(10\\left(\\frac{3}{10}x-\\phantom{\\rule{0.2em}{0ex}}\\frac{2}{5}\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">67. \\(12\\left(\\frac{1}{4}+\\frac{2}{3}r\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">68. \\(12\\left(\\frac{1}{6}+\\frac{3}{4}s\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">69. \\(r\\left(s-18\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">70. \\(u\\left(v-10\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">71. \\(\\left(y+4\\right)p\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">72. \\(\\left(a+7\\right)x\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">73. \\(-7\\left(4p+1\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">74. \\(-9\\left(9a+4\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">75. \\(-3\\left(x-6\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">76. \\(-4\\left(q-7\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">77. \\(-\\left(3x-7\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">78. \\(-\\left(5p-4\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">79. \\(16-3\\left(y+8\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">80. \\(18-4\\left(x+2\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">81. \\(4-11\\left(3c-2\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">82. \\(9-6\\left(7n-5\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">83. \\(22-\\left(a+3\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">84. \\(8-\\left(r-7\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">85. \\(\\left(5m-3\\right)-\\left(m+7\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">86. \\(\\left(4y-1\\right)-\\left(y-2\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">87. \\(5\\left(2n+9\\right)+12\\left(n-3\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">88. \\(9\\left(5u+8\\right)+2\\left(u-6\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">89. \\(9\\left(8x-3\\right)-\\left(-2\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">90. \\(4\\left(6x-1\\right)-\\left(-8\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">91. \\(14\\left(c-1\\right)-8\\left(c-6\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">92. \\(11\\left(n-7\\right)-5\\left(n-1\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px\">\r\n<td style=\"width: 50%;height: 14px\">93. \\(6\\left(7y+8\\right)-\\left(30y-15\\right)\\)<\/td>\r\n<td style=\"width: 50%;height: 14px\">94. \\(7\\left(3n+9\\right)-\\left(4n-13\\right)\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h2>Everyday Math<\/h2>\r\n<table style=\"border-collapse: collapse;width: 100%\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 50%\">\r\n<p id=\"fs-id1170654084031\">95. <strong data-effect=\"bold\">Insurance copayment<\/strong> Carrie had to have 5 fillings done. Each filling cost \\$80. Her dental insurance required her to pay 20% of the cost as a copay. Calculate Carrie\u2019s copay:<\/p>\r\na) First, by multiplying 0.20 by 80 to find her copay for each filling and then multiplying your answer by 5 to find her total copay for 5 fillings.\r\n\r\nb) Next, by multiplying [5(0.20)](80)\r\n\r\nc) Which of the properties of real numbers says that your answers to parts (a), where you multiplied 5[(0.20)(80)] and (b), where you multiplied [5(0.20)](80), should be equal?<\/td>\r\n<td style=\"width: 50%\">\r\n<p id=\"fs-id1170654084068\">96. <strong data-effect=\"bold\">Cooking time<\/strong> Matt bought a 24-pound turkey for his family\u2019s Thanksgiving dinner and wants to know what time to put the turkey in to the oven. He wants to allow 20 minutes per pound cooking time. Calculate the length of time needed to roast the turkey:<\/p>\r\na) First, by multiplying \\(24\\cdot 20\\) to find the total number of minutes and then multiplying the answer by \\(\\frac{1}{60}\\) to convert minutes into hours.\r\n\r\nb) Next, by multiplying \\(24\\left(20\\cdot \\frac{1}{60}\\right)\\).\r\n\r\nc) Which of the properties of real numbers says that your answers to parts (a), where you multiplied \\(\\left(24\\cdot 20\\right)\\frac{1}{60}\\), and (b), where you multiplied \\(24\\left(20\\cdot \\frac{1}{60}\\right)\\), should be equal?<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">\r\n<p id=\"fs-id1170654084193\">97.<strong data-effect=\"bold\"> Buying by the case.<\/strong> Trader Joe\u2019s grocery stores sold a can of Coke Zero for \\$1.99. They sold a case of 12 cans for \\$23.88. To find the cost of 12 cans at \\$1.99, notice that 1.99 is \\(2-0.01\\).<\/p>\r\na) Multiply 12(1.99) by using the distributive property to multiply \\(12\\left(2-0.01\\right)\\).\r\n\r\nb) Was it a bargain to buy Coke Zero by the case?<\/td>\r\n<td style=\"width: 50%\">\r\n<p id=\"fs-id1170654084256\">98.<strong data-effect=\"bold\"> Multi-pack purchase.<\/strong> Adele\u2019s shampoo sells for \\$3.99 per bottle at the grocery store. At the warehouse store, the same shampoo is sold as a 3 pack for \\$10.49. To find the cost of 3 bottles at \\$3.99, notice that 3.99 is \\(4-0.01\\).<\/p>\r\na) Multiply 3(3.99) by using the distributive property to multiply \\(3\\left(4-0.01\\right)\\).\r\n\r\nb) How much would Adele save by buying 3 bottles at the warehouse store instead of at the grocery store?<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div id=\"fs-id1170654084027\" data-type=\"exercise\">\r\n<h2 id=\"fs-id1170654084029\" data-type=\"problem\">Writing Exercises<\/h2>\r\n<\/div>\r\n<table style=\"border-collapse: collapse;width: 100%\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 50%\">99. In your own words, state the commutative property of addition.<\/td>\r\n<td style=\"width: 50%\">100. What is the difference between the additive inverse and the multiplicative inverse of a number?<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%\">101. Simplify \\(8\\left(x-\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{4}\\right)\\) using the distributive property and explain each step.<\/td>\r\n<td style=\"width: 50%\">102. Explain how you can multiply 4(\\$5.97) without paper or calculator by thinking of \\$5.97 as \\(6-0.03\\) and then using the distributive property.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h1>Answers<\/h1>\r\n<div data-type=\"glossary\">\r\n<table style=\"border-collapse: collapse;width: 100%;height: 288px\" border=\"0\">\r\n<tbody>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 33.3333%;height: 16px\">1. 12<em data-effect=\"italics\">x<\/em><\/td>\r\n<td style=\"width: 33.3333%;height: 16px\">3. \\(y+40\\)<\/td>\r\n<td style=\"width: 33.3333%;height: 16px\">5. \\(\\frac{7}{8}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 33.3333%;height: 16px\">7. \\(\\frac{49}{11}\\)<\/td>\r\n<td style=\"width: 33.3333%;height: 16px\">9. \\(-63\\)<\/td>\r\n<td style=\"width: 33.3333%;height: 16px\">11. \\(1\\frac{5}{6}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 33.3333%;height: 16px\">13. 17<\/td>\r\n<td style=\"width: 33.3333%;height: 16px\">15. 14.88<\/td>\r\n<td style=\"width: 33.3333%;height: 16px\">17. 28<em data-effect=\"italics\">a<\/em><\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 33.3333%;height: 16px\">19. \\(-75m\\)<\/td>\r\n<td style=\"width: 33.3333%;height: 16px\">21. 10<em data-effect=\"italics\">p<\/em><\/td>\r\n<td style=\"width: 33.3333%;height: 16px\">23. \\(27m+\\left(-21n\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 33.3333%;height: 16px\">25. \\(\\frac{5}{4}g+\\frac{1}{2}h\\)<\/td>\r\n<td style=\"width: 33.3333%;height: 16px\">27. \\(2.43p+8.26q\\)<\/td>\r\n<td style=\"width: 33.3333%;height: 16px\">29. a) \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{2}{5}\\) b) \\(-4.3\\) c) 8 d) \\(\\frac{10}{3}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 33.3333%;height: 16px\">31. a) \\(\\frac{7}{6}\\) b) 0.075 c) \\(-23\\) d) \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{4}\\)<\/td>\r\n<td style=\"width: 33.3333%;height: 16px\">33. a) \\(\\frac{1}{6}\\) b) \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{4}{3}\\) c) \\(\\frac{10}{7}\\)<\/td>\r\n<td style=\"width: 33.3333%;height: 16px\">35. a) \\(\\frac{12}{11}\\) b) \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{10}{11}\\) c) \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{4}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 33.3333%;height: 16px\">37. 0<\/td>\r\n<td style=\"width: 33.3333%;height: 16px\">39. 0<\/td>\r\n<td style=\"width: 33.3333%;height: 16px\">41. 0<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 33.3333%;height: 16px\">43. 0<\/td>\r\n<td style=\"width: 33.3333%;height: 16px\">45. 44<\/td>\r\n<td style=\"width: 33.3333%;height: 16px\">47. d<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 33.3333%;height: 16px\">49. 0<\/td>\r\n<td style=\"width: 33.3333%;height: 16px\">51. 0<\/td>\r\n<td style=\"width: 33.3333%;height: 16px\">53. undefined<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 33.3333%;height: 16px\">55. undefined<\/td>\r\n<td style=\"width: 33.3333%;height: 16px\">57. \\(36d+90\\)<\/td>\r\n<td style=\"width: 33.3333%;height: 16px\">59. \\(32y+72\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 33.3333%;height: 16px\">61. \\(6c-78\\)<\/td>\r\n<td style=\"width: 33.3333%;height: 16px\">63. \\(\\frac{3}{4}q+3\\)<\/td>\r\n<td style=\"width: 33.3333%;height: 16px\">65. \\(5y-3\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 33.3333%;height: 16px\">67. \\(3+8r\\)<\/td>\r\n<td style=\"width: 33.3333%;height: 16px\">69. \\(rs-18r\\)<\/td>\r\n<td style=\"width: 33.3333%;height: 16px\">71. \\(yp+4p\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 33.3333%;height: 16px\">73. \\(-28p-7\\)<\/td>\r\n<td style=\"width: 33.3333%;height: 16px\">75. \\(-3x+18\\)<\/td>\r\n<td style=\"width: 33.3333%;height: 16px\">77. \\(-3x+7\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 33.3333%;height: 16px\">79. \\(-3y-8\\)<\/td>\r\n<td style=\"width: 33.3333%;height: 16px\">81. \\(-33c+26\\)<\/td>\r\n<td style=\"width: 33.3333%;height: 16px\">83. \\(-a+19\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 33.3333%;height: 16px\">85. \\(4m-10\\)<\/td>\r\n<td style=\"width: 33.3333%;height: 16px\">87. \\(22n+9\\)<\/td>\r\n<td style=\"width: 33.3333%;height: 16px\">89. \\(72x-25\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 33.3333%;height: 16px\">91. \\(6c+34\\)<\/td>\r\n<td style=\"width: 33.3333%;height: 16px\">93. \\(12y+63\\)<\/td>\r\n<td style=\"width: 33.3333%;height: 16px\">95. a) \\$80 b) \\$80 c) answers will vary<\/td>\r\n<\/tr>\r\n<tr style=\"height: 16px\">\r\n<td style=\"width: 33.3333%;height: 16px\">97. a) \\$23.88 b) no, the price is the same<\/td>\r\n<td style=\"width: 33.3333%;height: 16px\">99. Answers may vary<\/td>\r\n<td style=\"width: 33.3333%;height: 16px\">101. Answers may vary<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h1>Attributions<\/h1>\r\nThis chapter has been adapted from \u201cProperties of Real Numbers\u201d in <a href=\"https:\/\/openstax.org\/details\/books\/elementary-algebra\"><em>Elementary Algebra<\/em><\/a> (OpenStax) by Lynn Marecek and MaryAnne Anthony-Smith, which is under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY 4.0 Licence<\/a>. Adapted by Izabela Mazur. See the Copyright page for more information.\r\n\r\n<\/div>","rendered":"<div class=\"textbox textbox--learning-objectives\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning Objectives<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>By the end of this section, you will be able to:<\/p>\n<ul>\n<li>Use the commutative and associative properties<\/li>\n<li>Use the identity and inverse properties of addition and multiplication<\/li>\n<li>Use the properties of zero<\/li>\n<li>Simplify expressions using the distributive property<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1>Use the Commutative and Associative Properties<\/h1>\n<p id=\"fs-id1170654026828\">Think about adding two numbers, say 5 and 3. The order we add them doesn\u2019t affect the result, does it?<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-ddad45a7986b84d1a54bc764a3ec2814_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#53;&#43;&#51;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#51;&#43;&#53;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#56;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#56;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"35\" width=\"128\" style=\"vertical-align: -11px;\" \/><\/p>\n<div id=\"fs-id1166426267603\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-0f43ed8b0f3e9406181b4f8590dce5b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#43;&#51;&#61;&#51;&#43;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"102\" style=\"vertical-align: -2px;\" \/><\/div>\n<p id=\"fs-id1170653891144\">The results are the same.<\/p>\n<p id=\"fs-id1170654031116\">As we can see, the order in which we add does not matter!<\/p>\n<p id=\"fs-id1170653884964\">What about multiplying <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-df1530adbe87e2b4ecea71e976f130f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#51;&#63;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"62\" style=\"vertical-align: -1px;\" \/><\/p>\n<div id=\"fs-id1170654014649\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-bf883a4264c1f891e1c62258981c9be2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#53;&#92;&#99;&#100;&#111;&#116;&#51;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#51;&#92;&#99;&#100;&#111;&#116;&#53;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#49;&#53;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#49;&#53;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"35\" width=\"109\" style=\"vertical-align: -11px;\" \/><\/div>\n<div id=\"fs-id1166424005906\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-ae1f86075eb2abb6193d02286b2ddd65_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#92;&#99;&#100;&#111;&#116;&#51;&#61;&#51;&#92;&#99;&#100;&#111;&#116;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"84\" style=\"vertical-align: 0px;\" \/><\/div>\n<p id=\"fs-id1170653771564\">Again, the results are the same!<\/p>\n<p id=\"fs-id1170654027262\">The order in which we multiply does not matter!<\/p>\n<p id=\"fs-id1170654013661\">These examples illustrate the commutative property. When adding or multiplying, changing the <em data-effect=\"italics\">order<\/em> gives the same result.<\/p>\n<div id=\"fs-id1170653917425\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Commutative Property<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-08d6e5114a5e5c5e1321d6240565aa29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#125;&#92;&#109;&#97;&#116;&#104;&#98;&#102;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#111;&#102;&#32;&#65;&#100;&#100;&#105;&#116;&#105;&#111;&#110;&#125;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#73;&#102;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#97;&#44;&#98;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#114;&#101;&#32;&#114;&#101;&#97;&#108;&#32;&#110;&#117;&#109;&#98;&#101;&#114;&#115;&#44;&#32;&#116;&#104;&#101;&#110;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#97;&#43;&#98;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#98;&#43;&#97;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#109;&#97;&#116;&#104;&#98;&#102;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#111;&#102;&#32;&#77;&#117;&#108;&#116;&#105;&#112;&#108;&#105;&#99;&#97;&#116;&#105;&#111;&#110;&#125;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#73;&#102;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#97;&#44;&#98;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#114;&#101;&#32;&#114;&#101;&#97;&#108;&#32;&#110;&#117;&#109;&#98;&#101;&#114;&#115;&#44;&#32;&#116;&#104;&#101;&#110;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#97;&#92;&#99;&#100;&#111;&#116;&#32;&#98;&#38;&#32;&#61;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#98;&#92;&#99;&#100;&#111;&#116;&#32;&#97;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"569\" style=\"vertical-align: -15px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170653751940\">When adding or multiplying, changing the <em data-effect=\"italics\">order<\/em> gives the same result.<\/p>\n<\/div>\n<p id=\"fs-id1170654011373\">The commutative property has to do with order. If you change the order of the numbers when adding or multiplying, the result is the same.<\/p>\n<p id=\"fs-id1170653758644\">What about subtraction? Does order matter when we subtract numbers? Does <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-d79e72f3d32181a11516b2b9301bd34c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"40\" style=\"vertical-align: 0px;\" \/> give the same result as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-ca22e01b59c69b787d89a288e8bae91b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#45;&#55;&#63;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"48\" style=\"vertical-align: 0px;\" \/><\/p>\n<div id=\"fs-id1170654027324\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-5511b66ed45397e56aeac77ecf51b83b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#55;&#45;&#51;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#51;&#45;&#55;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#52;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#45;&#52;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#52;&#92;&#110;&#101;&#32;&#45;&#52;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#55;&#45;&#51;&#92;&#110;&#101;&#32;&#51;&#45;&#55;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"127\" width=\"121\" style=\"vertical-align: -59px;\" \/><\/div>\n<p id=\"fs-id1170654013324\">The results are not the same.<\/p>\n<p id=\"fs-id1170653892774\">Since changing the order of the subtraction did not give the same result, we know that <em data-effect=\"italics\">subtraction is not commutative<\/em>.<\/p>\n<p>Let\u2019s see what happens when we divide two numbers. Is <span class=\"no-emphasis\" data-type=\"term\">division<\/span> commutative?<\/p>\n<div id=\"fs-id1170654031695\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-bd345d6414afc7a67f96c2b7f23065f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#49;&#50;&#92;&#100;&#105;&#118;&#32;&#52;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#52;&#92;&#100;&#105;&#118;&#32;&#49;&#50;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#50;&#125;&#123;&#52;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#49;&#50;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#51;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#51;&#92;&#110;&#101;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#49;&#50;&#92;&#100;&#105;&#118;&#32;&#52;&#92;&#110;&#101;&#32;&#52;&#92;&#100;&#105;&#118;&#32;&#49;&#50;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"104\" width=\"137\" style=\"vertical-align: -59px;\" \/><\/div>\n<p id=\"fs-id1170653797051\">The results are not the same.<\/p>\n<p id=\"fs-id1170653742804\">Since changing the order of the division did not give the same result, <em data-effect=\"italics\">division is not commutative<\/em>. The commutative properties only apply to addition and multiplication!<\/p>\n<ul id=\"fs-id1166426095775\" data-bullet-style=\"bullet\">\n<li>Addition and multiplication <em data-effect=\"italics\">are<\/em> commutative.<\/li>\n<li>Subtraction and Division <em data-effect=\"italics\">are not<\/em> commutative.<\/li>\n<\/ul>\n<p id=\"fs-id1170653898679\">If you were asked to simplify this expression, how would you do it and what would your answer be?<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-efbfef47570975470917ef48e2187b28_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#43;&#56;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"69\" style=\"vertical-align: -2px;\" \/><\/p>\n<p>Some people would think <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-2a915fe0b47a049f81744bc28d5a9bf7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#43;&#56;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#105;&#115;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"75\" style=\"vertical-align: -2px;\" \/> and then <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-9d663015706af7a26f0950ad5edf59b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;&#43;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#105;&#115;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#49;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"84\" style=\"vertical-align: -2px;\" \/>. Others might start with <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-ec448ecacddd5043214d9a34f71abbc8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#43;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#109;&#97;&#107;&#101;&#115;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"112\" style=\"vertical-align: -2px;\" \/> and then <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-cb9471039b3614168d05d7136e41da24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#43;&#49;&#48;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#109;&#97;&#107;&#101;&#115;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#49;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"121\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<p id=\"fs-id1170653887975\">Either way gives the same result. Remember, we use parentheses as grouping symbols to indicate which operation should be done first.<\/p>\n<table id=\"eip-252\" summary=\".\">\n<tbody>\n<tr>\n<td>Add <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-b43bcac58baa4675f735ecf539eede1d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#43;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"40\" style=\"vertical-align: -2px;\" \/>.<br \/>\nAdd.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-a34b2dfb9d24c26e402296f65ec441ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#43;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#50;&#92;&#92;&#32;&#49;&#53;&#43;&#50;&#92;&#92;&#32;&#49;&#55;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"58\" width=\"82\" style=\"vertical-align: -22px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Add <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-3da3ea5b9995a07d20d857beaf33fd8b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"39\" style=\"vertical-align: -2px;\" \/>.<br \/>\nAdd.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-73392a0c3de31e2cc465437c94d97ee4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#55;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#43;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#92;&#32;&#55;&#43;&#49;&#48;&#92;&#92;&#32;&#49;&#55;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"58\" width=\"83\" style=\"vertical-align: -22px;\" \/><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-70e61149bea95a05bf16b0bbb61ec985_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#43;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#50;&#61;&#55;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#43;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"189\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1170654015259\">When adding three numbers, changing the grouping of the numbers gives the same result.<\/p>\n<p id=\"fs-id1170654073631\">This is true for multiplication, too.<\/p>\n<table id=\"eip-989\" summary=\".\">\n<tbody>\n<tr>\n<td>Multiply. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-39be13b3bea795f4485380a390a226e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#92;&#99;&#100;&#111;&#116;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"31\" style=\"vertical-align: -6px;\" \/><br \/>\nMultiply.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-c349e9fb2c89c0357cae6093c6cabd71_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#92;&#99;&#100;&#111;&#116;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#99;&#100;&#111;&#116;&#51;&#92;&#92;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#51;&#125;&#92;&#99;&#100;&#111;&#116;&#51;&#92;&#92;&#32;&#53;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"60\" width=\"69\" style=\"vertical-align: -22px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Multiply. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-2346ec68d575cf9a20d5bf0ad0fbc130_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#92;&#99;&#100;&#111;&#116;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"31\" style=\"vertical-align: -6px;\" \/>.<br \/>\nMultiply.