{"id":13043,"date":"2020-08-21T19:43:30","date_gmt":"2020-08-21T23:43:30","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/chapter\/add-and-subtract-fractions\/"},"modified":"2021-03-04T12:06:08","modified_gmt":"2021-03-04T17:06:08","slug":"add-and-subtract-fractions","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/chapter\/add-and-subtract-fractions\/","title":{"raw":"2.2 Add and Subtract Fractions","rendered":"2.2 Add and Subtract Fractions"},"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>Add or subtract fractions with a common denominator<\/li>\r\n \t<li>Add or subtract fractions with different denominators<\/li>\r\n \t<li>Use the order of operations to simplify complex fractions<\/li>\r\n \t<li>Evaluate variable expressions with fractions<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<h1>Add or Subtract Fractions with a Common Denominator<\/h1>\r\n<p id=\"fs-id1170655354165\">When we multiplied fractions, we just multiplied the numerators and multiplied the denominators right straight across. To add or subtract fractions, they must have a common denominator.<\/p>\r\n\r\n<div id=\"fs-id1170654919725\" 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\">Fraction Addition and Subtraction<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<p id=\"fs-id1170655188656\">If \\(a,b,\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}c\\) are numbers where \\(c\\ne 0\\), then<\/p>\r\n\r\n<div id=\"fs-id1170655166745\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\r\n\r\n\\(\\frac{a}{c}+\\frac{b}{c}=\\frac{a+b}{c}\\phantom{\\rule{1em}{0ex}}\\text{and}\\phantom{\\rule{1em}{0ex}}\\frac{a}{c}-\\phantom{\\rule{0.2em}{0ex}}\\frac{b}{c}=\\frac{a-b}{c}\\)\r\n\r\nTo add or subtract fractions, add or subtract the numerators and place the result over the common denominator.\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"manipulative-math\" data-type=\"note\">\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-id1170655202348\" data-type=\"problem\">\r\n<p id=\"fs-id1170655132751\">Find the sum: \\(\\frac{x}{3}+\\frac{2}{3}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655126354\" 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-899\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>\\(\\frac{x}{3}+\\frac{2}{3}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add the numerators and place the sum over the common denominator.<\/td>\r\n<td>\\(\\frac{x+2}{3}\\)<\/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-id1170655171769\" data-type=\"problem\">\r\n<p id=\"fs-id1170655219838\">Find the sum: \\(\\frac{x}{4}+\\frac{3}{4}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655063055\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1170654965957\">\\(\\frac{x+3}{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\">TRY IT 1.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170655099386\" data-type=\"problem\">\r\n<p id=\"fs-id1170654914020\">Find the sum: \\(\\frac{y}{8}+\\frac{5}{8}\\).<\/p>\r\n\r\n<\/div>\r\n<div data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1170654860838\">\\(\\frac{y+5}{8}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1170655113498\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1170655174670\" data-type=\"exercise\">\r\n<div data-type=\"solution\">\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-id1170655083064\" data-type=\"exercise\">\r\n<div id=\"fs-id1170654878890\" data-type=\"problem\">\r\n<p id=\"fs-id1170655029152\">Find the difference: \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{23}{24}-\\phantom{\\rule{0.2em}{0ex}}\\frac{13}{24}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655120820\" data-type=\"solution\">\r\n<div data-type=\"title\"><\/div>\r\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\r\n<\/div>\r\n<\/div>\r\n<table id=\"eip-803\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>\\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{23}{24}-\\phantom{\\rule{0.2em}{0ex}}\\frac{13}{24}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Subtract the numerators and place the difference over the common denominator.<\/td>\r\n<td>\\(\\frac{-23-13}{24}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>\\(\\frac{-36}{24}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify. Remember, \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{a}{b}=\\frac{-a}{b}\\).<\/td>\r\n<td>\\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{3}{2}\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\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-id1170655107412\" data-type=\"problem\">\r\n<p id=\"fs-id1170654982582\">Find the difference: \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{19}{28}-\\phantom{\\rule{0.2em}{0ex}}\\frac{7}{28}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654984424\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1170654977278\">\\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{26}{28}\\)<\/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-id1170655126513\" data-type=\"problem\">\r\n<p id=\"fs-id1170654943302\">Find the difference: \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{27}{32}-\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{32}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654925186\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1170655000121\">\\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{7}{8}\\)<\/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-id1170655117407\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1170654861951\" data-type=\"exercise\">\r\n<div id=\"fs-id1170654925186\" data-type=\"solution\">\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-id1170654863148\" data-type=\"exercise\">\r\n<div id=\"fs-id1170655171423\" data-type=\"problem\">\r\n<p id=\"fs-id1170655151277\">Simplify: \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{10}{x}-\\phantom{\\rule{0.2em}{0ex}}\\frac{4}{x}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655111995\" 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<\/div>\r\n<\/div>\r\n<table id=\"eip-689\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>\\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{10}{x}-\\phantom{\\rule{0.2em}{0ex}}\\frac{4}{x}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Subtract the numerators and place the difference over the common denominator.<\/td>\r\n<td>\\(\\frac{-14}{x}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rewrite with the sign in front of the fraction.<\/td>\r\n<td>\\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{14}{x}\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\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 3.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div data-type=\"problem\">\r\n\r\nFind the difference: \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{9}{x}-\\phantom{\\rule{0.2em}{0ex}}\\frac{7}{x}\\).\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654983100\" data-type=\"solution\"><details><summary>Show answer<\/summary>\\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{16}{x}\\)\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 3.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div data-type=\"problem\">\r\n\r\nFind the difference: \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{17}{a}-\\phantom{\\rule{0.2em}{0ex}}\\frac{5}{a}\\).\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655006907\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1170655111959\">\\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{22}{a}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\nNow we will do an example that has both addition and subtraction.\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 4<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654958831\" data-type=\"problem\">\r\n<p id=\"fs-id1170655132925\">Simplify: \\(\\frac{3}{8}+\\left(-\\phantom{\\rule{0.2em}{0ex}}\\frac{5}{8}\\right)-\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{8}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655127415\" 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-89\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>Add and subtract fractions\u2014do they have a common denominator? Yes.<\/td>\r\n<td>\\(\\frac{3}{8}+\\left(-\\phantom{\\rule{0.2em}{0ex}}\\frac{5}{8}\\right)-\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{8}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add and subtract the numerators and place the difference over the common denominator.<\/td>\r\n<td>\\(\\frac{3+\\left(-5\\right)-1}{8}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify left to right.