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-612c016d2c01893eb63a10ab8f8119b8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#53;&#92;&#99;&#100;&#111;&#116;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#92;&#99;&#100;&#111;&#116;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#92;&#32;&#53;&#92;&#99;&#100;&#111;&#116;&#49;&#92;&#92;&#32;&#53;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"60\" width=\"68\" style=\"vertical-align: -22px;\" \/><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-8479952f141226492d7649d65c7248c1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#92;&#99;&#100;&#111;&#116;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#99;&#100;&#111;&#116;&#51;&#61;&#53;&#92;&#99;&#100;&#111;&#116;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#92;&#99;&#100;&#111;&#116;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"160\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1170653774811\">When multiplying three numbers, changing the grouping of the numbers gives the same result.<\/p>\n<p id=\"fs-id1170653916060\">You probably know this, but the terminology may be new to you. These examples illustrate the associative property.<\/p>\n<div id=\"fs-id1170653849240\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Associative Property<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-26d164869092474efac609d59ae07b05_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#92;&#109;&#97;&#116;&#104;&#98;&#102;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#111;&#102;&#32;&#65;&#100;&#100;&#105;&#116;&#105;&#111;&#110;&#125;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#73;&#102;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#97;&#44;&#98;&#44;&#99;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#114;&#101;&#32;&#114;&#101;&#97;&#108;&#32;&#110;&#117;&#109;&#98;&#101;&#114;&#115;&#44;&#32;&#116;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#43;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#99;&#61;&#97;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#43;&#99;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#109;&#97;&#116;&#104;&#98;&#102;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#111;&#102;&#32;&#77;&#117;&#108;&#116;&#105;&#112;&#108;&#105;&#99;&#97;&#116;&#105;&#111;&#110;&#125;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#73;&#102;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#97;&#44;&#98;&#44;&#99;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#114;&#101;&#32;&#114;&#101;&#97;&#108;&#32;&#110;&#117;&#109;&#98;&#101;&#114;&#115;&#44;&#32;&#116;&#104;&#101;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#92;&#99;&#100;&#111;&#116;&#32;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#99;&#100;&#111;&#116;&#32;&#99;&#61;&#97;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#92;&#99;&#100;&#111;&#116;&#32;&#99;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"41\" width=\"606\" style=\"vertical-align: -16px;\" \/><\/p>\n<p>When adding or multiplying, changing the <em data-effect=\"italics\">grouping<\/em> gives the same result.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170653894784\">Let\u2019s think again about multiplying <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-8bac39025c9f99afa1f6716900e2caf9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"54\" style=\"vertical-align: -6px;\" \/>. We got the same result both ways, but which way was easier? Multiplying <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-fe79d31f861f99f8dca3a195c524e899_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-ed6a7b46319a62fc49486a4451313505_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> first, as shown above on the right side, eliminates the fraction in the first step. Using the associative property can make the math easier!<\/p>\n<p>The <span class=\"no-emphasis\" data-type=\"term\">associative property<\/span> has to do with grouping. If we change how the numbers are grouped, the result will be the same. Notice it is the same three numbers in the same order\u2014the only difference is the grouping.<\/p>\n<p id=\"fs-id1170653894135\">We saw that subtraction and division were not commutative. They are not associative either.<\/p>\n<p id=\"fs-id1170653807341\">When simplifying an expression, it is always a good idea to plan what the steps will be. In order to combine like terms in the next example, we will use the commutative property of addition to write the like terms together.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654077092\" data-type=\"problem\">\n<p id=\"fs-id1170653907474\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-feb7be10acf36a91e012af7322981ee5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;&#112;&#43;&#54;&#113;&#43;&#49;&#53;&#112;&#43;&#53;&#113;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"152\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170653909769\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-193\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-feb7be10acf36a91e012af7322981ee5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;&#112;&#43;&#54;&#113;&#43;&#49;&#53;&#112;&#43;&#53;&#113;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"152\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Use the commutative property of addition to re-order so that like terms are together.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-6feb6763bb74b271b1085a7a19b39fc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;&#112;&#43;&#49;&#53;&#112;&#43;&#54;&#113;&#43;&#53;&#113;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"152\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Add like terms.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-872ae2a9adfcbda69bbcc1bf702468d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#51;&#112;&#43;&#49;&#49;&#113;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"74\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654076917\" data-type=\"problem\">\n<p id=\"fs-id1170653915616\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-d245f557e51d780958239ca5f85c3caf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#51;&#114;&#43;&#49;&#52;&#115;&#43;&#57;&#114;&#43;&#49;&#53;&#115;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"161\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170653906988\" data-type=\"solution\">\n<details>\n<summary>Answer<\/summary>\n<p id=\"fs-id1170654009182\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-f4b7fb39a6932512a4b4e5bb85cc9845_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#50;&#114;&#43;&#50;&#57;&#115;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"74\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170653795554\" data-type=\"problem\">\n<p id=\"fs-id1170653775684\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-eb4094a8aec3e33c09a963f01c6b7edf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#55;&#109;&#43;&#50;&#49;&#110;&#43;&#52;&#109;&#45;&#49;&#53;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"180\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654014491\" data-type=\"solution\">\n<details>\n<summary>Answer<\/summary>\n<p id=\"fs-id1170654030751\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-2996a35b1cab43a6436199f3c1e2f0b8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#49;&#109;&#43;&#54;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"75\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p>When we have to simplify algebraic <span class=\"no-emphasis\" data-type=\"term\">expression<\/span>s, we can often make the work easier by applying the commutative or associative property first, instead of automatically following the order of operations. When adding or subtracting fractions, combine those with a common denominator first.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170653890205\" data-type=\"problem\">\n<p id=\"fs-id1170653748931\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-a9aa2b2ea40b0b370ed3ffeef5f07914_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#49;&#51;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"95\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170653984832\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-8\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-a9aa2b2ea40b0b370ed3ffeef5f07914_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#49;&#51;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"95\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Notice that the last 2 terms have a common denominator, so change the grouping.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-d527ac43b0e99fb38fd1dcee3e5aa302_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#49;&#51;&#125;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"95\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Add in parentheses first.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-470026f0999e5b9591455c9b529c17f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#49;&#51;&#125;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"62\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify the fraction.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-5cbb121ffebc9c8013ccb309fa194aa2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#49;&#51;&#125;&#43;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"45\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-5e17c85bbe34101eac36ee8e8c3b6034_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#49;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"24\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Convert to an improper fraction.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-ed31765e99a90a667c7e85c6c6810966_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#56;&#125;&#123;&#49;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654044584\" data-type=\"problem\">\n<p id=\"fs-id1170654044586\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-2db75495d47053b71a47706c7afe7171_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#49;&#53;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#56;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"95\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170653901181\" data-type=\"solution\">\n<details>\n<summary>Answer<\/summary>\n<p id=\"fs-id1170653901183\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-399e4d382b74510d71e6db12ad18a141_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#49;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"24\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654077704\" data-type=\"problem\">\n<p id=\"fs-id1170654077707\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-183f5e79bd6fda282ce6fe9c242791f1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#57;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#49;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#49;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"102\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170653901148\" data-type=\"solution\">\n<details>\n<summary>Answer<\/summary>\n<p id=\"fs-id1170653901150\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-d9858f4baf0eccf0ea73a01be61b5a80_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"17\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1170654044578\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1170654044582\" data-type=\"exercise\">\n<div id=\"fs-id1170654044584\" data-type=\"problem\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 3<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654014667\" data-type=\"problem\">\n<p id=\"fs-id1170654014669\">Use the associative property to simplify <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-131d17d67a162cbad5540d034f6b335c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"44\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170653901248\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-519\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-131d17d67a162cbad5540d034f6b335c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"44\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Change the grouping.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-ebc3d612b2bce5a12c74dfcde5c3479e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"56\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Multiply in the parentheses.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-66d8012cf554b6b14fcced507a431a98_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"27\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1170654059651\">Notice that we can multiply <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-a9bdd47247976bf974a270a6b6528cfd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#92;&#99;&#100;&#111;&#116;&#32;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\" \/> but we could not multiply 3<em data-effect=\"italics\">x<\/em> without having a value for <em data-effect=\"italics\">x<\/em>.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY 3.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654077036\" data-type=\"problem\">\n<p id=\"fs-id1170654077038\">Use the associative property to simplify 8(4<em data-effect=\"italics\">x<\/em>).<\/p>\n<\/div>\n<div id=\"fs-id1170654077047\" data-type=\"solution\">\n<details>\n<summary>Answer<\/summary>\n<p id=\"fs-id1170654077049\">32<em data-effect=\"italics\">x<\/em><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1170654079038\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1170654079042\" data-type=\"exercise\">\n<div id=\"fs-id1170654079044\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654079044\" data-type=\"problem\">\n<p id=\"fs-id1170654079046\">Use the associative property to simplify <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-c856e81742edb2ede9323dd46b4192c8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#57;&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"56\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654077742\" data-type=\"solution\">\n<details>\n<summary>Answer<\/summary>\n<p id=\"fs-id1170654077744\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-6053784fb817061b8b3ddfbaeebe4110_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;&#51;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"40\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Use the Identity and Inverse Properties of Addition and Multiplication<\/h1>\n<p id=\"fs-id1170654077762\">What happens when we add 0 to any number? Adding 0 doesn\u2019t change the value. For this reason, we call 0 the additive identity.<\/p>\n<p id=\"fs-id1170654084972\">For example,<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-6fc92b9530f303136c40fddc814e4246_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#49;&#51;&#43;&#48;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#45;&#49;&#52;&#43;&#48;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#48;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#49;&#51;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#45;&#49;&#52;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#45;&#56;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"274\" style=\"vertical-align: -11px;\" \/><\/p>\n<p id=\"fs-id1170654073759\">These examples illustrate the Identity Property of Addition that states that for any real number <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-a8696e12e63d7e1c8d4af5f8c92abb3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-f2bc2786ce913c2ca215c0231e9eb220_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#43;&#48;&#61;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"73\" style=\"vertical-align: -2px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-994c719ab6343bc4efddf2d9e6c5b8c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#43;&#97;&#61;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"73\" style=\"vertical-align: -2px;\" \/>.<\/p>\n<p id=\"fs-id1170654078244\">What happens when we multiply any number by one? Multiplying by 1 doesn\u2019t change the value. So we call 1 the multiplicative identity.<\/p>\n<p id=\"fs-id1170654078252\">For example,<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-6b96560e4b48ed1846b39d75d40c382d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#52;&#51;&#92;&#99;&#100;&#111;&#116;&#49;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#45;&#50;&#55;&#92;&#99;&#100;&#111;&#116;&#49;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#49;&#92;&#99;&#100;&#111;&#116;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#53;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#52;&#51;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#45;&#50;&#55;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#53;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"220\" style=\"vertical-align: -17px;\" \/><\/p>\n<p id=\"fs-id1170654014513\">These examples illustrate the Identity Property of Multiplication that states that for any real number <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-a8696e12e63d7e1c8d4af5f8c92abb3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-a989416a534714a0a72a4586e208db60_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#99;&#100;&#111;&#116;&#49;&#61;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"64\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-1c0f2d006f3dc2720ecf5a7734f4df4d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#92;&#99;&#100;&#111;&#116;&#32;&#97;&#61;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"63\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<p id=\"fs-id1170653990233\">We summarize the Identity Properties below.<\/p>\n<div id=\"fs-id1170653990236\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Identity Property<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-ffb910a6843776177a53cbc624152c1d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#111;&#102;&#32;&#97;&#100;&#100;&#105;&#116;&#105;&#111;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#70;&#111;&#114;&#32;&#97;&#110;&#121;&#32;&#114;&#101;&#97;&#108;&#32;&#110;&#117;&#109;&#98;&#101;&#114;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#97;&#92;&#116;&#101;&#120;&#116;&#123;&#58;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#97;&#43;&#48;&#61;&#97;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#48;&#43;&#97;&#61;&#97;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#48;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#105;&#115;&#32;&#116;&#104;&#101;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#100;&#100;&#105;&#116;&#105;&#118;&#101;&#32;&#105;&#100;&#101;&#110;&#116;&#105;&#116;&#121;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#111;&#102;&#32;&#109;&#117;&#108;&#116;&#105;&#112;&#108;&#105;&#99;&#97;&#116;&#105;&#111;&#110;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#70;&#111;&#114;&#32;&#97;&#110;&#121;&#32;&#114;&#101;&#97;&#108;&#32;&#110;&#117;&#109;&#98;&#101;&#114;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#97;&#92;&#116;&#101;&#120;&#116;&#123;&#58;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#97;&#92;&#99;&#100;&#111;&#116;&#32;&#49;&#61;&#97;&#38;&#32;&#38;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#49;&#92;&#99;&#100;&#111;&#116;&#32;&#97;&#61;&#97;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#49;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#105;&#115;&#32;&#116;&#104;&#101;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#109;&#117;&#108;&#116;&#105;&#112;&#108;&#105;&#99;&#97;&#116;&#105;&#118;&#101;&#32;&#105;&#100;&#101;&#110;&#116;&#105;&#116;&#121;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"127\" width=\"518\" style=\"vertical-align: -59px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><span id=\"fs-id1170654036108\" data-type=\"media\" data-alt=\"In the top line of this figure, we have the question \u201cWhat number added to 5 gives the additive identity, 0?\u201d On the following line, we have 5 plus a blank space equals 0. Then it is stated that \u201cWe know 5 plus negative 5 equals 0.\u201d On the following line, we have the question \u201cWhat number added to negative 6 gives the additive identity, 0?\u201d On the following line, we have negative 6 plus a blank space equals 0. Then it is stated that \u201cWe know negative 6 plus 6 equals 0.\u201d\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/05\/CNX_ElemAlg_Figure_01_09_003_img_new.jpg\" alt=\"In the top line of this figure, we have the question \u201cWhat number added to 5 gives the additive identity, 0?\u201d On the following line, we have 5 plus a blank space equals 0. Then it is stated that \u201cWe know 5 plus negative 5 equals 0.\u201d On the following line, we have the question \u201cWhat number added to negative 6 gives the additive identity, 0?\u201d On the following line, we have negative 6 plus a blank space equals 0. Then it is stated that \u201cWe know negative 6 plus 6 equals 0.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1170654036114\">Notice that in each case, the missing number was the opposite of the number!<\/p>\n<p id=\"fs-id1170654036118\">We call <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-ea06e767761795c9461868fc0dcea0a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"22\" style=\"vertical-align: 0px;\" \/>. the additive inverse of <em data-effect=\"italics\">a<\/em>. <em data-effect=\"italics\">The opposite of a number is its additive inverse.<\/em> A number and its opposite add to zero, which is the additive identity. This leads to the Inverse Property of Addition that states for any real number <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-82c4ae888e292dbd63b1bacd6abbdb22_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#44;&#97;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#97;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"118\" style=\"vertical-align: -5px;\" \/>. Remember, a number and its opposite add to zero.<\/p>\n<p id=\"fs-id1170654014737\">What number multiplied by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-cc8acd49033fa821e1969b71311425b2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/> gives the multiplicative identity, 1? In other words, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-cc8acd49033fa821e1969b71311425b2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/> times what results in 1?<\/p>\n<p><span id=\"fs-id1170653797753\" data-type=\"media\" data-alt=\"We have the statement that 2\/3 times a blank space equals 1. Then it is stated that \u201cWe know 2\/3 times 3\/2 equals 1.\u201d\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_09_004_img_new.jpg\" alt=\"We have the statement that 2\/3 times a blank space equals 1. Then it is stated that \u201cWe know 2\/3 times 3\/2 equals 1.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1170653797762\">What number multiplied by 2 gives the multiplicative identity, 1? In other words 2 times what results in 1?<\/p>\n<p><span id=\"fs-id1170653797768\" data-type=\"media\" data-alt=\"We have the statement that 2 times a blank space equals 1. Then it is stated that \u201cWe know 2 times 1\/2 equals 1.\u201d\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_09_005_img_new.jpg\" alt=\"We have the statement that 2 times a blank space equals 1. Then it is stated that \u201cWe know 2 times 1\/2 equals 1.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1170653797777\">Notice that in each case, the missing number was the <span class=\"no-emphasis\" data-type=\"term\">reciprocal<\/span> of the number!<\/p>\n<p id=\"fs-id1170654030286\">We call <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-bffaba0ef46c90ca515fa3b0f34c5de6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#97;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"8\" style=\"vertical-align: -6px;\" \/> the multiplicative inverse of <em data-effect=\"italics\">a<\/em>. <em data-effect=\"italics\">The reciprocal of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-a8696e12e63d7e1c8d4af5f8c92abb3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/> number is its multiplicative inverse.<\/em> A number and its reciprocal multiply to one, which is the multiplicative identity. This leads to the Inverse Property of Multiplication that states that for any real number <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-80676cade3fe63ff7d00794f0905125b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#44;&#97;&#92;&#110;&#101;&#32;&#48;&#44;&#97;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#97;&#125;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"132\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<p id=\"fs-id1170654012966\">We\u2019ll formally state the inverse properties here:<\/p>\n<div id=\"fs-id1170654012970\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Inverse Property<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<table id=\"eip-73\" class=\"grid\" summary=\".