<\/td>\r\n<td>\\(\\frac{-2-1}{8}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>\\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{3}{8}\\)<\/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 4.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170655219867\" data-type=\"problem\">\r\n<p id=\"fs-id1170655197202\">Simplify: \\(\\frac{2}{5}+\\left(-\\phantom{\\rule{0.2em}{0ex}}\\frac{4}{9}\\right)-\\phantom{\\rule{0.2em}{0ex}}\\frac{7}{9}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654972445\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1170654981205\">\\(-1\\)<\/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 4.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654986125\" data-type=\"problem\">\r\n<p id=\"fs-id1170655029206\">Simplify: \\(\\frac{5}{9}+\\left(-\\phantom{\\rule{0.2em}{0ex}}\\frac{4}{9}\\right)-\\phantom{\\rule{0.2em}{0ex}}\\frac{7}{9}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654957671\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1170655117362\">\\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{2}{3}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<h1>Add or Subtract Fractions with Different Denominators<\/h1>\r\n<p id=\"fs-id1170655126325\">As we have seen, to add or subtract fractions, their denominators must be the same. The least common denominator (LCD) of two fractions is the smallest number that can be used as a common <span class=\"no-emphasis\" data-type=\"term\">denominator<\/span> of the fractions. The LCD of the two fractions is the least common multiple (LCM) of their denominators.<\/p>\r\n\r\n<div id=\"fs-id1170655194149\" 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\">Least Common Denominator<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nThe least common denominator (LCD) of two fractions is the least common multiple (LCM) of their denominators.\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1170655061300\">After we find the least common denominator of two fractions, we convert the fractions to equivalent fractions with the LCD. Putting these steps together allows us to add and subtract fractions because their denominators will be the same!<\/p>\r\n\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-id1170654983383\" data-type=\"exercise\">\r\n<div id=\"fs-id1170654938746\" data-type=\"problem\">\r\n<p id=\"fs-id1170655112854\">Add: \\(\\frac{7}{12}+\\frac{5}{18}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655216078\" 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<span id=\"fs-id1170655396298\" data-type=\"media\" data-alt=\"In this figure, we have a table with directions on the left, hints or explanations in the middle, and mathematical statements on the right. On the first line, we have \u201cStep 1. Do they have a common denominator? No \u2013 rewrite each fraction with the LCD (least common denominator).\u201d To the right of this, we have the statement \u201cNo. Find the LCD 12, 18.\u201d To the right of this, we have 12 equals 2 times 2 times 3 and 18 equals 2 times 3 times 3. The LCD is hence 2 times 2 times 3 times 3, which equals 36. As another hint, we have \u201cChange into equivalent fractions with the LCD,. Do not simplify the equivalent fractions! If you do, you\u2019ll get back to the original fractions and lose the common denominator!\u201d To the right of this, we have 7\/12 plus 5\/18, which becomes the quantity (7 times 3) over the quantity (12 times 3) plus the quantity (5 times 2) over the quantity (18 times 2), which becomes 21\/36 plus 10\/36.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_001a_new.jpg\" alt=\"In this figure, we have a table with directions on the left, hints or explanations in the middle, and mathematical statements on the right. On the first line, we have \u201cStep 1. Do they have a common denominator? No \u2013 rewrite each fraction with the LCD (least common denominator).\u201d To the right of this, we have the statement \u201cNo. Find the LCD 12, 18.\u201d To the right of this, we have 12 equals 2 times 2 times 3 and 18 equals 2 times 3 times 3. The LCD is hence 2 times 2 times 3 times 3, which equals 36. As another hint, we have \u201cChange into equivalent fractions with the LCD,. Do not simplify the equivalent fractions! If you do, you\u2019ll get back to the original fractions and lose the common denominator!\u201d To the right of this, we have 7\/12 plus 5\/18, which becomes the quantity (7 times 3) over the quantity (12 times 3) plus the quantity (5 times 2) over the quantity (18 times 2), which becomes 21\/36 plus 10\/36.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1170654914425\" data-type=\"media\" data-alt=\"The next step reads \u201cStep 2. Add or subtract the fractions.\u201d The hint reads \u201cAdd.\u201d And we have 31\/36.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_001b_new.jpg\" alt=\"The next step reads \u201cStep 2. Add or subtract the fractions.\u201d The hint reads \u201cAdd.\u201d And we have 31\/36.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1170654931846\" data-type=\"media\" data-alt=\"The final step reads \u201cStep 3. Simplify, if possible.\u201d The explanation reads \u201cBecause 31 is a prime number, it has no factors in common with 36. The answer is simplified.\u201d\"><img src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_001c_new.jpg\" alt=\"The final step reads \u201cStep 3. Simplify, if possible.\u201d The explanation reads \u201cBecause 31 is a prime number, it has no factors in common with 36. The answer is simplified.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span>\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 5.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170655123979\" data-type=\"problem\">\r\n<p id=\"fs-id1170655123981\">Add: \\(\\frac{7}{12}+\\frac{11}{15}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655223620\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1170655108732\">\\(\\frac{79}{60}\\)<\/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-id1170655194665\" data-type=\"problem\">\r\n<p id=\"fs-id1170655042204\">Add: \\(\\frac{13}{15}+\\frac{17}{20}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655062834\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1170655062836\">\\(\\frac{103}{60}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">HOW TO: Add or Subtract Fractions<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<ol id=\"fs-id1166424871688\" class=\"stepwise\" type=\"1\">\r\n \t<li>Do they have a common denominator?\r\n<ul id=\"fs-id1170655108352\" data-bullet-style=\"open-circle\">\r\n \t<li>Yes\u2014go to step 2.<\/li>\r\n \t<li>No\u2014rewrite each fraction with the LCD (least common denominator). Find the LCD. Change each fraction into an equivalent fraction with the LCD as its denominator.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>Add or subtract the fractions.<\/li>\r\n \t<li>Simplify, if possible.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1170655092253\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1170654903279\" data-type=\"exercise\">\r\n<div id=\"fs-id1170655062834\" data-type=\"solution\">\r\n\r\nWhen finding the equivalent fractions needed to create the common denominators, there is a quick way to find the number we need to multiply both the numerator and denominator. This method works if we found the LCD by factoring into primes.\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1170654940613\">Look at the factors of the LCD and then at each column above those factors. The \u201cmissing\u201d factors of each denominator are the numbers we need.<\/p>\r\n<span id=\"fs-id1170655102403\" data-type=\"media\" data-alt=\"The number 12 is factored into 2 times 2 times 3 with an extra space after the 3, and the number 18 is factored into 2 times 3 times 3 with an extra space between the 2 and the first 3. There are arrows pointing to these extra spaces that are marked \u201cmissing factors.\u201d The LCD is marked as 2 times 2 times 3 times 3, which is equal to 36. The numbers that create the LCD are the factors from 12 and 18, with the common factors counted only once (namely, the first 2 and the first 3).\"><img class=\"aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_002_img_new.jpg\" alt=\"The number 12 is factored into 2 times 2 times 3 with an extra space after the 3, and the number 18 is factored into 2 times 3 times 3 with an extra space between the 2 and the first 3. There are arrows pointing to these extra spaces that are marked \u201cmissing factors.\u201d The LCD is marked as 2 times 2 times 3 times 3, which is equal to 36. The numbers that create the LCD are the factors from 12 and 18, with the common factors counted only once (namely, the first 2 and the first 3).