\">\n<tbody>\n<tr>\n<td><strong>of addition<\/strong><\/td>\n<td>For any real number <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-a8696e12e63d7e1c8d4af5f8c92abb3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/>,<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-ea06e767761795c9461868fc0dcea0a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"22\" style=\"vertical-align: 0px;\" \/> is the <strong>additive inverse<\/strong> of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-a8696e12e63d7e1c8d4af5f8c92abb3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/>.<br \/>\nA number and its opposite add to zero.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-a31750509cd34e3c6c42a26039770c9c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#97;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"101\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td><strong>of multiplication<\/strong><\/td>\n<td>For any real number <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-a8696e12e63d7e1c8d4af5f8c92abb3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/>,<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-bffaba0ef46c90ca515fa3b0f34c5de6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#97;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"8\" style=\"vertical-align: -6px;\" \/> is the <strong>multiplicative inverse<\/strong> of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-a8696e12e63d7e1c8d4af5f8c92abb3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/>.<br \/>\nA number and its reciprocal multiply to one.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-d9a80eda2c925ab50819c0e64fbdc3dc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#97;&#125;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"65\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 4<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654075038\" data-type=\"problem\">\n<p id=\"fs-id1170654075040\">Find the additive inverse of a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-ce927b77c24dcc98a42ec41168b0cc47_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-f8ea974fbad1f97076c037429460212a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"23\" style=\"vertical-align: 0px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-892d6c8c7687279f24c71029a53a813e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/> d) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-6a2c82a650bf12014823d422afc91a18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"25\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654084880\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1170654084886\">To find the additive inverse, we find the opposite.<\/p>\n<ol id=\"fs-id1166423979092\" class=\"circled\" type=\"a\">\n<li>The additive inverse of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-ce927b77c24dcc98a42ec41168b0cc47_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/> is the opposite of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-ce927b77c24dcc98a42ec41168b0cc47_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/>. The additive inverse of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-ce927b77c24dcc98a42ec41168b0cc47_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/> is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-f02c76555d6f1dfee3fe992af78f0f1c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"25\" style=\"vertical-align: -6px;\" \/>.<\/li>\n<li>The additive inverse of 0.6 is the opposite of 0.6. The additive inverse of 0.6 is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-a221f723c4c25c68feba2d7252afc516_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#48;&#46;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"36\" style=\"vertical-align: 0px;\" \/>.<\/li>\n<li>The additive inverse of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-892d6c8c7687279f24c71029a53a813e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/> is the opposite of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-892d6c8c7687279f24c71029a53a813e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/>. We write the opposite of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-892d6c8c7687279f24c71029a53a813e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/> as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-2fa652c50d0afdc335ba2538135ee6ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"52\" style=\"vertical-align: -5px;\" \/>, and then simplify it to 8. Therefore, the additive inverse of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-892d6c8c7687279f24c71029a53a813e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/> is 8.<\/li>\n<li>The additive inverse of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-6a2c82a650bf12014823d422afc91a18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"25\" style=\"vertical-align: -6px;\" \/> is the opposite of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-6a2c82a650bf12014823d422afc91a18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"25\" style=\"vertical-align: -6px;\" \/>. We write this as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-0cba6abcd4bd12f41ae085826f3626c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"58\" style=\"vertical-align: -7px;\" \/>, and then simplify to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-1bb67dff91418ef4cd9ccaacae8c1e07_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/>. Thus, the additive inverse of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-6a2c82a650bf12014823d422afc91a18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"25\" style=\"vertical-align: -6px;\" \/> is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-1bb67dff91418ef4cd9ccaacae8c1e07_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/>.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170653800547\" data-type=\"problem\">\n<p id=\"fs-id1170653800549\">Find the additive inverse of: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-aa13889e842a4a13e1cfb73ed635aa5d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-f569b2977d3d32080a3c6a7db89f4411_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#46;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"21\" style=\"vertical-align: 0px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-b7f3765d0242e181ff47c03895c6b7fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\" \/> d) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-be9e09a4f1bd882915f0946ebdc198a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"25\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170653800585\" data-type=\"solution\">\n<details>\n<summary>Answer<\/summary>\n<p id=\"fs-id1170653800587\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-b8ee4119a72819b5fbbd663151fe4d99_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"25\" style=\"vertical-align: -6px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-2325a10609e2888c88f664de3e5f23b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#46;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"35\" style=\"vertical-align: 0px;\" \/> c)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-1f2a2e62379f3eeaab8fc2950f287113_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: 0px;\" \/> d) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-c5542726ecc501af1fe642291fc2083d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercises<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654073186\" data-type=\"problem\">\n<p id=\"fs-id1170654073188\">Find the additive inverse of: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-b3c771b4bcb096018ad09ddb9d39420e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#49;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-85952c8074af6c687210b433fe3c96b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#46;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"23\" style=\"vertical-align: 0px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-78ab2e8130c78d45d15ed5033feb9db5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\" \/> d) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-d06fb118d4d0b355bd61ef423e06e129_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"25\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654078943\" data-type=\"solution\">\n<details>\n<summary>Answer<\/summary>\n<p id=\"fs-id1170654078945\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-d9db05e874dcbfa2d14bb15ee1284413_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#49;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"32\" style=\"vertical-align: -6px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-62bc453837c1974456c418b039fc3994_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;&#46;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"36\" style=\"vertical-align: 0px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-85747a9c87e25385fbab1777cac6c891_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> d) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-c4d533b432cf63067237ac03f4742507_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 5<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654073241\" data-type=\"problem\">\n<p id=\"fs-id1170654073243\">Find the multiplicative inverse of a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-1a6eb0ef66d06e2573d6ded310829526_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-d9ce062a98584ffdd7e0f4f6b8e952f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"25\" style=\"vertical-align: -6px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-496644a4699e9349755f985adced96ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"23\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654073268\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1170654073274\">To find the multiplicative inverse, we find the reciprocal.<\/p>\n<ol id=\"fs-id1166426176898\" class=\"circled\" type=\"a\">\n<li>The multiplicative inverse of 9 is the reciprocal of 9, which is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-16dd7f7c890b2df4fbde39010552b70b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/>. Therefore, the multiplicative inverse of 9 is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-16dd7f7c890b2df4fbde39010552b70b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/>.<\/li>\n<li>The multiplicative inverse of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-d9ce062a98584ffdd7e0f4f6b8e952f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"25\" style=\"vertical-align: -6px;\" \/> is the reciprocal of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-d9ce062a98584ffdd7e0f4f6b8e952f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"25\" style=\"vertical-align: -6px;\" \/>, which is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-529e6d91e0c2c45294de3a86fabc2ce5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/>. Thus, the multiplicative inverse of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-d9ce062a98584ffdd7e0f4f6b8e952f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"25\" style=\"vertical-align: -6px;\" \/> is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-529e6d91e0c2c45294de3a86fabc2ce5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/>.<\/li>\n<li>To find the multiplicative inverse of 0.9, we first convert 0.9 to a fraction, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-702ea00a9cb5cf9e9245d3e5af359c9b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#125;&#123;&#49;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/>. Then we find the reciprocal of the fraction. The reciprocal of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-702ea00a9cb5cf9e9245d3e5af359c9b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#125;&#123;&#49;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/> is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-95caedaad7bf0ba029ea33df189d2721_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#48;&#125;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/>. So the multiplicative inverse of 0.9 is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-95caedaad7bf0ba029ea33df189d2721_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#48;&#125;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/>.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170653991352\" data-type=\"problem\">\n<p id=\"fs-id1170653991354\">Find the multiplicative inverse of a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-059fa0d3851fd88e5ec3b7014b96ee44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-b5391584d9f6ed23d13fb2ba85a1c8d7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"25\" style=\"vertical-align: -6px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-bffd429d2e0cf7e3b831b6db2847165e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"23\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/div>\n<div id=\"fs-id1170654073682\" data-type=\"solution\">\n<details>\n<summary>Answer<\/summary>\n<p id=\"fs-id1170654073684\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-a165915a521abefffbbe8a43a07a17a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-212ac331944e53364e6086359534d6c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: 0px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-4980918030597f78d41511c3dc31bba3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#48;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654073719\" data-type=\"problem\">\n<p id=\"fs-id1170654073721\">Find the multiplicative inverse of a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-9680adf5dc38b6539ff8daf04695d538_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-76437653f5e85fe75bd8f11b3b086b3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"25\" style=\"vertical-align: -6px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-f8ea974fbad1f97076c037429460212a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"23\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654036171\" data-type=\"solution\">\n<details>\n<summary>Answer<\/summary>\n<p id=\"fs-id1170654036173\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-01245ad07b7ddd38b0fede38ef45562f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-b328a2a6493421caa2c7d18f95036c6f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"25\" style=\"vertical-align: -6px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-9d71cdb1303c4ef7a037df859e93f33f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<h1>Use the Properties of Zero<\/h1>\n<p id=\"fs-id1170653800723\">The identity property of addition says that when we add 0 to any number, the result is that same number. What happens when we multiply a number by 0? Multiplying by 0 makes the <span class=\"no-emphasis\" data-type=\"term\">product<\/span> equal zero.<\/p>\n<div id=\"fs-id1170653800728\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Multiplication by Zero<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1170653800734\">For any real number <em data-effect=\"italics\">a<\/em>.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-f68597470aa98186ed516d908554ce26_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#99;&#100;&#111;&#116;&#32;&#48;&#61;&#48;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#54;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#48;&#92;&#99;&#100;&#111;&#116;&#32;&#97;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"234\" style=\"vertical-align: 0px;\" \/><\/p>\n<p id=\"fs-id1170653800771\">The product of any real number and 0 is 0.<\/p>\n<\/div>\n<\/div>\n<p>What about division involving zero? What is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-95f249483d8f3fc87dd8e9fba12c68ee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#92;&#100;&#105;&#118;&#32;&#51;&#63;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"48\" style=\"vertical-align: -1px;\" \/> Think about a real example: If there are no cookies in the cookie jar and 3 people are to share them, how many cookies does each person get? There are no cookies to share, so each person gets 0 cookies. So,<\/p>\n<\/div>\n<\/div>\n<div id=\"fs-id1170654014380\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-d7d7b4c3e76a21d1342e214ee10841b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#92;&#100;&#105;&#118;&#32;&#51;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"72\" style=\"vertical-align: -1px;\" \/><\/div>\n<p id=\"fs-id1170654014398\">We can check division with the related multiplication fact.<\/p>\n<div id=\"fs-id1166426254494\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-3df4b2dbeb48fa97c1c94139eee6ec49_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#92;&#100;&#105;&#118;&#32;&#54;&#61;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#98;&#101;&#99;&#97;&#117;&#115;&#101;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#54;&#61;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"218\" style=\"vertical-align: -1px;\" \/>.<\/div>\n<p id=\"fs-id1170654014427\">So we know <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-d7d7b4c3e76a21d1342e214ee10841b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#92;&#100;&#105;&#118;&#32;&#51;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"72\" style=\"vertical-align: -1px;\" \/> because <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-6b8df63e9359a895bfa2e7d030034c0f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"63\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<div id=\"fs-id1170654076119\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Division of Zero<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>For any real number <em data-effect=\"italics\">a<\/em>, except <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-08de599a523a89c96a7fbfe91ad85781_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/>, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-177382779452c5b6fbdc7b6117227799_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#48;&#125;&#123;&#97;&#125;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"42\" style=\"vertical-align: -6px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-f110d8314c76a9748b09ee1a759d6d90_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#92;&#100;&#105;&#118;&#32;&#97;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"73\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<p>Zero divided by any real number except zero is zero.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170654076171\">Now think about dividing <em data-effect=\"italics\">by<\/em> zero. What is the result of dividing 4 by 0? Think about the related multiplication fact: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-303f89c0b4c9c4224520137e066d7bf7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#100;&#105;&#118;&#32;&#48;&#61;&#63;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"66\" style=\"vertical-align: -1px;\" \/> means <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-4b146c372feb9b8bfdf75b42fee5cf4f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#63;&#92;&#99;&#100;&#111;&#116;&#32;&#48;&#61;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"63\" style=\"vertical-align: 0px;\" \/>. Is there a number that multiplied by 0 gives 4? Since any real number multiplied by 0 gives 0, there is no real number that can be multiplied by 0 to obtain 4<\/p>\n<p id=\"fs-id1170653991470\">We conclude that there is no answer to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-f6011ce7f45e2d4ba5199f5fe6313a0d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#100;&#105;&#118;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"40\" style=\"vertical-align: -1px;\" \/> and so we say that division by 0 is undefined.<\/p>\n<div id=\"fs-id1170653991484\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Division by Zero<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1170653991489\">For any real number <em data-effect=\"italics\">a<\/em>, except 0, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-fa3f3f9bfb1332825b37a0d7552a3932_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"8\" style=\"vertical-align: -6px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-9342473d8d8a4441663c7b2fca92f0ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#100;&#105;&#118;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"40\" style=\"vertical-align: -1px;\" \/> are undefined.<\/p>\n<p id=\"fs-id1170653991514\">Division by zero is undefined.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170653991519\">We summarize the properties of zero below.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Properties of Zero<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1170653991528\"><strong data-effect=\"bold\">Multiplication by Zero:<\/strong> For any real number <em data-effect=\"italics\">a<\/em>,<\/p>\n<table id=\"eip-18\" summary=\".\">\n<tbody>\n<tr>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-48c8b3827bc92458c3feef7bd7d99fbf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#99;&#100;&#111;&#116;&#32;&#48;&#61;&#48;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#48;&#92;&#99;&#100;&#111;&#116;&#32;&#97;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"145\" style=\"vertical-align: 0px;\" \/><\/td>\n<td>The product of any number and 0 is 0.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1170654014590\"><strong data-effect=\"bold\">Division of Zero, Division by Zero:<\/strong> For any real number <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-df7b2e47dc1a9092d80de94d3067c66b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#44;&#97;&#92;&#110;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"59\" style=\"vertical-align: -4px;\" \/><\/p>\n<table id=\"eip-866\" summary=\".\">\n<tbody>\n<tr>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-177382779452c5b6fbdc7b6117227799_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#48;&#125;&#123;&#97;&#125;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"42\" style=\"vertical-align: -6px;\" \/><\/td>\n<td>Zero divided by any real number except itself is zero.<\/td>\n<\/tr>\n<tr>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-896ba83b88d13b85c0895c563609f2f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#48;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#105;&#115;&#32;&#117;&#110;&#100;&#101;&#102;&#105;&#110;&#101;&#100;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"107\" style=\"vertical-align: -6px;\" \/><\/td>\n<td>Division by zero is undefined.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 6<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654012883\" data-type=\"problem\">\n<p id=\"fs-id1170654012885\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-2cdb58cd5d3b63b0fd92928ecac715bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;&#92;&#99;&#100;&#111;&#116;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"43\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-29cceb125e88e770dd235729c94c04a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#48;&#125;&#123;&#45;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"18\" style=\"vertical-align: -6px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-adb5a1308925ff2cdcd756d23c451c3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#45;&#51;&#50;&#125;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"25\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654012915\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-223\" summary=\".\">\n<tbody>\n<tr>\n<td>a)<br \/>\nThe product of any real number and 0 is 0.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-30cb472b0471735cadea497f31e4c169_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#45;&#56;&#92;&#99;&#100;&#111;&#116;&#32;&#48;&#92;&#92;&#32;&#48;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"34\" width=\"44\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>b)<br \/>\nZero divided by any real number except itself is zero.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-1b13210524a214f890ac09d87387ea53_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#48;&#125;&#123;&#45;&#50;&#125;&#92;&#92;&#32;&#48;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"18\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>c)<br \/>\nDivision by 0 is undefined.