\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n<p id=\"fs-id1170654967245\">In <a class=\"autogenerated-content\" href=\"#fs-id1170654983383\">(Example 5)<\/a>, the LCD, 36, has two factors of 2 and two factors of \\(3\\).<\/p>\r\n<p id=\"fs-id1170655175041\">The numerator 12 has two factors of 2 but only one of 3\u2014so it is \u201cmissing\u201d one 3\u2014we multiply the numerator and denominator by 3<\/p>\r\n<p id=\"fs-id1170655175044\">The numerator 18 is missing one factor of 2\u2014so we multiply the numerator and denominator by 2<\/p>\r\n<p id=\"fs-id1170654972409\">We will apply this method as we subtract the fractions in <a class=\"autogenerated-content\" href=\"#fs-id1170655000686\">(Example 6)<\/a>.<\/p>\r\n\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-id1170655000686\" data-type=\"problem\">\r\n<p id=\"fs-id1170655081926\">Subtract: \\(\\frac{7}{15}-\\phantom{\\rule{0.2em}{0ex}}\\frac{19}{24}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655200456\" 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-id1170655150350\">Do the fractions have a common denominator? No, so we need to find the LCD.<\/p>\r\n\r\n<table id=\"eip-id1169754059819\" class=\"unnumbered unstyled can-break has-images\" summary=\"In the first line of this problem, the expression 7\/15 minus 19\/24 is given. On the following line, we have the direction \u201cFind the LCD.\u201d The number 15 is factored into 3 times 5 with three extra spaces before the 3, and the number 24 is factored into 2 times 2 times 2 times 3 with an extra space after the 3. The LCD is marked as 2 times 2 times 2 times 3 times 5, which is equal to 120. On the following line, we have the direction \u201cMultiply 8 in the first fraction and 5 in the second fraction to get the LCD.\u201d Under this reads, Rewrite as equivalent fractions with the LCD.\u201d We have the quantity (7 times 8) divided by the quantity (15 times 8) minus the fraction with (19 times 5) as the numerator and (24 times 5) as the denominator. The following line tells us to \u201cSimplify each numerator and denominator.\u201d Hence, we have 56\/120 minus 95\/120. The next lines tells us to \u201cSubtract.\u201d Hence, we have negative 39\/120. The next line tells us to \u201cRewrite showing the common factor of 3.\u201d We have negative (13 times 3) divided by the quantity (40 times 3). We are then instructed to \u201cRemove the common factor to simplify.\u201d We obtain negative 13\/40.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td>Find the LCD.\\(\\phantom{\\rule{5em}{0ex}}\\)<span id=\"eip-id1169754362252\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_003a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Notice, 15 is \u201cmissing\u201d three factors of 2 and 24 is \u201cmissing\u201d the 5 from the factors of the LCD. So we multiply 8 in the first fraction and 5 in the second fraction to get the LCD.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rewrite as equivalent fractions with the LCD.<\/td>\r\n<td><span id=\"eip-id1169754058803\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_003b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td><span id=\"eip-id1169754058820\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_003c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Subtract.<\/td>\r\n<td>\\(\\phantom{\\rule{2em}{0ex}}-\\phantom{\\rule{0.2em}{0ex}}\\frac{39}{120}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Check to see if the answer can be simplified.<\/td>\r\n<td>\\(\\phantom{\\rule{2em}{0ex}}-\\phantom{\\rule{0.2em}{0ex}}\\frac{13\\cdot 3}{40\\cdot 3}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Both 39 and 120 have a factor of 3.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>\\(\\phantom{\\rule{2em}{0ex}}-\\phantom{\\rule{0.2em}{0ex}}\\frac{13}{40}\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nDo not simplify the equivalent fractions! If you do, you\u2019ll get back to the original fractions and lose the common denominator!\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 6.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654968270\" data-type=\"problem\">\r\n<p id=\"fs-id1170655175417\">Subtract: \\(\\frac{13}{24}-\\phantom{\\rule{0.2em}{0ex}}\\frac{17}{32}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655164359\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1170655164361\">\\(\\frac{1}{96}\\)<\/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-id1170655098048\" data-type=\"problem\">\r\n<p id=\"fs-id1170655098050\">Subtract: \\(\\frac{21}{32}-\\phantom{\\rule{0.2em}{0ex}}\\frac{9}{28}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655111921\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1170655111923\">\\(\\frac{75}{224}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1170655129917\">In the next example, one of the fractions has a variable in its numerator. Notice that we do the same steps as when both numerators are numbers.<\/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-id1170655201164\" data-type=\"problem\">\r\n<p id=\"fs-id1170655201167\">Add: \\(\\frac{3}{5}+\\frac{x}{8}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655114432\" 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-id1170655120660\">The fractions have different denominators.<\/p>\r\n\r\n<table id=\"eip-id1169752964735\" class=\"unnumbered unstyled can-break\" summary=\"In the first line of this problem, the expression 3\/5 plus x\/8 is given. On the following line, we have the direction \u201cFind the LCD.\u201d The number 5 is factored into 5 with three extra spaces before the 5, and the number 8 is factored into 2 times 2 times 2 with an extra space after the 2. The LCD is marked as 2 times 2 times 2 times 5, which is equal to 40. On the following line, we have the direction \u201cRewrite as equivalent fractions with the LCD.\u201d We have the quantity (3 times 8) divided by the quantity (5 times 8) plus the fraction with (x times 5) as the numerator and (8 times 5) as the denominator. The following line tells us to \u201cSimplify.\u201d Hence, we have 24\/40 plus 5x\/40. The next line tells us to \u201cAdd.\u201d Hence, we have the quantity (24 + 5x) divided by 40.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td><\/td>\r\n<td>\\(\\phantom{\\rule{2em}{0ex}}\\)<span id=\"eip-id1169752980194\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_004a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Find the LCD.\\(\\phantom{\\rule{4em}{0ex}}\\)<span id=\"eip-id1169752827456\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_004b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rewrite as equivalent fractions with the LCD.<\/td>\r\n<td><\/td>\r\n<td>\\(\\phantom{\\rule{2em}{0ex}}\\)<span id=\"eip-id1169753158504\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_004c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td><\/td>\r\n<td>\\(\\phantom{\\rule{2em}{0ex}}\\)<span id=\"eip-id1169753130877\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_004d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add.<\/td>\r\n<td><\/td>\r\n<td>\\(\\phantom{\\rule{2em}{0ex}}\\)<span id=\"eip-id1169753130893\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_004e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n&nbsp;\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 7.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170655226887\" data-type=\"problem\">\r\n<p id=\"fs-id1170654954496\">Add: \\(\\frac{y}{6}+\\frac{7}{9}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655224317\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1170655224319\">\\(\\frac{9y+42}{54}\\)<\/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 7.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170655111439\" data-type=\"problem\">\r\n\r\nAdd: \\(\\frac{x}{6}+\\frac{7}{15}\\).\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654990354\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1170655150393\">\\(\\frac{15x+42}{135}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1170655189510\">We now have all four operations for fractions. The table below summarizes <span class=\"no-emphasis\" data-type=\"term\">fraction operations<\/span>.<\/p>\r\n\r\n<div class=\"textbox shaded\">\r\n<table border=\"0\"><caption>Summary of Fraction Operations<\/caption>\r\n<tbody>\r\n<tr>\r\n<th scope=\"col\">Fraction Operation<\/th>\r\n<th scope=\"col\">Sample Equation<\/th>\r\n<th scope=\"col\">What to Do<\/th>\r\n<\/tr>\r\n<tr>\r\n<td>Fraction multiplication<\/td>\r\n<td>\\(\\frac{a}{b} \\cdot \\frac{c}{d}=\\frac{ac}{bd}\\)<\/td>\r\n<td>Multiply the numerators and multiply the denominators<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Fraction division<\/td>\r\n<td>\\(\\frac{a}{b} \\div \\frac{c}{d}=\\frac{a}{b}\\cdot \\frac{d}{c}\\)<\/td>\r\n<td>Multiply the first fraction by the reciprocal of the second.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Fraction addition<\/td>\r\n<td>\\(\\frac{a}{c}+\\frac{b}{c}=\\frac{a+b}{c}\\)<\/td>\r\n<td>Add the numerators and place the sum over the common denominator.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Fraction subtraction<\/td>\r\n<td>\\(\\frac{a}{c}-\\phantom{\\rule{0.2em}{0ex}}\\frac{b}{c}=\\frac{a-b}{c}\\)<\/td>\r\n<td>Subtract the numerators and place the difference over the common denominator.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nTo multiply or divide fractions, an LCD is NOT needed. To add or subtract fractions, an LCD is needed.\r\n\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-id1170655061519\" data-type=\"exercise\">\r\n<div id=\"fs-id1170655061521\" data-type=\"problem\">\r\n<p id=\"fs-id1170655061523\">Simplify: a) \\(\\frac{5x}{6}-\\phantom{\\rule{0.2em}{0ex}}\\frac{3}{10}\\) b) \\(\\frac{5x}{6}\\cdot\\frac{3}{10}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654944167\" data-type=\"solution\">\r\n<div data-type=\"title\"><strong>\r\nSolution<\/strong><\/div>\r\n<div data-type=\"title\"><\/div>\r\n<p id=\"fs-id1170654936746\">First ask, \u201cWhat is the operation?\u201d Once we identify the operation that will determine whether we need a common denominator. Remember, we need a common denominator to add or subtract, but not to multiply or divide.<\/p>\r\n\r\n<table style=\"border-collapse: collapse; width: 100%; height: 70px;\" border=\"0\">\r\n<tbody>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 50%; height: 14px;\">a) <strong>What is the operation? The operation is subtraction.<\/strong><\/td>\r\n<td style=\"width: 50%; height: 14px;\"><\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 50%; height: 14px;\">Do the fractions have a common denominator? No.<\/td>\r\n<td style=\"width: 50%; height: 14px;\">\\(\\frac{5x}{6}-\\frac{3}{10}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 50%; height: 14px;\">Rewrite each fraction as an equivalent fraction with the LCD.<\/td>\r\n<td style=\"width: 50%; height: 14px;\">\\(\\frac{5x\\cdot5}{6\\cdot5}-\\frac{3\\cdot3}{10\\cdot3}\\)\r\n\r\n\\(\\frac{25x}{30}-\\frac{9}{30}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 50%; height: 14px;\">Subtract the numerators and place the difference over the common denominators.<\/td>\r\n<td style=\"width: 50%; height: 14px;\">\\(\\frac{25x-9}{30}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 50%; height: 14px;\">Simplify, if possible.<\/td>\r\n<td style=\"width: 50%; height: 14px;\">There are no common factors. The fraction is simplified.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\r\n<tbody>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 50%; height: 14px;\">b) <strong>What is the operation? Multiplication.<\/strong><\/td>\r\n<td style=\"width: 50%; height: 14px;\">\\(\\frac{5x}{6}\\cdot\\frac{3}{10}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 50%; height: 14px;\">To multiply fractions, multiply the numerators and multiply the denominators.<\/td>\r\n<td style=\"width: 50%; height: 14px;\">\\(\\frac{5x\\cdot3}{6\\cdot10}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 50%; height: 14px;\">Rewrite, showing common factors. Remove common factors.<\/td>\r\n<td style=\"width: 50%; height: 14px;\">\\(\\frac{\\overline{)5}x \\cdot \\overline{)3}}{2\\cdot\\overline{)3}\\cdot2\\cdot\\overline{)5}}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 50%; height: 14px;\">Simplify.<\/td>\r\n<td style=\"width: 50%; height: 14px;\">\\(\\frac{x}{4}\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<span style=\"orphans: 1; text-align: initial; font-size: 0.9em; word-spacing: normal;\">Notice we needed an LCD to add \\(\\frac{5x}{6}-\\phantom{\\rule{0.2em}{0ex}}\\frac{3}{10}\\), but not to multiply \\(\\frac{5x}{6}\\cdot\\frac{3}{10}\\).<\/span>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1170655104899\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1170655195238\" data-type=\"exercise\">\r\n<div id=\"fs-id1170655199104\" data-type=\"solution\">\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\r\nSimplify. a) \\(\\frac{27a-32}{36}\\) b) \\(\\frac{2a}{3}\\)\r\n<div id=\"fs-id1170655132961\" data-type=\"solution\"><details><summary>Show answer<\/summary>a) \\(\\frac{27a-32}{36}\\) b) \\(\\frac{2a}{3}\\)\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-id1170655165629\" data-type=\"problem\">\r\n<p id=\"fs-id1170655165632\">Simplify: a) \\(\\frac{4k}{5}-\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{6}\\) b) \\(\\frac{4k}{5}\\cdot \\frac{1}{6}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655132961\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1170655132963\">a) \\(\\frac{24k-5}{30}\\) b) \\(\\frac{2k}{15}\\)<\/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 Order of Operations to Simplify Complex Fractions<\/h1>\r\n<p id=\"fs-id1170654969636\">We have seen that a complex fraction is a fraction in which the numerator or denominator contains a fraction. The fraction bar indicates <span class=\"no-emphasis\" data-type=\"term\">division<\/span>. We simplified the complex fraction \\(\\frac{\\frac{3}{4}}{\\frac{5}{8}}\\) by dividing \\(\\frac{3}{4}\\) by \\(\\frac{5}{8}\\).<\/p>\r\n<p id=\"fs-id1170655111615\">Now we\u2019ll look at complex fractions where the numerator or denominator contains an expression that can be simplified. So we first must completely simplify the numerator and denominator separately using the order of operations. Then we divide the numerator by the denominator.<\/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-id1170655189464\" data-type=\"exercise\">\r\n<div id=\"fs-id1170655189466\" data-type=\"problem\">\r\n<p id=\"fs-id1170654962386\">Simplify: \\(\\frac{{\\left(\\frac{1}{2}\\right)}^{2}}{4+{3}^{2}}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654953233\" 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<span id=\"fs-id1170654968903\" data-type=\"media\" data-alt=\"In this figure, we have a table with directions on the left and mathematical statements on the right. On the first line, we have \u201cStep 1. Simplify the numerator. Remember one half squared means one half times one half.\u201d To the right of this, we have the quantity (1\/2) squared all over the quantity (4 plus 3 squared). Then, we have 1\/4 over the quantity (4 plus 3 squared).\"><img src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_010a_new.jpg\" alt=\"In this figure, we have a table with directions on the left and mathematical statements on the right. On the first line, we have \u201cStep 1. Simplify the numerator. Remember one half squared means one half times one half.\u201d To the right of this, we have the quantity (1\/2) squared all over the quantity (4 plus 3 squared). Then, we have 1\/4 over the quantity (4 plus 3 squared).\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1170655096686\" data-type=\"media\" data-alt=\"The next line\u2019s direction reads \u201cStep 2. Simplify the denominator.\u201d To the right of this, we have 1\/4 over the quantity (4 plus 9), under which we have 1\/4 over 13.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_010b_new.jpg\" alt=\"The next line\u2019s direction reads \u201cStep 2. Simplify the denominator.\u201d To the right of this, we have 1\/4 over the quantity (4 plus 9), under which we have 1\/4 over 13.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1170655090064\" data-type=\"media\" data-alt=\"The final step is \u201cStep 3. Divide the numerator by the denominator. Simplify if possible. Remember, thirteen equals thirteen over 1.\u201d To the right we have 1\/4 divided by 13. Then we have 1\/4 times 1\/13, which equals 1\/52.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_010c_new.jpg\" alt=\"The final step is \u201cStep 3. Divide the numerator by the denominator. Simplify if possible. Remember, thirteen equals thirteen over 1.\u201d To the right we have 1\/4 divided by 13. Then we have 1\/4 times 1\/13, which equals 1\/52.\" data-media-type=\"image\/jpeg\" \/><\/span>\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 9.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170655029722\" data-type=\"problem\">\r\n<p id=\"fs-id1170655029724\">Simplify: \\(\\frac{{\\left(\\frac{1}{3}\\right)}^{2}}{{2}^{3}+2}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655178937\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1170655178939\">\\(\\frac{1}{90}\\)<\/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 9.