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-fdeba0113ba20cc40dce2e74a8dfa26e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#45;&#51;&#50;&#125;&#123;&#48;&#125;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#85;&#110;&#100;&#101;&#102;&#105;&#110;&#101;&#100;&#125;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"79\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654077664\" data-type=\"problem\">\n<p id=\"fs-id1170654077666\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-bbbecaaedaf8e57dc4a43e14837be180_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#52;&#92;&#99;&#100;&#111;&#116;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"52\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-e322ee887dc05b9b88abeeb8adc25799_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#48;&#125;&#123;&#45;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"18\" style=\"vertical-align: -6px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-dcf1e31a50d327746d368f38abd0138f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#45;&#50;&#125;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"18\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654035978\" data-type=\"solution\">\n<details>\n<summary>Answer<\/summary>\n<p id=\"fs-id1170654035980\">a) 0 b) 0 c) undefined<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654035992\" data-type=\"problem\">\n<p id=\"fs-id1170654035994\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-2e3b4bc66010c253a399c0bcdfc7a91e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"57\" style=\"vertical-align: -5px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-41d24ab7746d60935c98f7491bb72a0c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#48;&#125;&#123;&#45;&#49;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"25\" style=\"vertical-align: -6px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-f3c80e408e9398c5f7843b23755096a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#45;&#53;&#125;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"18\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654036032\" data-type=\"solution\">\n<details>\n<summary>Answer<\/summary>\n<p id=\"fs-id1170654036035\">a) 0 b) 0 c) undefined<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170654036041\">We will now practice using the properties of identities, inverses, and zero to simplify expressions.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 7<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654014354\" data-type=\"problem\">\n<p id=\"fs-id1170654014356\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-990bc2d40f42a22743f2110920545f92_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#48;&#125;&#123;&#110;&#43;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"26\" style=\"vertical-align: -8px;\" \/>, where <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-5f1f5b2364bc1809a55ebc2b82ab0ec5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#110;&#92;&#110;&#101;&#32;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"56\" style=\"vertical-align: -4px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-62e33e842e52c1a91b0ba97c9707c28f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#48;&#45;&#51;&#112;&#125;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"39\" style=\"vertical-align: -6px;\" \/>, where <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-9bd2ddfaa9c2b83e03391ddde3b0f9a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#45;&#51;&#112;&#92;&#110;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"89\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654075609\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-851\" summary=\"\/\">\n<tbody>\n<tr>\n<td>a)<br \/>\nZero divided by any real number except itself is 0.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-31ce5ca5a1dd5216bcc598a6501d748d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#48;&#125;&#123;&#110;&#43;&#53;&#125;&#92;&#92;&#32;&#48;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"26\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>b)<br \/>\nDivision by 0 is undefined.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-733a14aa59112adf5ed5a345c7cf0b11_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#48;&#45;&#51;&#112;&#125;&#123;&#48;&#125;&#92;&#92;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#85;&#110;&#100;&#101;&#102;&#105;&#110;&#101;&#100;&#125;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"79\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654069194\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1170654069198\" data-type=\"exercise\">\n<div id=\"fs-id1170654069200\" data-type=\"problem\">\n<p id=\"fs-id1170654069203\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-af2b75491658a69aa5dff781e01a94ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#48;&#125;&#123;&#109;&#43;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"30\" style=\"vertical-align: -8px;\" \/>, where <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-f9c19097541679abe0ab1f788c26ccbb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#109;&#92;&#110;&#101;&#32;&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"62\" style=\"vertical-align: -4px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-41887d2b5c6a3a21e08e79fa728b459d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#56;&#45;&#54;&#99;&#125;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"38\" style=\"vertical-align: -6px;\" \/>, where <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-17883c3017c983960b32816786ef0651_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;&#45;&#54;&#99;&#92;&#110;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"88\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654069270\" data-type=\"solution\">\n<details>\n<summary>Answer<\/summary>\n<p id=\"fs-id1170654069272\">a) 0 b) undefined<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654069285\" data-type=\"problem\">\n<p id=\"fs-id1170654069287\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-780f6df02ad5489340f18d4d62cb67b4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#48;&#125;&#123;&#100;&#45;&#52;&#125;&#44;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#114;&#101;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#100;&#92;&#110;&#101;&#32;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"125\" style=\"vertical-align: -6px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-ff454d29d68ad9f0bcc25aff1bc68fd6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#53;&#45;&#52;&#113;&#125;&#123;&#48;&#125;&#44;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#104;&#101;&#114;&#101;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#49;&#53;&#45;&#52;&#113;&#92;&#110;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"186\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654034465\" data-type=\"solution\">\n<details>\n<summary>Answer<\/summary>\n<p id=\"fs-id1170654034468\">a) 0 b) undefined<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 8<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654036048\" data-type=\"problem\">\n<p id=\"fs-id1170654036051\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-7ca0bb682014e078934448dacc4e63ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;&#52;&#110;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#55;&#51;&#110;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#56;&#52;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"169\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654075181\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-616\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-7ca0bb682014e078934448dacc4e63ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;&#52;&#110;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#55;&#51;&#110;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#56;&#52;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"169\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Notice that the first and third terms are opposites; use the<br \/>\ncommutative property of addition to re-order the terms.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-ea99db256ecace4fadc962a659ba7561_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;&#52;&#110;&#43;&#56;&#52;&#110;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#55;&#51;&#110;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"169\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Add left to right.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-1b130fb201b7dcc97b079eb224c4702a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#55;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"75\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-383182f18e3a94d525c2c72431811c50_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#55;&#51;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"42\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1170653800644\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1170653800647\" data-type=\"exercise\">\n<div id=\"fs-id1170653800649\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170653800649\" data-type=\"problem\">\n<p id=\"fs-id1170653800651\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-d4970c822ecdea1d2cf439721393fc4a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#55;&#97;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#56;&#97;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#50;&#55;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"165\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170653800683\" data-type=\"solution\">\n<details>\n<summary>Answer<\/summary>\n<p id=\"fs-id1170653800685\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-74d75f8d9133dbf4e243e1d5bbdeaa74_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#56;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"40\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170653800702\" data-type=\"problem\">\n<p id=\"fs-id1170653800704\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-2de096ebfa3eb16e65e4a943c133081f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#57;&#120;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#57;&#50;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#57;&#120;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"182\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654059538\" data-type=\"solution\">\n<details>\n<summary>Answer<\/summary>\n<p id=\"fs-id1170654059540\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-107d5997374d4f0728f23db6cab35951_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#57;&#50;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"41\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170654059552\">Now we will see how recognizing reciprocals is helpful. Before multiplying left to right, look for reciprocals\u2014their product is 1<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 9<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654059561\" data-type=\"problem\">\n<p id=\"fs-id1170654059563\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-cd30bf998b241fb87746fd7f3f86cf36_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#49;&#53;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#56;&#125;&#123;&#50;&#51;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#53;&#125;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"75\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654059595\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-950\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-cd30bf998b241fb87746fd7f3f86cf36_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#49;&#53;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#56;&#125;&#123;&#50;&#51;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#53;&#125;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"75\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Notice that the first and third terms are reciprocals, so use the<br \/>\ncommutative property of multiplication to re-order the factors.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-7601d0fbc5c6b1e696d0c6792ab86b7b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#49;&#53;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#53;&#125;&#123;&#55;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#56;&#125;&#123;&#50;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"75\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Multiply left to right.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-0a84b7950c35ca024750a5d2888ffaf4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#56;&#125;&#123;&#50;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"37\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-c42232bb30555c3d79ec1fd35700afc0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#56;&#125;&#123;&#50;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654069484\" data-type=\"problem\">\n<p id=\"fs-id1170654069486\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-aacd485589b816b6be8a34079f293cd6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#125;&#123;&#49;&#54;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#52;&#57;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#54;&#125;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"75\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654014276\" data-type=\"solution\">\n<details>\n<summary>Answer<\/summary>\n<p id=\"fs-id1170654014278\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-7e047be9738dfb736b60513d48c98c79_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#52;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/details>\n<div id=\"fs-id1170654014298\" data-type=\"problem\"><\/div>\n<div id=\"fs-id1170654014333\" data-type=\"solution\">\n<p id=\"fs-id1170654014335\">\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654014298\" data-type=\"problem\">\n<p id=\"fs-id1170654014300\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-b8ce6f03932ee2945c47e58ee2df5426_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#54;&#125;&#123;&#49;&#55;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#49;&#125;&#123;&#50;&#53;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#55;&#125;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"75\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654014333\" data-type=\"solution\">\n<details>\n<summary>Answer<\/summary>\n<p id=\"fs-id1170654014335\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-1a7b72eece0b70f4cfc99a1583947f2a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#49;&#125;&#123;&#50;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1170654069479\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1170654069482\" data-type=\"exercise\">\n<div id=\"fs-id1170654069484\" data-type=\"problem\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 10<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654034479\" data-type=\"problem\">\n<p id=\"fs-id1170654034481\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-6cfbc2937502984b4bb6a59e771df07f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#51;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#120;&#43;&#49;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"107\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654034517\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-386\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-6cfbc2937502984b4bb6a59e771df07f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#51;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#120;&#43;&#49;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"107\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>There is nothing to do in the parentheses, so multiply the<br \/>\ntwo fractions first\u2014notice, they are reciprocals.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-ca01b81ebf890037db8d9001ad4b8de0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#120;&#43;&#49;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"82\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify by recognizing the multiplicative identity.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-a97eb1176020a3784eb30964e16bcbbc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#120;&#43;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"58\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654073889\" data-type=\"problem\">\n<p id=\"fs-id1170654073891\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-173fba0b99c6a9936aadc56cff37a2f5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#50;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#48;&#121;&#43;&#53;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"115\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654073928\" data-type=\"solution\">\n<details>\n<summary>Answer<\/summary>\n<p id=\"fs-id1170654073930\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-201ce009c862c689948d9a63861221a0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#48;&#121;&#43;&#53;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"67\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654073952\" data-type=\"problem\">\n<p id=\"fs-id1170654073954\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-105bd556ec71969fda8ff1edc29aaf19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#56;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#56;&#125;&#123;&#51;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#50;&#122;&#43;&#49;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"115\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654073990\" data-type=\"solution\">\n<details>\n<summary>Answer<\/summary>\n<p id=\"fs-id1170654073993\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-e682c28b29632aa63eb00d15296734e4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#122;&#43;&#49;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"65\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Simplify Expressions Using the Distributive Property<\/h1>\n<p id=\"fs-id1170654074015\">Suppose that three friends are going to the movies. They each need &#36;9.25\u2014that\u2019s 9 dollars and 1 quarter\u2014to pay for their tickets. How much money do they need all together?<\/p>\n<p id=\"fs-id1170654074022\">You can think about the dollars separately from the quarters. They need 3 times &#36;9 so &#36;27, and 3 times 1 quarter, so 75 cents. In total, they need &#36;27.75. If you think about doing the math in this way, you are using the <strong data-effect=\"bold\">distributive property<\/strong>.<\/p>\n<div id=\"fs-id1170654074032\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Distributive Property<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-c6b012bafb7d143b97f63e34938bc03b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#73;&#102;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#97;&#44;&#98;&#44;&#99;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#97;&#114;&#101;&#32;&#114;&#101;&#97;&#108;&#32;&#110;&#117;&#109;&#98;&#101;&#114;&#115;&#44;&#32;&#116;&#104;&#101;&#110;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#97;&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#43;&#99;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#97;&#98;&#43;&#97;&#99;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#65;&#108;&#115;&#111;&#44;&#125;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#43;&#99;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#97;&#61;&#98;&#97;&#43;&#99;&#97;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#97;&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#45;&#99;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#97;&#98;&#45;&#97;&#99;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#45;&#99;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#97;&#61;&#98;&#97;&#45;&#99;&#97;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"129\" width=\"425\" style=\"vertical-align: -60px;\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170654077873\">Back to our friends at the movies, we could find the total amount of money they need like this:<\/p>\n<table style=\"border-collapse: collapse;width: 100%\">\n<tbody>\n<tr>\n<td style=\"width: 100%;text-align: center\">3(9.25)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 100%;text-align: center\">3(9 + 0.25)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 100%;text-align: center\">3(9) + 3(0.25)<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 100%;text-align: center\">27 + 0.75<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 100%;text-align: center\">27.75<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1170654077971\">In algebra, we use the distributive property to remove parentheses as we simplify expressions.<\/p>\n<p id=\"fs-id1170654077977\">For example, if we are asked to simplify the expression <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-932b366673fdab39791e17ba5cd3f025_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"66\" style=\"vertical-align: -5px;\" \/>, the order of operations says to work in the parentheses first. But we cannot add <em data-effect=\"italics\">x<\/em> and 4, since they are not like terms. So we use the distributive property, as shown in <a class=\"autogenerated-content\" href=\"#fs-id1170654078015\">(Example 11)<\/a>.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 11<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654078015\" data-type=\"problem\">\n<p id=\"fs-id1170654078018\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-932b366673fdab39791e17ba5cd3f025_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"66\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654078041\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-922\" style=\"height: 42px\" summary=\".\">\n<tbody>\n<tr style=\"height: 14px\">\n<td style=\"height: 14px;width: 225.406px\"><\/td>\n<td style=\"height: 14px;width: 384.406px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-932b366673fdab39791e17ba5cd3f025_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"66\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"height: 14px;width: 225.406px\">Distribute.<\/td>\n<td style=\"height: 14px;width: 384.406px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-99036dc6bcf367d7ce2f99c5f5b5574c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#120;&#43;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"84\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"height: 14px;width: 225.406px\">Multiply.<\/td>\n<td style=\"height: 14px;width: 384.406px\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-ab47a12d2e1c4502149f1da3ec965401_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#43;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"58\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654078131\" data-type=\"problem\">\n<p id=\"fs-id1170654078133\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-5c5d3d744c86221187fd5a84c602b5af_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"66\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654078156\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Answer<\/summary>\n<p id=\"fs-id1170654078158\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-bdabb6d6f372acd7181da53f42ddd142_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#43;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"50\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 11.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654078181\" data-type=\"problem\">\n<p id=\"fs-id1170654078183\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-8861cab834d2d7823a16ef16fa32962a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"66\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654078206\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Answer<\/summary>\n<p id=\"fs-id1170654078208\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-3d22cb6729f962c9cbf447ab57cf6213_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#120;&#43;&#52;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"58\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170654075701\">Some students find it helpful to draw in arrows to remind them how to use the distributive property. Then the first step in <a class=\"autogenerated-content\" href=\"#fs-id1170654078015\">(Example 11)<\/a> would look like this:<\/p>\n<p><span id=\"fs-id1170654075709\" data-type=\"media\" data-alt=\"We have the expression 3 times (x plus 4) with two arrows coming from the 3. One arrow points to the x, and the other arrow points to the 4.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_09_006_img_new.jpg\" alt=\"We have the expression 3 times (x plus 4) with two arrows coming from the 3. One arrow points to the x, and the other arrow points to the 4.