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170654943859\" data-type=\"problem\">\r\n\r\nSimplify: \\(\\frac{1+{4}^{2}}{{\\left(\\frac{1}{4}\\right)}^{2}}\\).\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655354060\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1170655213977\">\\(272\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">HOW TO: Simplify Complex Fractions<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<ol id=\"fs-id1166424845977\" class=\"stepwise\" type=\"1\">\r\n \t<li>Simplify the numerator.<\/li>\r\n \t<li>Simplify the denominator.<\/li>\r\n \t<li>Divide the numerator by the denominator. Simplify if possible.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1170654962204\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1170654962207\" data-type=\"exercise\">\r\n<div id=\"fs-id1170655029722\" 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-id1170654968376\" data-type=\"problem\">\r\n<p id=\"fs-id1170655021220\">Simplify: \\(\\frac{\\frac{1}{2}+\\frac{2}{3}}{\\frac{3}{4}-\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{6}}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655102612\" 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-id1170655102617\">It may help to put parentheses around the numerator and the denominator.<\/p>\r\n\r\n<table id=\"eip-20\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>\\(\\frac{\\left(\\frac{1}{2}+\\frac{2}{3}\\right)}{\\left(\\frac{3}{4}-\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{6}\\right)}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify the numerator (LCD = 6) and simplify the denominator (LCD = 12).<\/td>\r\n<td>\\(\\frac{\\left(\\frac{3}{6}+\\frac{4}{6}\\right)}{\\left(\\frac{9}{12}-\\phantom{\\rule{0.2em}{0ex}}\\frac{2}{12}\\right)}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>\\(\\frac{\\left(\\frac{7}{6}\\right)}{\\left(\\frac{7}{12}\\right)}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide the numerator by the denominator.<\/td>\r\n<td>\\(\\frac{7}{6}\\div \\frac{7}{12}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>\\(\\frac{7}{6}\\cdot\\frac{12}{7}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide out common factors.<\/td>\r\n<td>\\(\\frac{7\\cdot6\\cdot2}{6\\cdot7}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>\\(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 10.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170655213970\" data-type=\"problem\">\r\n<p id=\"fs-id1170655213972\">Simplify: \\(\\frac{\\frac{1}{3}+\\frac{1}{2}}{\\frac{3}{4}-\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{3}}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655166560\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1170655166563\">2<\/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-id1170655027368\" data-type=\"problem\">\r\n<p id=\"fs-id1170655232373\">Simplify: \\(\\frac{\\frac{2}{3}-\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{2}}{\\frac{1}{4}+\\frac{1}{3}}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655224374\" data-type=\"solution\"><details><summary>Show answer<\/summary>\r\n<p id=\"fs-id1170655154600\">\\(\\frac{2}{7}\\)<\/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>Evaluate Variable Expressions with Fractions<\/h1>\r\n<p id=\"fs-id1170654943331\">We have evaluated expressions before, but now we can evaluate expressions with fractions. Remember, to evaluate an expression, we substitute the value of the variable into the expression and then simplify.<\/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-id1170654920102\" data-type=\"problem\">\r\n<p id=\"fs-id1170655151128\">Evaluate \\(x+\\frac{1}{3}\\) when a) \\(x=-\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{3}\\) b) \\(x=-\\phantom{\\rule{0.2em}{0ex}}\\frac{3}{4}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655151791\" 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<ol id=\"fs-id1166425002264\" class=\"circled\" type=\"a\">\r\n \t<li>To evaluate \\(x+\\frac{1}{3}\\) when \\(x=-\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{3}\\), substitute \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{3}\\) for \\(x\\) in the expression.\r\n<table id=\"eip-id1169754119484\" style=\"width: 100%;\" summary=\"In the first line of this problem, the expression x plus 1\/3 is given. On the following line, we have the direction \u201cSubstitute negative 1\/3 for x.\u201d Then our expression reads as negative 1\/3 plus 1\/3. The following line tells us to \u201cSimplify.\u201d Hence, we have 0.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td><span id=\"eip-id1169754119503\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_005b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><span id=\"eip-id1169754119516\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_005a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<td><span id=\"eip-id1169754060494\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_005c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.\\(\\phantom{\\rule{18em}{0ex}}\\)<\/td>\r\n<td data-align=\"center\">0<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n&nbsp;<\/li>\r\n \t<li>To evaluate \\(x+\\frac{1}{3}\\) when \\(x=-\\phantom{\\rule{0.2em}{0ex}}\\frac{3}{4}\\), we substitute \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{3}{4}\\) for <em data-effect=\"italics\">x<\/em> in the expression.\r\n<table id=\"eip-id1169752950666\" style=\"width: 100%;\" summary=\"In the first line of this problem, the expression x plus 1\/3 is given. On the following line, we have the direction \u201cSubstitute negative 3\/4 for x.\u201d Then our expression reads as negative 3\/4 plus 1\/3. The following line instructs us to \u201cRewrite as equivalent fractions with the LCD, 12.\u201d Our expression thus reads as negative (3 times 3) divided by (4 times 3) plus the quantity (1 times 4) divided by (3 times 4). The following line tells us to \u201cSimplify.\u201d Hence, we have negative 9\/12 + 4\/12. The last line tells us to \u201cAdd.\u201d Hence, we have negative 5\/12.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td><span id=\"eip-id1169750875592\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_006b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><span id=\"eip-id1169750875606\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_006a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<td><span id=\"eip-id1169750580487\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_006c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rewrite as equivalent fractions with the LCD, 12.<\/td>\r\n<td><span id=\"eip-id1169750580506\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_006d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td><span id=\"eip-id1169752933600\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_006e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add.<\/td>\r\n<td data-align=\"center\">\\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{5}{12}\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/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 11.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170655029358\" data-type=\"problem\">\r\n<p id=\"fs-id1170655029360\">Evaluate \\(x+\\frac{3}{4}\\) when a) \\(x=-\\phantom{\\rule{0.2em}{0ex}}\\frac{7}{4}\\) b) \\(x=-\\phantom{\\rule{0.2em}{0ex}}\\frac{5}{4}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655081366\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1170655081368\">a) \\(-1\\) b) \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{2}\\)<\/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-id1170654905739\" data-type=\"problem\">\r\n<p id=\"fs-id1170654905741\">Evaluate \\(y+\\frac{1}{2}\\) when a) \\(y=\\frac{2}{3}\\) b) \\(y=-\\phantom{\\rule{0.2em}{0ex}}\\frac{3}{4}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655174530\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1170654953613\">a) \\(\\frac{7}{6}\\) b) \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{12}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-id1170654937339\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1170654937342\" data-type=\"exercise\">\r\n<div id=\"fs-id1170654905739\" data-type=\"problem\">\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-id1170655348076\" data-type=\"problem\">\r\n\r\nEvaluate \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{5}{6}-y\\) when \\(y=-\\phantom{\\rule{0.2em}{0ex}}\\frac{2}{3}\\).\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655029899\" 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-id1169750824026\" class=\"unnumbered unstyled\" summary=\"In the first line of this problem, the expression negative 5\/6 minus y is given. On the following line, we have the direction \u201cSubstitute negative 2\/3 for y.\u201d Then our expression reads as negative 5\/6 minus negative 2\/3. The following line instructs us to \u201cRewrite as equivalent fractions with the LCD, 6.\u201d Our expression thus reads as negative 5\/6 minus negative 4\/6. The following line tells us to \u201cSubtract.\u201d Hence, we have the quantity (negative 5 minus negative 4) divided by 6. The following line instructs us to \u201cSimplify\u201d, which becomes one sixth.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td><span id=\"eip-id1169750785591\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_007b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><span id=\"eip-id1169750785605\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_007a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<td><span id=\"eip-id1169750785615\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_007c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rewrite as equivalent fractions with the LCD, 6.<\/td>\r\n<td><span id=\"eip-id1169750995278\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_007d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Subtract.<\/td>\r\n<td><span id=\"eip-id1169750995294\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_007e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td data-align=\"center\">\\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{6}\\)<\/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 id=\"fs-id1170655174530\" data-type=\"solution\">\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 data-type=\"problem\">\r\n<p id=\"fs-id1170655166336\">Evaluate \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{2}-y\\) when \\(y=-\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{4}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655189969\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1170655189972\">\\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{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\">TRY IT 12.2<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170655112594\" data-type=\"problem\">\r\n<p id=\"fs-id1170655112596\">Evaluate \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{3}{8}-y\\) when \\(x=-\\phantom{\\rule{0.2em}{0ex}}\\frac{5}{2}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654972309\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1170654972312\">\\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{17}{8}\\)<\/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-id1170655232453\" class=\"try\" data-type=\"note\">\r\n<div id=\"fs-id1170655112591\" data-type=\"exercise\">\r\n<div id=\"fs-id1170654972309\" data-type=\"solution\">\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-id1170655120764\" data-type=\"problem\">\r\n<p id=\"fs-id1170655108542\">Evaluate \\(2{x}^{2}y\\) when \\(x=\\frac{1}{4}\\) and \\(y=-\\phantom{\\rule{0.2em}{0ex}}\\frac{2}{3}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654969427\" 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-id1170655193059\">Substitute the values into the expression.<\/p>\r\n\r\n<table id=\"eip-id1169751865150\" class=\"unnumbered unstyled\" summary=\"In the first line of this problem, the expression 2 times (x squared) times y is given. On the following line, we have the direction \u201cSubstitute 1\/4 for x and negative 2\/3 for y.\u201d Then our expression reads as 2 times (the quantity (1\/4) squared) times (negative 2\/3). The following line instructs us to \u201cSimplify exponents first.\u201d Our expression thus reads as 2 times (1\/16) times (negative 2\/3). The following line tells us to \u201cMultiply. Divide out the common factors.\u201d The common factors are crossed out. The following line instructs us to \u201cSimplify.\u201d We further simplify on the last line to obtain negative one twelfth.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td data-align=\"center\">\\(2{x}^{2}y\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><span id=\"eip-id1169754068123\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_008a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<td data-align=\"center\"><span id=\"eip-id1169754138748\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_008b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify exponents first.<\/td>\r\n<td data-align=\"center\">\\(2\\left(\\frac{1}{16}\\right)\\left(-\\phantom{\\rule{0.2em}{0ex}}\\frac{2}{3}\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply. Divide out the common factors. Notice we write 16 as \\(2\\cdot 2\\cdot 4\\) to make it easy to remove common factors.<\/td>\r\n<td data-align=\"center\">\\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{\\overline{)2}\\cdot 1\\cdot \\overline{)2}}{\\overline{)2}\\cdot \\overline{)2}\\cdot 4\\cdot 3}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td data-align=\"center\">\\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{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 13.1<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<div id=\"fs-id1170655202092\" data-type=\"problem\">\r\n<p id=\"fs-id1170655202094\">Evaluate \\(3a{b}^{2}\\) when \\(a=-\\phantom{\\rule{0.2em}{0ex}}\\frac{2}{3}\\) and \\(b=-\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{2}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655189288\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1170655189290\">\\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{2}\\)<\/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-id1170655205665\" data-type=\"problem\">\r\n<p id=\"fs-id1170655090914\">Evaluate \\(4{c}^{3}d\\) when \\(c=-\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{2}\\) and \\(d=-\\phantom{\\rule{0.2em}{0ex}}\\frac{4}{3}\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655170246\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1170654939677\">\\(\\frac{2}{3}\\)<\/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-id1170654904864\">The next example will have only variables, no constants.<\/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-id1170655121184\" data-type=\"problem\">\r\n<p id=\"fs-id1170655121186\">Evaluate \\(\\frac{p+q}{r}\\) when \\(p=-4,q=-2,\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}r=8\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655112870\" 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-id1170655189822\">To evaluate \\(\\frac{p+q}{r}\\) when \\(p=-4,q=-2,\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}r=8\\), we substitute the values into the expression.<\/p>\r\n\r\n<table id=\"eip-id1169753258394\" class=\"unnumbered unstyled\" summary=\"In the first line of this problem, the quantity (p plus q) divided by r is given. On the following line, we have the direction \u201cSubstitute negative 4 for p, negative 2 for q and 8 for r.\u201d Then our expression reads as the quantity negative 4 plus negative 2 divided by 8. The following line instructs us to \u201cAdd in the numerator first.\u201d Our expression thus reads as negative 6\/8. The following line tells us to \u201cSimplify.\u201d Hence, we have the quantity negative three fourths.\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td data-align=\"center\">\\(\\frac{p+q}{r}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><span id=\"eip-id1169750995237\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_009a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<td data-align=\"center\"><span id=\"eip-id1169750995249\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_009b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add in the numerator first.<\/td>\r\n<td data-align=\"center\">\\(\\frac{-6}{8}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td data-align=\"center\">\\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{3}{4}\\)<\/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-id1170655121362\" data-type=\"problem\">\r\n<p id=\"fs-id1170655121364\">Evaluate \\(\\frac{a+b}{c}\\) when \\(a=-8,b=-7,\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}c=6\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170654940661\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1170654977155\">\\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{5}{2}\\)<\/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-id1170654966036\" data-type=\"problem\">\r\n<p id=\"fs-id1170654966038\">Evaluate \\(\\frac{x+y}{z}\\) when \\(x=9,y=-18,\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}z=-6\\).