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 12<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654075726\" data-type=\"problem\">\n<p id=\"fs-id1170654075729\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-d2403f8ce3e68908650701a9014b528b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#56;&#125;&#120;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"79\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654075761\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1169750566181\" class=\"unnumbered unstyled\" summary=\"We have a table with directions on the left side and mathematical steps on the right. The first step says \u201cDistribute.\u201d To the right of this, we have the expression 8 times ((3\/8) times x plus 1\/4) with two arrows coming from the 8. One arrow points to the (3\/8) times x, and the other arrow points to the 1\/4. The next line says \u201cMultiply.\u201d To the right of this we have an equals sign and then 8 times ((3\/8) times x) plus 8 times 1\/4. On the following line, we have another equals sign followed by 3x plus 2.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1169750566196\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_09_007a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td><span id=\"eip-id1169750566213\" data-type=\"media\" data-alt=\".\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-f5d728060d8ab540e926923714cb8c6e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#56;&#125;&#32;&#120;&#43;&#56;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"95\" style=\"vertical-align: -6px;\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-319939f6a26dc7d6bcea8f9e1df8d53c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"49\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 12.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654075789\" data-type=\"problem\">\n<p id=\"fs-id1170654075791\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-6454367d242e168378430f97f275bf9f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#54;&#125;&#121;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"78\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654075823\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Answer<\/summary>\n<p id=\"fs-id1170654075825\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-82cd5682dbf1b42a4c83046be442a31c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#121;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"49\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 12.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654075848\" data-type=\"problem\">\n<p id=\"fs-id1170654075850\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-611ac8c75d08d14e1d9cbe36643f74bd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#110;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"88\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654075882\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Answer<\/summary>\n<p id=\"fs-id1170654075884\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-c91961fe00d621859b454474591ee925_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#110;&#43;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"50\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170654075900\">Using the distributive property as shown in <a class=\"autogenerated-content\" href=\"#fs-id1170654075912\">(Example 13)<\/a> will be very useful when we solve money applications in later chapters.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 13<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654075912\" data-type=\"problem\">\n<p id=\"fs-id1170654075915\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-4dc00fc23dfb0bdf499c05bd82f6b453_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#48;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#46;&#51;&#43;&#48;&#46;&#50;&#53;&#113;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"126\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654075940\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1169751856555\" class=\"unnumbered unstyled\" summary=\"We have a table with directions on the left side and mathematical steps on the right. The first step says \u201cDistribute.\u201d To the right of this, we have the expression 100 times (0.3 plus 0.25 times q) with two arrows coming from the 100. One arrow points to the 0.3, and the other arrow points to the 0.25 times q. The next line says \u201cMultiply.\u201d To the right of this we have an equals sign and then 100 times 0.3 plus 100 times the quantity (0.25 times q). On the following line, we have another equals sign followed by 30 plus 25q.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1169751856571\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_09_008a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td><span id=\"eip-id1169751856588\" data-type=\"media\" data-alt=\".\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-7c5c66ecfb5c8ec6a458dffd63423082_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#48;&#40;&#48;&#46;&#51;&#41;&#43;&#49;&#48;&#48;&#40;&#48;&#46;&#50;&#53;&#32;&#113;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"163\" style=\"vertical-align: -5px;\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td><span id=\"eip-id1169751856604\" data-type=\"media\" data-alt=\".\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-8f1f0b7b9c9c9ebb3700fa3797f7cf26_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#48;&#43;&#50;&#53;&#113;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"65\" style=\"vertical-align: -4px;\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 13.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654075969\" data-type=\"problem\">\n<p id=\"fs-id1170654075971\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-0aed77bf8fad9156c33f10ff75312114_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#48;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#46;&#55;&#43;&#48;&#46;&#49;&#53;&#112;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"127\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654075999\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Answer<\/summary>\n<p id=\"fs-id1170654076001\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-c8070d3bb6dc0a377f66793c88cceb5c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#48;&#43;&#49;&#53;&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"66\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 13.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654076023\" data-type=\"problem\">\n<p id=\"fs-id1170654076025\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-97c52d5aaa009f54ed1bcf510f395fde_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#48;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#46;&#48;&#52;&#43;&#48;&#46;&#51;&#53;&#100;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"136\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654076051\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Answer<\/summary>\n<p id=\"fs-id1170654076053\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-ab229ee0dc4f12c4d79b123724e1b88e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#43;&#51;&#53;&#100;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"59\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170654076069\">When we distribute a negative number, we need to be extra careful to get the signs correct!<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 14<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654076078\" data-type=\"problem\">\n<p id=\"fs-id1170654076080\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-b5cce280d64df7f14ab9eb8fd2180e70_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#121;&#43;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"86\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654076105\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1169750823178\" class=\"unnumbered unstyled\" summary=\"We have a table with directions on the left side and mathematical steps on the right. The first step says \u201cDistribute.\u201d To the right of this, we have the expression negative 2 times (4y plus 1) with two arrows coming from the negative 2. One arrow points to the 4y, and the other arrow points to the 1. The next line gives negative 2 times 4y plus negative 2 times 1. On the following line, we have the command \u201cSimplify.\u201d To the right of this, we have negative 8y minus 2.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1169750823194\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_09_009a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-425bfc15f9aba13f5abfd725d1849ff8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#52;&#32;&#121;&#43;&#40;&#45;&#50;&#41;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#40;&#49;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"146\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td><span id=\"eip-id1169750823228\" data-type=\"media\" data-alt=\".\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-aad9e1ff11307a9235b433ae5a4d60d1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;&#121;&#45;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"61\" style=\"vertical-align: -4px;\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 14.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654067335\" data-type=\"problem\">\n<p id=\"fs-id1170654067337\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-1948a0131a1bd3dcc5b94279cb6f6c03_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#109;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"93\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654067363\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Answer<\/summary>\n<p id=\"fs-id1170654067365\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-635df6d996ce4c3db511f641fd4c1465_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#56;&#109;&#45;&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"85\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 14.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654067387\" data-type=\"problem\">\n<p id=\"fs-id1170654067389\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-816032655e7c92ecfa66d74abe2c33c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#110;&#43;&#49;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"97\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654067415\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Answer<\/summary>\n<p id=\"fs-id1170654067417\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-f01536437150ed6d57d516a772936f4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#56;&#110;&#45;&#54;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"81\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1170654067381\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1170654067385\" data-type=\"exercise\">\n<div id=\"fs-id1170654067415\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 15<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654067437\" data-type=\"problem\">\n<p id=\"fs-id1170654067440\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-58cd5efbeb885019c6e916ffd1b3e8e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#49;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#45;&#51;&#97;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"95\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654067465\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1169751973914\" class=\"unnumbered unstyled\" summary=\"We have a table with directions on the left side and mathematical steps on the right. The first step says \u201cDistribute.\u201d To the right of this, we have the expression negative 11 times (4 minus 3a) with two arrows coming from the negative 11. One arrow points to the 4, and the other arrow points to the 3a. On the next line, we have the command \u201cMultiply.\u201d To the right of this, we have negative 11 times 4 minus negative 11 times 3a. Below this, we have negative 44 minus negative 33a. On the following line, we have the command \u201cSimplify.\u201d To the right of this, we have negative 44 plus 33a.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Distribute.<\/td>\n<td><span id=\"eip-id1169751973931\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/math52\/wp-content\/uploads\/sites\/1439\/2021\/06\/CNX_ElemAlg_Figure_01_09_010a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-fd0ae44d5e5a4cdb2b619d5f925223b0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#108;&#105;&#103;&#110;&#101;&#100;&#125;&#32;&#38;&#45;&#49;&#49;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#52;&#32;&#45;&#40;&#45;&#49;&#49;&#41;&#92;&#99;&#100;&#111;&#116;&#32;&#40;&#51;&#97;&#41;&#32;&#92;&#92;&#32;&#38;&#61;&#45;&#52;&#52;&#45;&#40;&#45;&#51;&#51;&#97;&#41;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#108;&#105;&#103;&#110;&#101;&#100;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"46\" width=\"167\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1169754247268\" data-type=\"media\" data-alt=\".\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-25f2f910ad06f77c274e32691fb7b8a6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#52;&#43;&#51;&#51;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"79\" style=\"vertical-align: -2px;\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1170654067485\">Notice that you could also write the result as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-a1fe5ce71a7844f04a7616b5601a7b23_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#51;&#97;&#45;&#52;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"67\" style=\"vertical-align: 0px;\" \/>. Do you know why?<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 15.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654067512\" data-type=\"problem\">\n<p id=\"fs-id1170654067514\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-eef8c18ff00f0ca822478d074c91bdce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#45;&#51;&#97;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"86\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654067540\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Answer<\/summary>\n<p id=\"fs-id1170654067542\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-107d1a411b9ba4ce6717c2c286a8e0d1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#48;&#43;&#49;&#53;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"79\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 15.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654067564\" data-type=\"problem\">\n<p id=\"fs-id1170654067566\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-5b4f750f127afbe959f6aafd36084492_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#55;&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#45;&#49;&#53;&#121;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"95\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654067592\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Answer<\/summary>\n<p id=\"fs-id1170654067594\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-6711a9c853f2a7b05b0a4bf6b5344879_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;&#54;&#43;&#49;&#48;&#53;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"88\" style=\"vertical-align: -4px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170654067610\"><a class=\"autogenerated-content\" href=\"#fs-id1170654067621\">(Example 16)<\/a> will show how to use the distributive property to find the opposite of an expression.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 16<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654067621\" data-type=\"problem\">\n<p id=\"fs-id1170654067623\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-ce41d82abb5aa0bbf987da913b686a13_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"69\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654067647\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-636\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-146b93bc8d87f2d05ead40d760cc54b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"52\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Multiplying by \u22121 results in the opposite.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-0650246b4847554f366519786aed8b3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"77\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-8ca959211e2a8c06eb7ceab2d492a646_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#92;&#99;&#100;&#111;&#116;&#32;&#121;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#99;&#100;&#111;&#116;&#32;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"123\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-10399ddbd82045621d4e5ce362dbb12c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#121;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"80\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-225a4d6d19c816d262b33e2aad9dd39b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#121;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"52\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 16.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654067804\" data-type=\"problem\">\n<p id=\"fs-id1170654067806\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-3dc95a901eb72fcf77bb53b59585fd93_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#122;&#45;&#49;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"77\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654067830\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Answer<\/summary>\n<p id=\"fs-id1170654067832\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-d9b9def7a08b0d8b5f5119c5ddd66264_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#122;&#43;&#49;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"60\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 16.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654067854\" data-type=\"problem\">\n<p id=\"fs-id1170654067856\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-537c2d60a3a4503d5979cc64cf6fe92e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"69\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654067880\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Answer<\/summary>\n<p id=\"fs-id1170654067882\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-4aa0695430936e6b6de725df7e071f02_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#120;&#43;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"54\" style=\"vertical-align: -2px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1170654067848\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1170654067852\" data-type=\"exercise\">\n<div id=\"fs-id1170654067880\" data-type=\"solution\">\n<p id=\"fs-id1170654067882\">There will be times when we\u2019ll need to use the distributive property as part of the order of operations. Start by looking at the parentheses. If the expression inside the parentheses cannot be simplified, the next step would be multiply using the distributive property, which removes the parentheses. The next two examples will illustrate this.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 17<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654067912\" data-type=\"problem\">\n<p id=\"fs-id1170654067914\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-2945442360f067116f20fc44fc9ee38e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#45;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"96\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<p id=\"fs-id1170654067941\">Be sure to follow the order of operations. Multiplication comes before subtraction, so we will distribute the 2 first and then subtract.<\/p>\n<\/div>\n<div id=\"fs-id1170654067946\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-501\" summary=\"\/\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-2945442360f067116f20fc44fc9ee38e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#45;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"96\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-bebe360b3c29085a8aa29b3483513157_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#45;&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#120;&#45;&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"115\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-88c94d582a3ab697d04a845ae2611995_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#45;&#50;&#120;&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"80\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-1609933c9ce26f9a423aa72e8f9d4421_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#120;&#43;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"61\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 17.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654068319\" data-type=\"problem\">\n<p id=\"fs-id1170654068322\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-3fa220bb86c203dec756cf104ff3f8e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#45;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"96\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654068349\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Answer<\/summary>\n<p id=\"fs-id1170654068351\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-3ba539bfd09764633d1807d4b540423c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#45;&#51;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"50\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 17.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654068374\" data-type=\"problem\">\n<p id=\"fs-id1170654068376\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-031134cd983844c9768818eeef3de51b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#120;&#45;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"106\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654068406\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Answer<\/summary>\n<p id=\"fs-id1170654068408\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-b0a235d5cc51bc01e16149d66c001616_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#120;&#45;&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"59\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1170654068367\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1170654068372\" data-type=\"exercise\">\n<div id=\"fs-id1170654068406\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 18<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654068428\" data-type=\"problem\">\n<p id=\"fs-id1170654068430\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-ade3d46631bbb1d12701f4728c84d50f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"142\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654068469\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<table id=\"eip-496\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-ade3d46631bbb1d12701f4728c84d50f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"142\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-ae92d1e97761ceae1f9e0a662a3fad90_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#120;&#45;&#51;&#50;&#45;&#120;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"121\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-e764e7b799d0aadbbce9615bbf7d868f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#120;&#45;&#51;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"58\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1170654068573\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1170654068578\" data-type=\"exercise\">\n<div id=\"fs-id1170654068580\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 18.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654068580\" data-type=\"problem\">\n<p id=\"fs-id1170654068582\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-6b7e822b3e08319e3f50c398ec65115e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#49;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"151\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654068620\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Answer<\/summary>\n<p id=\"fs-id1170654068622\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-5bec6d60dbf638a2bd682ec4ca348a6f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#120;&#45;&#54;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"59\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 18.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654068645\" data-type=\"problem\">\n<p id=\"fs-id1170654068647\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-40c01326cabb49c988aaed9b610c693f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"142\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654068685\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Answer<\/summary>\n<p id=\"fs-id1170654068687\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-b984e361e600b9b677e9b9684b03d32c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#120;&#45;&#49;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"59\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170654068703\">All the properties of real numbers we have used in this chapter are summarized in the table below.<\/p>\n<table style=\"border-collapse: collapse;width: 100%\">\n<tbody>\n<tr>\n<td style=\"width: 33.3333%\" rowspan=\"2\">Commutative Property<\/td>\n<td style=\"width: 33.3333%\"><strong data-effect=\"bold\">of addition<\/strong>\u2003If <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-2ff5ade9b2522831dd13d5e18748fe71_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#44;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"25\" style=\"vertical-align: -4px;\" \/> are real numbers, then<\/td>\n<td style=\"width: 33.3333%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-70a50b09995e1cebbf5fcf5741b9c0c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#43;&#98;&#61;&#98;&#43;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"101\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%\"><strong data-effect=\"bold\">of multiplication<\/strong>\u2003If <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-2ff5ade9b2522831dd13d5e18748fe71_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#44;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"25\" style=\"vertical-align: -4px;\" \/> are real numbers, then<\/td>\n<td style=\"width: 33.3333%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-3927e0da074ebc6f9b287e84805ada79_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#99;&#100;&#111;&#116;&#32;&#98;&#61;&#98;&#92;&#99;&#100;&#111;&#116;&#32;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"83\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%\" rowspan=\"2\">Associative Property<\/td>\n<td style=\"width: 33.3333%\"><strong data-effect=\"bold\">of addition<\/strong>\u2003If <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-00b629395aa8a5452196baac2e77b444_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#44;&#98;&#44;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"41\" style=\"vertical-align: -4px;\" \/> are real numbers, then<\/td>\n<td style=\"width: 33.3333%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-c7764857672de548fb1557617aecbb49_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#43;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#99;&#61;&#97;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#43;&#99;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"186\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%\"><strong data-effect=\"bold\">of multiplication<\/strong>\u2003If <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-00b629395aa8a5452196baac2e77b444_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#44;&#98;&#44;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"41\" style=\"vertical-align: -4px;\" \/> are real numbers, then<\/td>\n<td style=\"width: 33.3333%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-e583597fd4664144b235093f93fb5cce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#92;&#99;&#100;&#111;&#116;&#32;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#99;&#100;&#111;&#116;&#32;&#99;&#61;&#97;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#92;&#99;&#100;&#111;&#116;&#32;&#99;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"150\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%\">Distributive Property<\/td>\n<td style=\"width: 33.3333%\">If <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-00b629395aa8a5452196baac2e77b444_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#44;&#98;&#44;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"41\" style=\"vertical-align: -4px;\" \/> are real numbers, then<\/td>\n<td style=\"width: 33.3333%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-80288954f649b57f2148e44c3bb4fdf8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#43;&#99;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#97;&#98;&#43;&#97;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"142\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%\" rowspan=\"2\">Identity Property<\/td>\n<td style=\"width: 33.3333%\"><strong data-effect=\"bold\">of addition<\/strong>\u2003For any real number <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-b8b48e6a81d81b190b0bbb6714f14b43_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#116;&#101;&#120;&#116;&#123;&#58;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"13\" style=\"vertical-align: 0px;\" \/><br \/>\n0 is the <strong data-effect=\"bold\">additive identity<\/strong><\/td>\n<td style=\"width: 33.3333%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-e7dbfc9091b806a71f8a84407c4c136c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#97;&#43;&#48;&#61;&#97;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#48;&#43;&#97;&#61;&#97;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"73\" style=\"vertical-align: -24px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%\"><strong data-effect=\"bold\">of multiplication<\/strong>\u2003For any real number <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-b8b48e6a81d81b190b0bbb6714f14b43_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#116;&#101;&#120;&#116;&#123;&#58;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"13\" style=\"vertical-align: 0px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-e79f5262533d4afca7593790a1c80b40_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"7\" style=\"vertical-align: 0px;\" \/> is the <strong data-effect=\"bold\">multiplicative identity<\/strong><\/td>\n<td style=\"width: 33.3333%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-f3effd8577c7209f9264ced5e1deb138_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#97;&#92;&#99;&#100;&#111;&#116;&#32;&#49;&#61;&#97;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#49;&#92;&#99;&#100;&#111;&#116;&#32;&#97;&#61;&#97;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"34\" width=\"64\" style=\"vertical-align: -11px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%\" rowspan=\"2\">Inverse Property<\/td>\n<td style=\"width: 33.3333%\"><strong data-effect=\"bold\">of addition<\/strong>\u2003For any real number <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-a8696e12e63d7e1c8d4af5f8c92abb3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/>,<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-ea06e767761795c9461868fc0dcea0a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"22\" style=\"vertical-align: 0px;\" \/> is the <strong data-effect=\"bold\">additive inverse<\/strong> of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-a8696e12e63d7e1c8d4af5f8c92abb3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 33.3333%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-a31750509cd34e3c6c42a26039770c9c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#97;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"101\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%\"><strong data-effect=\"bold\">of multiplication<\/strong>\u2003For any real number <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-df7b2e47dc1a9092d80de94d3067c66b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#44;&#97;&#92;&#110;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"59\" style=\"vertical-align: -4px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-bffaba0ef46c90ca515fa3b0f34c5de6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#97;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"8\" style=\"vertical-align: -6px;\" \/> is the <strong data-effect=\"bold\">multiplicative inverse<\/strong> of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-a8696e12e63d7e1c8d4af5f8c92abb3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/>.<\/td>\n<td style=\"width: 33.3333%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-1c53a020b515677dfb46b9745a411562_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#97;&#125;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"65\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%\">Properties of Zero<\/td>\n<td style=\"width: 33.3333%\">For any real number <em data-effect=\"italics\">a<\/em>,<\/p>\n<p>For any real number <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-df7b2e47dc1a9092d80de94d3067c66b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#44;&#97;&#92;&#110;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"59\" style=\"vertical-align: -4px;\" \/><\/p>\n<p>For any real number <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-df7b2e47dc1a9092d80de94d3067c66b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#44;&#97;&#92;&#110;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"59\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 33.3333%\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-da76a1c26dcc726c1de1a50365ee60bc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#125;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#97;&#92;&#99;&#100;&#111;&#116;&#32;&#48;&#61;&#48;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#48;&#92;&#99;&#100;&#111;&#116;&#32;&#97;&#61;&#48;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"34\" width=\"64\" style=\"vertical-align: -22px;\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-177382779452c5b6fbdc7b6117227799_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#48;&#125;&#123;&#97;&#125;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"42\" style=\"vertical-align: -6px;\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-fa3f3f9bfb1332825b37a0d7552a3932_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"8\" style=\"vertical-align: -6px;\" \/> is undefined<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Key Concepts<\/h1>\n<ul id=\"fs-id1170654053692\" data-bullet-style=\"bullet\">\n<li><strong data-effect=\"bold\">Commutative Property of<\/strong>\n<ul id=\"fs-id1170654053705\" data-bullet-style=\"open-circle\">\n<li><strong data-effect=\"bold\">Addition:<\/strong> If <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-2ff5ade9b2522831dd13d5e18748fe71_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#44;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"25\" style=\"vertical-align: -4px;\" \/> are real numbers, then <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-70a50b09995e1cebbf5fcf5741b9c0c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#43;&#98;&#61;&#98;&#43;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"101\" style=\"vertical-align: -2px;\" \/>.<\/li>\n<li><strong data-effect=\"bold\">Multiplication:<\/strong> If <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-2ff5ade9b2522831dd13d5e18748fe71_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#44;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"25\" style=\"vertical-align: -4px;\" \/> are real numbers, then <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-3927e0da074ebc6f9b287e84805ada79_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#99;&#100;&#111;&#116;&#32;&#98;&#61;&#98;&#92;&#99;&#100;&#111;&#116;&#32;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"83\" style=\"vertical-align: 0px;\" \/>. When adding or multiplying, changing the <em data-effect=\"italics\">order<\/em> gives the same result.<\/li>\n<\/ul>\n<\/li>\n<li><strong data-effect=\"bold\">Associative Property of<\/strong>\n<ul id=\"fs-id1170654053796\" data-bullet-style=\"open-circle\">\n<li><strong data-effect=\"bold\">Addition:<\/strong> If <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-00b629395aa8a5452196baac2e77b444_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#44;&#98;&#44;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"41\" style=\"vertical-align: -4px;\" \/> are real numbers, then <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-c7764857672de548fb1557617aecbb49_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#43;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#99;&#61;&#97;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#43;&#99;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"186\" style=\"vertical-align: -5px;\" \/>.<\/li>\n<li><strong data-effect=\"bold\">Multiplication:<\/strong> If <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-00b629395aa8a5452196baac2e77b444_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#44;&#98;&#44;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"41\" style=\"vertical-align: -4px;\" \/> are real numbers, then <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-e583597fd4664144b235093f93fb5cce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#92;&#99;&#100;&#111;&#116;&#32;&#98;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#99;&#100;&#111;&#116;&#32;&#99;&#61;&#97;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#92;&#99;&#100;&#111;&#116;&#32;&#99;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"150\" style=\"vertical-align: -5px;\" \/>.<br \/>\nWhen adding or multiplying, changing the <em data-effect=\"italics\">grouping<\/em> gives the same result.<\/li>\n<\/ul>\n<\/li>\n<li><strong data-effect=\"bold\">Distributive Property:<\/strong> If <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-00b629395aa8a5452196baac2e77b444_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#44;&#98;&#44;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"41\" style=\"vertical-align: -4px;\" \/> are real numbers, then\n<ul id=\"fs-id1170654071317\" data-bullet-style=\"open-circle\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-80288954f649b57f2148e44c3bb4fdf8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#43;&#99;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#97;&#98;&#43;&#97;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"142\" style=\"vertical-align: -5px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-70d9905aca7a14f0cd3332dff2cd3914_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#43;&#99;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#97;&#61;&#98;&#97;&#43;&#99;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"141\" style=\"vertical-align: -5px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-1e2de211c81accbbd42ebb566fc94bc1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#45;&#99;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#97;&#98;&#45;&#97;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"142\" style=\"vertical-align: -5px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-cbce87c62bc4d275c0dcef542e788c1e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#98;&#45;&#99;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#97;&#61;&#98;&#97;&#45;&#99;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"141\" style=\"vertical-align: -5px;\" \/><\/li>\n<\/ul>\n<\/li>\n<li><strong data-effect=\"bold\">Identity Property<\/strong>\n<ul id=\"fs-id1170654071460\" data-bullet-style=\"open-circle\">\n<li><strong data-effect=\"bold\">of Addition:<\/strong> For any real number <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-3ac6611358e10632a9529c10520ff886_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#116;&#101;&#120;&#116;&#123;&#58;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#97;&#43;&#48;&#61;&#97;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#54;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#48;&#43;&#97;&#61;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"174\" style=\"vertical-align: -2px;\" \/><br \/>\n<strong data-effect=\"bold\">0<\/strong> is the <strong data-effect=\"bold\">additive identity<\/strong><\/li>\n<li><strong data-effect=\"bold\">of Multiplication:<\/strong> For any real number <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-4acfe506d3ed81b9217fa221d61ae8b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#116;&#101;&#120;&#116;&#123;&#58;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#97;&#92;&#99;&#100;&#111;&#116;&#32;&#49;&#61;&#97;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#54;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#49;&#92;&#99;&#100;&#111;&#116;&#32;&#97;&#61;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"156\" style=\"vertical-align: 0px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-e79f5262533d4afca7593790a1c80b40_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"7\" style=\"vertical-align: 0px;\" \/> is the <strong data-effect=\"bold\">multiplicative identity<\/strong><\/li>\n<\/ul>\n<\/li>\n<li><strong data-effect=\"bold\">Inverse Property<\/strong>\n<ul id=\"fs-id1170654071587\" data-bullet-style=\"open-circle\">\n<li><strong data-effect=\"bold\">of Addition:<\/strong> For any real number <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-82c4ae888e292dbd63b1bacd6abbdb22_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#44;&#97;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#97;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"118\" style=\"vertical-align: -5px;\" \/>. A number and its <em data-effect=\"italics\">opposite<\/em> add to zero. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-ea06e767761795c9461868fc0dcea0a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"22\" style=\"vertical-align: 0px;\" \/> is the <strong data-effect=\"bold\">additive inverse<\/strong> of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-a8696e12e63d7e1c8d4af5f8c92abb3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/>.<\/li>\n<li><strong data-effect=\"bold\">of Multiplication:<\/strong> For any real number <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-45c9431b1978dbcceadfdee96dc7ca4d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#44;&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#92;&#110;&#101;&#32;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#97;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#97;&#125;&#61;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"144\" style=\"vertical-align: -6px;\" \/>. A number and its <em data-effect=\"italics\">reciprocal<\/em> multiply to one. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-bffaba0ef46c90ca515fa3b0f34c5de6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#97;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"8\" style=\"vertical-align: -6px;\" \/> is the <strong data-effect=\"bold\">multiplicative inverse<\/strong> of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-a8696e12e63d7e1c8d4af5f8c92abb3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/>.<\/li>\n<\/ul>\n<\/li>\n<li><strong data-effect=\"bold\">Properties of Zero<\/strong>\n<ul id=\"fs-id1170654071732\" data-bullet-style=\"open-circle\">\n<li>For any real number <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-a8696e12e63d7e1c8d4af5f8c92abb3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\" \/>,<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-605123c166c903153775b90ce4d9b3de_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#99;&#100;&#111;&#116;&#32;&#48;&#61;&#48;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#48;&#92;&#99;&#100;&#111;&#116;&#32;&#97;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"136\" style=\"vertical-align: 0px;\" \/> \u2013 The product of any real number and 0 is 0.<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-177382779452c5b6fbdc7b6117227799_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#48;&#125;&#123;&#97;&#125;&#61;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"42\" style=\"vertical-align: -6px;\" \/> for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-b191041a61a6cb0bd7b31c617a9c66af_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#92;&#110;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"42\" style=\"vertical-align: -4px;\" \/> \u2013 Zero divided by any real number except zero is zero.<\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-fa3f3f9bfb1332825b37a0d7552a3932_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"8\" style=\"vertical-align: -6px;\" \/> is undefined \u2013 Division by zero is undefined.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h1>Glossary<\/h1>\n<div class=\"textbox shaded\">\n<dl id=\"fs-id1166426340719\">\n<dt>additive identity<\/dt>\n<dd id=\"fs-id1166426340725\">The additive identity is the number 0; adding 0 to any number does not change its value.<\/dd>\n<\/dl>\n<dl id=\"fs-id1166426272008\">\n<dt>additive inverse<\/dt>\n<dd id=\"fs-id1166426272014\">The opposite of a number is its additive inverse. A number and it additive inverse add to 0.<\/dd>\n<\/dl>\n<dl id=\"fs-id1166426274404\">\n<dt>multiplicative identity<\/dt>\n<dd id=\"fs-id1166426274410\">The multiplicative identity is the number 1; multiplying 1 by any number does not change the value of the number.<\/dd>\n<\/dl>\n<dl id=\"fs-id1166426154985\">\n<dt>multiplicative inverse<\/dt>\n<dd id=\"fs-id1166426154990\">The reciprocal of a number is its multiplicative inverse. A number and its multiplicative inverse multiply to one.<\/dd>\n<\/dl>\n<\/div>\n<h1>Practice Makes Perfect<\/h1>\n<h2>Use the Commutative and Associative Properties<\/h2>\n<p id=\"fs-id1166423746090\">In the following exercises, use the associative property to simplify.<\/p>\n<table style=\"border-collapse: collapse;width: 100%;height: 28px\">\n<tbody>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">1. 3(4<em data-effect=\"italics\">x<\/em>)<\/td>\n<td style=\"width: 50%;height: 14px\">2. 4(7<em data-effect=\"italics\">m<\/em>)<\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">3. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-137c47e33b843575169bba697fb20583_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#43;&#49;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#50;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"101\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">4. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-5525257aa8ad533abdf7938cfa0efd33_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#110;&#43;&#49;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#51;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"102\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div id=\"fs-id1170654071839\" data-type=\"exercise\">\n<div id=\"fs-id1170654071842\" data-type=\"problem\">In the following exercises, simplify.<\/div>\n<\/div>\n<table style=\"border-collapse: collapse;width: 100%;height: 112px\">\n<tbody>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">5. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-475faabbe668d347428ee99c6d88ee31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#56;&#125;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"105\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">6. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-116cf3555b59445ed2a6a0b100d2aab3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#49;&#50;&#125;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"112\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">7. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-8273f2039f50a7dbfdf54bedd89799cf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#50;&#48;&#125;&#92;&#99;&#100;&#111;&#116;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#57;&#125;&#123;&#49;&#49;&#125;&#92;&#99;&#100;&#111;&#116;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#48;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"75\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">8. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-732ddc6d87b4d360e476deb34ed13862_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#51;&#125;&#123;&#49;&#56;&#125;&#92;&#99;&#100;&#111;&#116;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#53;&#125;&#123;&#55;&#125;&#92;&#99;&#100;&#111;&#116;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#56;&#125;&#123;&#49;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"75\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">9. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-dc5d36abcb0e231933ada70c4d0ba79d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#52;&#92;&#99;&#100;&#111;&#116;&#32;&#55;&#32;&#92;&#99;&#100;&#111;&#116;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"74\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">10. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-44e4ce235085a4d32c95da172685b95c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#54;&#92;&#99;&#100;&#111;&#116;&#32;&#49;&#49;&#92;&#99;&#100;&#111;&#116;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"83\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">11. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-454f72de9f54d3a9b03880e0f96f94f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#54;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#56;&#125;&#123;&#49;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#49;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"102\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">12. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-9d10e89e31eda898359b75d1165350e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#49;&#125;&#123;&#49;&#50;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#57;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"95\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">13. 17(0.25)(4)<\/td>\n<td style=\"width: 50%;height: 14px\">14. 36(0.2)(5)<\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">15. [2.48(12)](0.5)<\/td>\n<td style=\"width: 50%;height: 14px\">16. [9.731(4)](0.75)<\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">17. 7(4<em data-effect=\"italics\">a<\/em>)<\/td>\n<td style=\"width: 50%;height: 14px\">18. 9(8<em data-effect=\"italics\">w<\/em>)<\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">19. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-4734c23314ccefaaf6110d182e3ce6d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#109;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"71\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">20. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-54a99a9882d14e168c95e116ecfbfd12_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#110;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"66\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">21. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-f3c08bbe059b836261ec92db2a179ee9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#54;&#125;&#112;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"54\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%\">22. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-9938cb93cd1fb8748a7fb0bb6779cdce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#48;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#53;&#125;&#113;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"54\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">23. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-914f42abe28353b755a87aa66aa058a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#51;&#109;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#50;&#110;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#49;&#54;&#109;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#57;&#110;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"262\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%\">24. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-e41d7470b5e22bf7d6e57a2dcdecba46_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#50;&#112;&#43;&#49;&#55;&#113;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#53;&#112;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#55;&#113;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"238\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">25. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-2972641fa22e15a2375d310aa949ec99_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#56;&#125;&#103;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#50;&#125;&#104;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#56;&#125;&#103;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#49;&#50;&#125;&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"158\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%\">26. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-5530c40d1908592486342d2c65314fd2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#54;&#125;&#97;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#49;&#48;&#125;&#98;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#54;&#125;&#97;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#125;&#123;&#49;&#48;&#125;&#98;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"154\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">27. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-5a7b4fac88cc1d34831e1d54bd3c5597_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#46;&#56;&#112;&#43;&#57;&#46;&#49;&#52;&#113;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#52;&#46;&#51;&#55;&#112;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#48;&#46;&#56;&#56;&#113;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"271\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%\">28. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-1c1f7ea350a232eb7ce19c0f84ec7dea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#46;&#54;&#109;&#43;&#55;&#46;&#50;&#50;&#110;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#46;&#49;&#57;&#109;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#48;&#46;&#54;&#53;&#110;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"290\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div id=\"fs-id1170654071977\" data-type=\"exercise\">\n<h2>Use the Identity and Inverse Properties of Addition and Multiplication<\/h2>\n<\/div>\n<p id=\"fs-id1166414478758\">In the following exercises, find the additive inverse of each number.<\/p>\n<table style=\"border-collapse: collapse;width: 100%\">\n<tbody>\n<tr>\n<td style=\"width: 50%\">29.<br \/>\na) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-197bcf0737c95c4bf57860790b9862f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/><br \/>\nb) 4.3<br \/>\nc) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-892d6c8c7687279f24c71029a53a813e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/><br \/>\nd) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-045de475c5a5e89f5f59070c9d400cfa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#48;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"32\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%\">30.<br \/>\na) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-34449f58abed3e17174f324d59b5ddd8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/><br \/>\nb) 2.1<br \/>\nc) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-a30a1b51f06501cff6c46fb8833b9729_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/><br \/>\nd) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-6b84dfee88625e0aafc23e4d8bfca41b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"25\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">31.<br \/>\na) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-9ea9e9b66a4c069739f4eed4a9c0a94d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"25\" style=\"vertical-align: -6px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-60d5e9237faac2341c216c3e65cd967c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#48;&#46;&#48;&#55;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"53\" style=\"vertical-align: 0px;\" \/><br \/>\nc) 23<br \/>\nd) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-a165915a521abefffbbe8a43a07a17a1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%\">32.<br \/>\na) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-c238785503f21e9131a5d2e75c582ddc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#56;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"25\" style=\"vertical-align: -6px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-7d3ac71d964f16ec717536ed1b297fa9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#48;&#46;&#48;&#49;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"54\" style=\"vertical-align: 0px;\" \/><br \/>\nc) 52<br \/>\nd) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-36c9e509863bea72f9d282c13c99387b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div id=\"fs-id1170653990564\" data-type=\"exercise\">\n<div id=\"fs-id1170653990566\" data-type=\"problem\">In the following exercises, find the multiplicative inverse of each number.<\/div>\n<\/div>\n<table style=\"border-collapse: collapse;width: 100%\">\n<tbody>\n<tr>\n<td style=\"width: 50%\">33. a) 6 b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-08eeadad6c733226f4887e051604ca66_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"25\" style=\"vertical-align: -6px;\" \/> c) 0.7<\/td>\n<td style=\"width: 50%\">34. a) 12 b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-d7dd6818b1355369f96984d1ad595d05_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"25\" style=\"vertical-align: -6px;\" \/> c) 0.13<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">35. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-06fd5b2083a7746a9abab31a806fce3f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#49;&#125;&#123;&#49;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-e04400304f7ca054945c75c3148f2783_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#46;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"35\" style=\"vertical-align: 0px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-7809e6692ccc09d2db4fb4d5197b4ae9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 50%\">36. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-3a66e7678108ddbbeae9c35e1851f03e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#55;&#125;&#123;&#50;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-cfd377c5e42c5cacd910fe0db2041646_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"35\" style=\"vertical-align: 0px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-a30a1b51f06501cff6c46fb8833b9729_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Use the Properties of Zero<\/h2>\n<p id=\"fs-id1166425983092\">In the following exercises, simplify.<\/p>\n<table style=\"border-collapse: collapse;width: 100%\">\n<tbody>\n<tr>\n<td style=\"width: 50%\">37. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-3f91a2ffe971f912232d96e26702db15_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#48;&#125;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%\">38. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-bf30acbb6b62d919ce4fe745a2ec9086_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">39. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-612816d56b1d58de2da963e3fa2b2e6b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#92;&#100;&#105;&#118;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#49;&#125;&#123;&#49;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"46\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%\">40. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-02e56ba94eef42745321026fc96f31da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#54;&#125;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">41. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-c26405231d17c7fc35dcd162796521dd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#48;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%\">42. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-9dc730dfe4e58f6ceb53b99295b74c87_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#56;&#125;&#123;&#49;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"38\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">43. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-af47002eb232527ecdfabb27bc459ebc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#51;&#46;&#49;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"83\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%\">44. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-8b80d5234eae15db39fbdcaae595ac7d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#48;&#125;&#125;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"29\" width=\"16\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Mixed Practice<\/h2>\n<p id=\"fs-id1166426154959\">In the following exercises, simplify.<\/p>\n<table style=\"border-collapse: collapse;width: 100%;height: 126px\">\n<tbody>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">45. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-77b5e4da38b7be3a9efeeed44623a777_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#57;&#97;&#43;&#52;&#52;&#45;&#49;&#57;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"114\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">46. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-72c468d63409165b31bdda66f062dc37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#55;&#99;&#43;&#49;&#54;&#45;&#50;&#55;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"112\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">47. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-33104f359083135f81e6ba918b13f361_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#46;&#49;&#100;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"65\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">48. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-62c79bf5a5cd171c5eaccdfd2f1a9f3e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#48;&#92;&#108;&#101;&#102;&#116;&#40;&#48;&#46;&#48;&#49;&#112;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"82\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">49. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-d53540d673d3a7ac0edeab72cea5f54b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#48;&#125;&#123;&#117;&#45;&#52;&#46;&#57;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"44\" style=\"vertical-align: -6px;\" \/>, where <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-9aa662e599392c5aca67a756865418b3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#117;&#92;&#110;&#101;&#32;&#52;&#46;&#57;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"66\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">50. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-a8bac90e48ab80679b704f3413371087_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#48;&#125;&#123;&#118;&#45;&#54;&#53;&#46;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"43\" style=\"vertical-align: -6px;\" \/>, where <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-64bbe244a9ce8329d0de9959e0d9e90c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#118;&#92;&#110;&#101;&#32;&#54;&#53;&#46;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"64\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">51. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-7885c1e079666b39477df979ad2f9e5b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#92;&#100;&#105;&#118;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"91\" style=\"vertical-align: -7px;\" \/>, where <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-e2834aee8973754feabf49b14875faea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#92;&#110;&#101;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"43\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">52. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-5af21ce834437043830538620d0cf979_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#92;&#100;&#105;&#118;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#45;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#54;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"90\" style=\"vertical-align: -7px;\" \/>, where <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-e223e076641667b05906e75cb53c0dba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#92;&#110;&#101;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"43\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">53. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-c6c85a57bc56b6a47897acac78e196fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#50;&#45;&#53;&#97;&#125;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"39\" style=\"vertical-align: -6px;\" \/>, where <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-c3320dc25fc162f9495ccffc4ae8c7f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#50;&#45;&#53;&#97;&#92;&#110;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"90\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">54. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-9281b72ff161ad3ba05e2c50f9b72624_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#56;&#45;&#57;&#98;&#125;&#123;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"38\" style=\"vertical-align: -6px;\" \/>, where <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-11f8608769ca720e3a4ad0cb1d8d91b8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#56;&#45;&#57;&#98;&#92;&#110;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"89\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">55. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-6b1b8eb43ab0ad66ff37da106a037ecb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#125;&#123;&#49;&#48;&#125;&#109;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#100;&#105;&#118;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"111\" style=\"vertical-align: -7px;\" \/> where <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-7518a4d92b11afe8283af7e9b1427603_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#125;&#123;&#49;&#48;&#125;&#109;&#92;&#110;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"96\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">56. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-a5ab69caf3476734143032575b7aea8c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#49;&#54;&#125;&#110;&#45;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#55;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#100;&#105;&#118;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"109\" style=\"vertical-align: -7px;\" \/> where <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-800baf1de517f9a13490727dc143cc22_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#49;&#54;&#125;&#110;&#45;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#55;&#125;&#92;&#110;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"95\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">57. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-7b36324b1b0b9bb1515175b66f640217_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;&#92;&#99;&#100;&#111;&#116;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#53;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#100;&#43;&#49;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"114\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">58. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-4f449d378d09aad64b4bc4d6675cde7d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;&#92;&#99;&#100;&#111;&#116;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#54;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#53;&#104;&#43;&#50;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"124\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Simplify Expressions Using the Distributive Property<\/h2>\n<p id=\"fs-id1166423978166\">In the following exercises, simplify using the distributive property.<\/p>\n<table style=\"border-collapse: collapse;width: 100%;height: 266px\">\n<tbody>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">59. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-792922539a85ea25ce54641481195087_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#121;&#43;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"74\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">60. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-c90c884fc7c650be23f0ee1b92952198_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#119;&#43;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"77\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">61. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-55ee715334a90c613b464c9bd61d030b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#92;&#108;&#101;&#102;&#116;&#40;&#99;&#45;&#49;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"72\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">62. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-73d86b155724de5eb835995854b99d86_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#45;&#49;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"74\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">63. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-cdc36a93c23262577d2bb54672dbc563_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#113;&#43;&#49;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"82\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">64. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-c730ae630eafd9488c2db1a290189611_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#53;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#109;&#43;&#50;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"89\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">65. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-b942bef6a7b40a6835e2480c305d6159_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#57;&#125;&#121;&#45;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"82\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">66. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-f0942f33eedd4ea857f6cbf4e622bf22_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#49;&#48;&#125;&#120;&#45;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"98\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">67. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-6a41d94951895b0ffbca3896164acfad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#114;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"85\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">68. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-6e6436925e87637f137cbcda0055dd31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#54;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#115;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"85\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">69. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-75541469ad3310674b32aab34a107820_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;&#92;&#108;&#101;&#102;&#116;&#40;&#115;&#45;&#49;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"72\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">70. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-ce3ace732a321d348caeb525d98f75f4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#117;&#92;&#108;&#101;&#102;&#116;&#40;&#118;&#45;&#49;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"75\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">71. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-2663508d908c3b0df9201ca8b9847f0c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"65\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">72. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-7fc6b54ceab6ceddfa0855c5115d4dba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#43;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"66\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">73. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-de0ff307d888387aa27a60ddf3baafc5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#55;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#112;&#43;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"86\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">74. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-845c4c3c25672a1eeefa57eeb802b346_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#57;&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#97;&#43;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"86\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">75. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-207269e50d6b71d32cd8ddc709eb62e4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"78\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">76. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-594dcaf272867207fef6e23128a287dc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#113;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"77\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">77. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-f42e91502eab4a7519680b0b9591372c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#120;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"78\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">78. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-41f9e9c64f9d44778f980a898f7a5cb6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#112;&#45;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"77\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">79. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-6ca6520ad79665cc7a0d558f77bde88b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#54;&#45;&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#43;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"103\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">80. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-ce829d9e399af55986dcec549540f33a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;&#45;&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#43;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"104\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">81. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-30d1a98bbb4b9d32c3c1246423f25074_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#45;&#49;&#49;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#99;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"111\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">82. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-9052000a7a85167f6447a0eb4c6fd687_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#45;&#54;&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#110;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"105\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">83. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-5a4a00658cf63b6e3a4e4df0f99b9b10_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#50;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#97;&#43;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"92\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">84. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-6e953d580e32eef4da6fc4c017cf1bd6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#114;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"83\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">85. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-9c6441b369309960a2d97fc5a80d5b9b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#109;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#109;&#43;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"149\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">86. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-48e7b41a1337bbb71128955febd5328e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#121;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#121;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"136\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">87. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-a3e0f82ab2ed8df30ec79e627a66e332_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#110;&#43;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#49;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#110;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"172\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">88. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-7ff3732a1380f3fdd76f2c753225be26_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#92;&#108;&#101;&#102;&#116;&#40;&#53;&#117;&#43;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#117;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"162\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">89. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-53952b64ea5037f7a1db918a284b216a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#120;&#45;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"133\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">90. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-7e1ff4f454a48b6dcf44c5fc5d7c1999_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#120;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"133\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">91. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-bf929511b9bb416233f352b101044622_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#99;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#56;&#92;&#108;&#101;&#102;&#116;&#40;&#99;&#45;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"156\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">92. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-9e5096e5327e92c325f6fa817a7e2b0e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#49;&#92;&#108;&#101;&#102;&#116;&#40;&#110;&#45;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#53;&#92;&#108;&#101;&#102;&#116;&#40;&#110;&#45;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"162\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px\">\n<td style=\"width: 50%;height: 14px\">93. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-2a49e53ab654b17c841b2afe4a87bc4c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#92;&#108;&#101;&#102;&#116;&#40;&#55;&#121;&#43;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#48;&#121;&#45;&#49;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"176\" style=\"vertical-align: -5px;\" \/><\/td>\n<td style=\"width: 50%;height: 14px\">94. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-dd1f444c3896092ca8544806e4443f78_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#110;&#43;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#110;&#45;&#49;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"169\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Everyday Math<\/h2>\n<table style=\"border-collapse: collapse;width: 100%\">\n<tbody>\n<tr>\n<td style=\"width: 50%\">\n<p id=\"fs-id1170654084031\">95. <strong data-effect=\"bold\">Insurance copayment<\/strong> Carrie had to have 5 fillings done. Each filling cost &#36;80. Her dental insurance required her to pay 20% of the cost as a copay. Calculate Carrie\u2019s copay:<\/p>\n<p>a) First, by multiplying 0.20 by 80 to find her copay for each filling and then multiplying your answer by 5 to find her total copay for 5 fillings.<\/p>\n<p>b) Next, by multiplying [5(0.20)](80)<\/p>\n<p>c) Which of the properties of real numbers says that your answers to parts (a), where you multiplied 5[(0.20)(80)] and (b), where you multiplied [5(0.20)](80), should be equal?<\/td>\n<td style=\"width: 50%\">\n<p id=\"fs-id1170654084068\">96. <strong data-effect=\"bold\">Cooking time<\/strong> Matt bought a 24-pound turkey for his family\u2019s Thanksgiving dinner and wants to know what time to put the turkey in to the oven. He wants to allow 20 minutes per pound cooking time. Calculate the length of time needed to roast the turkey:<\/p>\n<p>a) First, by multiplying <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-27c5a53d40f5c4be8bd37ed386029b6c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#52;&#92;&#99;&#100;&#111;&#116;&#32;&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"49\" style=\"vertical-align: 0px;\" \/> to find the total number of minutes and then multiplying the answer by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-09f550fed6180a47e712ad802c0cb246_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#54;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/> to convert minutes into hours.<\/p>\n<p>b) Next, by multiplying <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-c2778a71242e69fce867df080a01cb40_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#48;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#54;&#48;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"83\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<p>c) Which of the properties of real numbers says that your answers to parts (a), where you multiplied <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-bfa34af9c005c05ff4f161b0aa604b7c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#52;&#92;&#99;&#100;&#111;&#116;&#32;&#50;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#54;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"80\" style=\"vertical-align: -6px;\" \/>, and (b), where you multiplied <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-c2778a71242e69fce867df080a01cb40_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#48;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#54;&#48;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"83\" style=\"vertical-align: -7px;\" \/>, should be equal?<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">\n<p id=\"fs-id1170654084193\">97.<strong data-effect=\"bold\"> Buying by the case.<\/strong> Trader Joe\u2019s grocery stores sold a can of Coke Zero for &#36;1.99. They sold a case of 12 cans for &#36;23.88. To find the cost of 12 cans at &#36;1.99, notice that 1.99 is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-6a268ebd28ca49085de2a9df03f5e70d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#45;&#48;&#46;&#48;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"62\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<p>a) Multiply 12(1.99) by using the distributive property to multiply <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-c5c4d75143d939c12869e6536dcbbb3d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#45;&#48;&#46;&#48;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"95\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<p>b) Was it a bargain to buy Coke Zero by the case?<\/td>\n<td style=\"width: 50%\">\n<p id=\"fs-id1170654084256\">98.<strong data-effect=\"bold\"> Multi-pack purchase.<\/strong> Adele\u2019s shampoo sells for &#36;3.99 per bottle at the grocery store. At the warehouse store, the same shampoo is sold as a 3 pack for &#36;10.49. To find the cost of 3 bottles at &#36;3.99, notice that 3.99 is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-198b43da2ae60a47884533246fcba8d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#45;&#48;&#46;&#48;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"62\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<p>a) Multiply 3(3.99) by using the distributive property to multiply <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-833da28441e74ef19bfb1d5b0aba61e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#45;&#48;&#46;&#48;&#49;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"87\" style=\"vertical-align: -5px;\" \/>.<\/p>\n<p>b) How much would Adele save by buying 3 bottles at the warehouse store instead of at the grocery store?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div id=\"fs-id1170654084027\" data-type=\"exercise\">\n<h2 id=\"fs-id1170654084029\" data-type=\"problem\">Writing Exercises<\/h2>\n<\/div>\n<table style=\"border-collapse: collapse;width: 100%\">\n<tbody>\n<tr>\n<td style=\"width: 50%\">99. In your own words, state the commutative property of addition.<\/td>\n<td style=\"width: 50%\">100. What is the difference between the additive inverse and the multiplicative inverse of a number?<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%\">101. Simplify <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-f0ff252571e6accb80e3a797d1b63f9f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#92;&#108;&#101;&#102;&#116;&#40;&#120;&#45;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"72\" style=\"vertical-align: -7px;\" \/> using the distributive property and explain each step.<\/td>\n<td style=\"width: 50%\">102. Explain how you can multiply 4(&#36;5.97) without paper or calculator by thinking of &#36;5.97 as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-83ace1c0720f86dc9b86d0a350cbf4b7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#45;&#48;&#46;&#48;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"63\" style=\"vertical-align: 0px;\" \/> and then using the distributive property.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Answers<\/h1>\n<div data-type=\"glossary\">\n<table style=\"border-collapse: collapse;width: 100%;height: 288px\">\n<tbody>\n<tr style=\"height: 16px\">\n<td style=\"width: 33.3333%;height: 16px\">1. 12<em data-effect=\"italics\">x<\/em><\/td>\n<td style=\"width: 33.3333%;height: 16px\">3. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-74be3a903b2fa71ff1cc1b04cf6940ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#43;&#52;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"49\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 16px\">5. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-e7d4bdda4a90ca4faeb20c3aa42d1937_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 33.3333%;height: 16px\">7. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-3c69d2cfa64ee32b533ac84672f021f5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#57;&#125;&#123;&#49;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 16px\">9. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-8b7896a9061cc89fcb9f137de010fa35_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#54;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 16px\">11. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-adc6b24a41e0a24f31b6d00af5ae2620_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"17\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 33.3333%;height: 16px\">13. 17<\/td>\n<td style=\"width: 33.3333%;height: 16px\">15. 14.88<\/td>\n<td style=\"width: 33.3333%;height: 16px\">17. 28<em data-effect=\"italics\">a<\/em><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 33.3333%;height: 16px\">19. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-d4abb44219e001224f05ab38f39a1185_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#55;&#53;&#109;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"46\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 16px\">21. 10<em data-effect=\"italics\">p<\/em><\/td>\n<td style=\"width: 33.3333%;height: 16px\">23. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-9e6d38347c83e382edc20f38464d46ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#55;&#109;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#50;&#49;&#110;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"111\" style=\"vertical-align: -5px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 33.3333%;height: 16px\">25. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-db3011fcb26574b1f7717cc7ba130d28_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#52;&#125;&#103;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"60\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 16px\">27. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-3faa324821f78e6a5f71982abb78dbef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#46;&#52;&#51;&#112;&#43;&#56;&#46;&#50;&#54;&#113;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"102\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 16px\">29. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-6fb5c64d8bafb10f8a45892e1b1106a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"25\" style=\"vertical-align: -6px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-2055874a4f314758bfac07753c26a5e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#52;&#46;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"36\" style=\"vertical-align: 0px;\" \/> c) 8 d) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-4980918030597f78d41511c3dc31bba3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#48;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 33.3333%;height: 16px\">31. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-fcba539a463852f739d48d4feb2b7539_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/> b) 0.075 c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-99bc725047a808a5eb54faaf3966d1ce_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"31\" style=\"vertical-align: 0px;\" \/> d) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-2036d82bcfaf518563645d1e42ab535f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"25\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 16px\">33. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-4394c579544fcc941410a186ae9de36f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-6a2c82a650bf12014823d422afc91a18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"25\" style=\"vertical-align: -6px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-a0cea72cab5d52103be19e53887796ed_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#48;&#125;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 16px\">35. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-6c626fdc5b97fa25342f915f04e60502_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#50;&#125;&#123;&#49;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-15fffa18fd875ad76d73cceb06e72c2a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#48;&#125;&#123;&#49;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"32\" style=\"vertical-align: -6px;\" \/> c) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-2036d82bcfaf518563645d1e42ab535f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"25\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 33.3333%;height: 16px\">37. 0<\/td>\n<td style=\"width: 33.3333%;height: 16px\">39. 0<\/td>\n<td style=\"width: 33.3333%;height: 16px\">41. 0<\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 33.3333%;height: 16px\">43. 0<\/td>\n<td style=\"width: 33.3333%;height: 16px\">45. 44<\/td>\n<td style=\"width: 33.3333%;height: 16px\">47. d<\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 33.3333%;height: 16px\">49. 0<\/td>\n<td style=\"width: 33.3333%;height: 16px\">51. 0<\/td>\n<td style=\"width: 33.3333%;height: 16px\">53. undefined<\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 33.3333%;height: 16px\">55. undefined<\/td>\n<td style=\"width: 33.3333%;height: 16px\">57. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-3830a78bb0e2c49fe059940bbbb4edf2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#54;&#100;&#43;&#57;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"67\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 16px\">59. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-4efb5dfeb6b20d5b2c978d71fcfb539c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#50;&#121;&#43;&#55;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"66\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 33.3333%;height: 16px\">61. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-b803411bc32aca84727588ad0fcfd6eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#99;&#45;&#55;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"56\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 16px\">63. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-9b5338dcbbcb4620433efaa34358fd93_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#113;&#43;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"48\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 16px\">65. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-7cf05fb27f6b7cec8dd71800a06002ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#121;&#45;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"49\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 33.3333%;height: 16px\">67. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-47cde68575611d97dd0e73022ed71212_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#43;&#56;&#114;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"48\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 16px\">69. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-66165f2265b93836898e7092573b005a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;&#115;&#45;&#49;&#56;&#114;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"64\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 16px\">71. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-3f4dc0894b969877a2ea0f7661ebb304_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#112;&#43;&#52;&#112;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"58\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 33.3333%;height: 16px\">73. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-2c975a66f3a104e7d5699e31a37e0d1a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#50;&#56;&#112;&#45;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"70\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 16px\">75. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-767caf2c9a0ec3c45e1de4e45037565b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#120;&#43;&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"71\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 16px\">77. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-2627dc6107b3e0c0e55ba1cebb7ddcda_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#120;&#43;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"62\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 33.3333%;height: 16px\">79. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-563bc7a37853002e9a542838b90d145b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#121;&#45;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"62\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 16px\">81. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-f4100f7baee5eaade2763c1e1d648d2b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#51;&#51;&#99;&#43;&#50;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"78\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 16px\">83. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-9a17c59c3618826c8adc12696dc80c64_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#97;&#43;&#49;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"62\" style=\"vertical-align: -2px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 33.3333%;height: 16px\">85. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-d5169deb8f7f33dab76acde8ad9dad87_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#109;&#45;&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"64\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 16px\">87. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-822dbaf836502e55d66f81c1aecd1f92_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#50;&#110;&#43;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"59\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 16px\">89. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-829caf1ff9bb2c81b319753bba9538fc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#50;&#120;&#45;&#50;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"67\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 33.3333%;height: 16px\">91. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-0fee071427886a080dce09c575731917_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#99;&#43;&#51;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"56\" style=\"vertical-align: -2px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 16px\">93. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-content\/ql-cache\/quicklatex.com-72a23faeae624c0f1149afdb881e69be_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#121;&#43;&#54;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"66\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 33.3333%;height: 16px\">95. a) &#36;80 b) &#36;80 c) answers will vary<\/td>\n<\/tr>\n<tr style=\"height: 16px\">\n<td style=\"width: 33.3333%;height: 16px\">97. a) &#36;23.88 b) no, the price is the same<\/td>\n<td style=\"width: 33.3333%;height: 16px\">99. Answers may vary<\/td>\n<td style=\"width: 33.3333%;height: 16px\">101. Answers may vary<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Attributions<\/h1>\n<p>This chapter has been adapted from \u201cProperties of Real Numbers\u201d in <a href=\"https:\/\/openstax.org\/details\/books\/elementary-algebra\"><em>Elementary Algebra<\/em><\/a> (OpenStax) by Lynn Marecek and MaryAnne Anthony-Smith, which is under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY 4.0 Licence<\/a>. Adapted by Izabela Mazur. See the Copyright page for more information.<\/p>\n<\/div>\n","protected":false},"author":999,"menu_order":5,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[48],"contributor":[],"license":[],"class_list":["post-388","chapter","type-chapter","status-publish","hentry","chapter-type-numberless"],"part":251,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-json\/pressbooks\/v2\/chapters\/388","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-json\/wp\/v2\/users\/999"}],"version-history":[{"count":7,"href":"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-json\/pressbooks\/v2\/chapters\/388\/revisions"}],"predecessor-version":[{"id":4018,"href":"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-json\/pressbooks\/v2\/chapters\/388\/revisions\/4018"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-json\/pressbooks\/v2\/parts\/251"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-json\/pressbooks\/v2\/chapters\/388\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-json\/wp\/v2\/media?parent=388"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-json\/pressbooks\/v2\/chapter-type?post=388"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-json\/wp\/v2\/contributor?post=388"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/basicreview\/wp-json\/wp\/v2\/license?post=388"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}