<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-id1170655083076\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\r\n<p id=\"fs-id1170655083078\">\\(\\frac{3}{2}\\)<\/p>\r\n\r\n<\/details><\/div>\r\n<\/div>\r\n<\/div>\r\n<h1>Key Concepts<\/h1>\r\n<ul id=\"fs-id1170655194091\" data-bullet-style=\"bullet\">\r\n \t<li><strong data-effect=\"bold\">Fraction Addition and Subtraction:<\/strong> If \\(a,b,\\phantom{\\rule{0.2em}{0ex}}\\text{and}\\phantom{\\rule{0.2em}{0ex}}c\\) are numbers where \\(c\\ne 0\\), then\r\n\\(\\frac{a}{c}+\\frac{b}{c}=\\frac{a+b}{c}\\) and \\(\\frac{a}{c}-\\phantom{\\rule{0.2em}{0ex}}\\frac{b}{c}=\\frac{a-b}{c}\\).\r\nTo add or subtract fractions, add or subtract the numerators and place the result over the common denominator.<\/li>\r\n \t<li><strong data-effect=\"bold\">Strategy for Adding or Subtracting Fractions<\/strong>\r\n<ol id=\"fs-id1170654966823\" class=\"stepwise\" type=\"1\">\r\n \t<li>Do they have a common denominator?\r\nYes\u2014go to step 2.\r\nNo\u2014Rewrite each fraction with the LCD (Least Common Denominator). Find the LCD. Change each fraction into an equivalent fraction with the LCD as its denominator.<\/li>\r\n \t<li>Add or subtract the fractions.<\/li>\r\n \t<li>Simplify, if possible. To multiply or divide fractions, an LCD IS NOT needed. To add or subtract fractions, an LCD IS needed.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li><strong data-effect=\"bold\">Simplify Complex Fractions<\/strong>\r\n<ol id=\"fs-id1170655260316\" class=\"stepwise\" type=\"1\">\r\n \t<li>Simplify the numerator.<\/li>\r\n \t<li>Simplify the denominator.<\/li>\r\n \t<li>Divide the numerator by the denominator. Simplify if possible.<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ul>\r\n<h1>Glossary<\/h1>\r\n<div class=\"textbox shaded\">\r\n<dl id=\"fs-id1166424922293\">\r\n \t<dt>least common denominator<\/dt>\r\n \t<dd id=\"fs-id1166424922299\">The least common denominator (LCD) of two fractions is the Least common multiple (LCM) of their denominators.<\/dd>\r\n<\/dl>\r\n<\/div>\r\n<h1>Practice Makes Perfect<\/h1>\r\n<h2>Add and Subtract Fractions with a Common Denominator<\/h2>\r\n<p id=\"fs-id1166425099458\">In the following exercises, add.<\/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%;\">1. \\(\\frac{6}{13}+\\frac{5}{13}\\)<\/td>\r\n<td style=\"width: 50%;\">2. \\(\\frac{4}{15}+\\frac{7}{15}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%;\">3. \\(\\frac{x}{4}+\\frac{3}{4}\\)<\/td>\r\n<td style=\"width: 50%;\">4. \\(\\frac{8}{q}+\\frac{6}{q}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%;\">5. \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{3}{16}+\\left(-\\phantom{\\rule{0.2em}{0ex}}\\frac{7}{16}\\right)\\)<\/td>\r\n<td style=\"width: 50%;\">6. \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{5}{16}+\\left(-\\phantom{\\rule{0.2em}{0ex}}\\frac{9}{16}\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%;\">7. \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{8}{17}+\\frac{15}{17}\\)<\/td>\r\n<td style=\"width: 50%;\">8. \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{9}{19}+\\frac{17}{19}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%;\">9. \\(\\frac{6}{13}+\\left(-\\phantom{\\rule{0.2em}{0ex}}\\frac{10}{13}\\right)+\\left(-\\phantom{\\rule{0.2em}{0ex}}\\frac{12}{13}\\right)\\)<\/td>\r\n<td style=\"width: 50%;\">10. \\(\\frac{5}{12}+\\left(-\\phantom{\\rule{0.2em}{0ex}}\\frac{7}{12}\\right)+\\left(-\\phantom{\\rule{0.2em}{0ex}}\\frac{11}{12}\\right)\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div id=\"fs-id1170655121728\" data-type=\"exercise\">\r\n<div id=\"fs-id1170655121730\" data-type=\"problem\">In the following exercises, subtract.<\/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%;\">11. \\(\\frac{11}{15}-\\phantom{\\rule{0.2em}{0ex}}\\frac{7}{15}\\)<\/td>\r\n<td style=\"width: 50%;\">12. \\(\\frac{9}{13}-\\phantom{\\rule{0.2em}{0ex}}\\frac{4}{13}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%;\">13. \\(\\frac{11}{12}-\\phantom{\\rule{0.2em}{0ex}}\\frac{5}{12}\\)<\/td>\r\n<td style=\"width: 50%;\">14. \\(\\frac{7}{12}-\\phantom{\\rule{0.2em}{0ex}}\\frac{5}{12}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%;\">15. \\(\\frac{19}{21}-\\phantom{\\rule{0.2em}{0ex}}\\frac{4}{21}\\)<\/td>\r\n<td style=\"width: 50%;\">16. \\(\\frac{17}{21}-\\phantom{\\rule{0.2em}{0ex}}\\frac{8}{21}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%;\">17. \\(\\frac{5y}{8}-\\phantom{\\rule{0.2em}{0ex}}\\frac{7}{8}\\)<\/td>\r\n<td style=\"width: 50%;\">18. \\(\\frac{11z}{13}-\\phantom{\\rule{0.2em}{0ex}}\\frac{8}{13}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%;\">19. \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{23}{u}-\\phantom{\\rule{0.2em}{0ex}}\\frac{15}{u}\\)<\/td>\r\n<td style=\"width: 50%;\">20. \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{29}{v}-\\phantom{\\rule{0.2em}{0ex}}\\frac{26}{v}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%;\">21. \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{3}{5}-\\left(-\\phantom{\\rule{0.2em}{0ex}}\\frac{4}{5}\\right)\\)<\/td>\r\n<td style=\"width: 50%;\">22. \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{3}{7}-\\left(-\\phantom{\\rule{0.2em}{0ex}}\\frac{5}{7}\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%;\">23. \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{7}{9}-\\left(-\\phantom{\\rule{0.2em}{0ex}}\\frac{5}{9}\\right)\\)<\/td>\r\n<td style=\"width: 50%;\">24. \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{8}{11}-\\left(-\\phantom{\\rule{0.2em}{0ex}}\\frac{5}{11}\\right)\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h2>Mixed Practice<\/h2>\r\n<p id=\"fs-id1166422823760\">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%;\">25. \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{5}{18}\\cdot \\frac{9}{10}\\)<\/td>\r\n<td style=\"width: 50%;\">26. \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{3}{14}\\cdot \\frac{7}{12}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%;\">27. \\(\\frac{n}{5}-\\phantom{\\rule{0.2em}{0ex}}\\frac{4}{5}\\)<\/td>\r\n<td style=\"width: 50%;\">28. \\(\\frac{6}{11}-\\phantom{\\rule{0.2em}{0ex}}\\frac{s}{11}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%;\">29. \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{7}{24}+\\frac{2}{24}\\)<\/td>\r\n<td style=\"width: 50%;\">30. \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{5}{18}+\\frac{1}{18}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%;\">31. \\(\\frac{8}{15}\\div \\frac{12}{5}\\)<\/td>\r\n<td style=\"width: 50%;\">32. \\(\\frac{7}{12}\\div\\frac{9}{28}\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h2>Add or Subtract Fractions with Different Denominators<\/h2>\r\n<p id=\"fs-id1166422823699\">In the following exercises, add or subtract.<\/p>\r\n\r\n<table style=\"border-collapse: collapse; width: 100%; height: 150px;\" border=\"0\">\r\n<tbody>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"width: 50%; height: 15px;\">33. \\(\\frac{1}{2}+\\frac{1}{7}\\)<\/td>\r\n<td style=\"width: 50%; height: 15px;\">34. \\(\\frac{1}{3}+\\frac{1}{8}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"width: 50%; height: 15px;\">35. \\(\\frac{1}{3}-\\left(-\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{9}\\right)\\)<\/td>\r\n<td style=\"width: 50%; height: 15px;\">36. \\(\\frac{1}{4}-\\left(-\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{8}\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"width: 50%; height: 15px;\">37. \\(\\frac{7}{12}+\\frac{5}{8}\\)<\/td>\r\n<td style=\"width: 50%; height: 15px;\">38. \\(\\frac{5}{12}+\\frac{3}{8}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"width: 50%; height: 15px;\">39. \\(\\frac{7}{12}-\\phantom{\\rule{0.2em}{0ex}}\\frac{9}{16}\\)<\/td>\r\n<td style=\"width: 50%; height: 15px;\">40. \\(\\frac{7}{16}-\\phantom{\\rule{0.2em}{0ex}}\\frac{5}{12}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"width: 50%; height: 15px;\">41. \\(\\frac{2}{3}-\\phantom{\\rule{0.2em}{0ex}}\\frac{3}{8}\\)<\/td>\r\n<td style=\"width: 50%; height: 15px;\">42. \\(\\frac{5}{6}-\\phantom{\\rule{0.2em}{0ex}}\\frac{3}{4}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"width: 50%; height: 15px;\">43. \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{11}{30}+\\frac{27}{40}\\)<\/td>\r\n<td style=\"width: 50%; height: 15px;\">44. \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{9}{20}+\\frac{17}{30}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"width: 50%; height: 15px;\">45. \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{13}{30}+\\frac{25}{42}\\)<\/td>\r\n<td style=\"width: 50%; height: 15px;\">46. \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{23}{30}+\\frac{5}{48}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"width: 50%; height: 15px;\">47. \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{39}{56}-\\phantom{\\rule{0.2em}{0ex}}\\frac{22}{35}\\)<\/td>\r\n<td style=\"width: 50%; height: 15px;\">48. \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{33}{49}-\\phantom{\\rule{0.2em}{0ex}}\\frac{18}{35}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"width: 50%; height: 15px;\">49. \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{2}{3}-\\left(-\\phantom{\\rule{0.2em}{0ex}}\\frac{3}{4}\\right)\\)<\/td>\r\n<td style=\"width: 50%; height: 15px;\">50. \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{3}{4}-\\left(-\\phantom{\\rule{0.2em}{0ex}}\\frac{4}{5}\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"width: 50%; height: 15px;\">51. \\(1+\\frac{7}{8}\\)<\/td>\r\n<td style=\"width: 50%; height: 15px;\">52. \\(1-\\phantom{\\rule{0.2em}{0ex}}\\frac{3}{10}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%;\">53. \\(\\frac{x}{3}+\\frac{1}{4}\\)<\/td>\r\n<td style=\"width: 50%;\">54. \\(\\frac{y}{2}+\\frac{2}{3}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%;\">55. \\(\\frac{y}{4}-\\phantom{\\rule{0.2em}{0ex}}\\frac{3}{5}\\)<\/td>\r\n<td style=\"width: 50%;\">56. \\(\\frac{x}{5}-\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{4}\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h2>Mixed Practice<\/h2>\r\n<p id=\"fs-id1166424777198\">In the following exercises, simplify.<\/p>\r\n\r\n<table style=\"border-collapse: collapse; width: 100%; height: 136px;\" border=\"0\">\r\n<tbody>\r\n<tr style=\"height: 31px;\">\r\n<td style=\"width: 50%; height: 31px;\">57. a) \\(\\frac{2}{3}+\\frac{1}{6}\\) b) \\(\\frac{2}{3}\\div \\frac{1}{6}\\)<\/td>\r\n<td style=\"width: 50%; height: 31px;\">58. a) \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{2}{5}-\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{8}\\) b) \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{2}{5}\\cdot \\frac{1}{8}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"width: 50%; height: 15px;\">59. a) \\(\\frac{5n}{6}\\div \\frac{8}{15}\\) b) \\(\\frac{5n}{6}-\\phantom{\\rule{0.2em}{0ex}}\\frac{8}{15}\\)<\/td>\r\n<td style=\"width: 50%; height: 15px;\">60. a) \\(\\frac{3a}{8}\\div \\frac{7}{12}\\) b) \\(\\frac{3a}{8}-\\phantom{\\rule{0.2em}{0ex}}\\frac{7}{12}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"width: 50%; height: 15px;\">61. \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{3}{8}\\div \\left(-\\phantom{\\rule{0.2em}{0ex}}\\frac{3}{10}\\right)\\)<\/td>\r\n<td style=\"width: 50%; height: 15px;\">62. \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{5}{12}\\div \\left(-\\phantom{\\rule{0.2em}{0ex}}\\frac{5}{9}\\right)\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"width: 50%; height: 15px;\">63. \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{3}{8}+\\frac{5}{12}\\)<\/td>\r\n<td style=\"width: 50%; height: 15px;\">64. \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{8}+\\frac{7}{12}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"width: 50%; height: 15px;\">65. \\(\\frac{5}{6}-\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{9}\\)<\/td>\r\n<td style=\"width: 50%; height: 15px;\">66. \\(\\frac{5}{9}-\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{6}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"width: 50%; height: 15px;\">67. \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{7}{15}-\\phantom{\\rule{0.2em}{0ex}}\\frac{y}{4}\\)<\/td>\r\n<td style=\"width: 50%; height: 15px;\">68. \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{3}{8}-\\phantom{\\rule{0.2em}{0ex}}\\frac{x}{11}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"width: 50%; height: 15px;\">69. \\(\\frac{11}{12a}\\cdot \\frac{9a}{16}\\)<\/td>\r\n<td style=\"width: 50%; height: 15px;\">70. \\(\\frac{10y}{13}\\cdot \\frac{8}{15y}\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div id=\"fs-id1170655105139\" data-type=\"exercise\">\r\n<h2>Use the Order of Operations to Simplify Complex Fractions<\/h2>\r\n<\/div>\r\n<p id=\"fs-id1166422535949\">In the following exercises, simplify.<\/p>\r\n\r\n<table style=\"border-collapse: collapse; width: 100%; height: 135px;\" border=\"0\">\r\n<tbody>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"width: 50%; height: 15px;\">71. \\(\\frac{{2}^{3}+{4}^{2}}{{\\left(\\frac{2}{3}\\right)}^{2}}\\)<\/td>\r\n<td style=\"width: 50%; height: 15px;\">72. \\(\\frac{{3}^{3}-{3}^{2}}{{\\left(\\frac{3}{4}\\right)}^{2}}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"width: 50%; height: 15px;\">73. \\(\\frac{{\\left(\\frac{3}{5}\\right)}^{2}}{{\\left(\\frac{3}{7}\\right)}^{2}}\\)<\/td>\r\n<td style=\"width: 50%; height: 15px;\">74. \\(\\frac{{\\left(\\frac{3}{4}\\right)}^{2}}{{\\left(\\frac{5}{8}\\right)}^{2}}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"width: 50%; height: 15px;\">75. \\(\\frac{2}{\\frac{1}{3}+\\frac{1}{5}}\\)<\/td>\r\n<td style=\"width: 50%; height: 15px;\">76. \\(\\frac{5}{\\frac{1}{4}+\\frac{1}{3}}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"width: 50%; height: 15px;\">77. \\(\\frac{\\frac{7}{8}-\\phantom{\\rule{0.2em}{0ex}}\\frac{2}{3}}{\\frac{1}{2}+\\frac{3}{8}}\\)<\/td>\r\n<td style=\"width: 50%; height: 15px;\">78. \\(\\frac{\\frac{3}{4}-\\phantom{\\rule{0.2em}{0ex}}\\frac{3}{5}}{\\frac{1}{4}+\\frac{2}{5}}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"width: 50%; height: 15px;\">79. \\(\\frac{1}{2}+\\frac{2}{3}\\cdot \\frac{5}{12}\\)<\/td>\r\n<td style=\"width: 50%; height: 15px;\">80. \\(\\frac{1}{3}+\\frac{2}{5}\\cdot \\frac{3}{4}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"width: 50%; height: 15px;\">81. \\(1-\\phantom{\\rule{0.2em}{0ex}}\\frac{3}{5}\\div \\frac{1}{10}\\)<\/td>\r\n<td style=\"width: 50%; height: 15px;\">82. \\(1-\\phantom{\\rule{0.2em}{0ex}}\\frac{5}{6}\\div \\frac{1}{12}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"width: 50%; height: 15px;\">83. \\(\\frac{2}{3}+\\frac{1}{6}+\\frac{3}{4}\\)<\/td>\r\n<td style=\"width: 50%; height: 15px;\">84. \\(\\frac{2}{3}+\\frac{1}{4}+\\frac{3}{5}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"width: 50%; height: 15px;\">85. \\(\\frac{3}{8}-\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{6}+\\frac{3}{4}\\)<\/td>\r\n<td style=\"width: 50%; height: 15px;\">86. \\(\\frac{2}{5}+\\frac{5}{8}-\\phantom{\\rule{0.2em}{0ex}}\\frac{3}{4}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"width: 50%; height: 15px;\">87. \\(12\\left(\\frac{9}{20}-\\phantom{\\rule{0.2em}{0ex}}\\frac{4}{15}\\right)\\)<\/td>\r\n<td style=\"width: 50%; height: 15px;\">88. \\(8\\left(\\frac{15}{16}-\\phantom{\\rule{0.2em}{0ex}}\\frac{5}{6}\\right)\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%;\">89. \\(\\frac{\\frac{5}{8}+\\frac{1}{6}}{\\frac{19}{24}}\\)<\/td>\r\n<td style=\"width: 50%;\">90. \\(\\frac{\\frac{1}{6}+\\frac{3}{10}}{\\frac{14}{30}}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%;\">91. \\(\\left(\\frac{5}{9}+\\frac{1}{6}\\right)\\div \\left(\\frac{2}{3}-\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{2}\\right)\\)<\/td>\r\n<td style=\"width: 50%;\">92. \\(\\left(\\frac{3}{4}+\\frac{1}{6}\\right)\\div \\left(\\frac{5}{8}-\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{3}\\right)\\)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div id=\"fs-id1170654962656\" data-type=\"exercise\">\r\n<h2>Evaluate Variable Expressions with Fractions<\/h2>\r\n<\/div>\r\n<p id=\"fs-id1166422832732\">In the following exercises, evaluate.<\/p>\r\n\r\n<table style=\"border-collapse: collapse; width: 100%; height: 219px;\" border=\"0\">\r\n<tbody>\r\n<tr style=\"height: 48px;\">\r\n<td style=\"width: 50%; height: 48px;\">93. \\(x+\\left(-\\phantom{\\rule{0.2em}{0ex}}\\frac{5}{6}\\right)\\) when\r\na) \\(x=\\frac{1}{3}\\)\r\nb) \\(x=-\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{6}\\)<\/td>\r\n<td style=\"width: 50%; height: 48px;\">94. \\(x+\\left(-\\phantom{\\rule{0.2em}{0ex}}\\frac{11}{12}\\right)\\) when\r\na) \\(x=\\frac{11}{12}\\)\r\nb) \\(x=\\frac{3}{4}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 48px;\">\r\n<td style=\"width: 50%; height: 48px;\">95. \\(x-\\phantom{\\rule{0.2em}{0ex}}\\frac{2}{5}\\) when\r\na) \\(x=\\frac{3}{5}\\)\r\nb) \\(x=-\\phantom{\\rule{0.2em}{0ex}}\\frac{3}{5}\\)<\/td>\r\n<td style=\"width: 50%; height: 48px;\">96. \\(x-\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{3}\\) when\r\na) \\(x=\\frac{2}{3}\\)\r\nb) \\(x=-\\phantom{\\rule{0.2em}{0ex}}\\frac{2}{3}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 48px;\">\r\n<td style=\"width: 50%; height: 48px;\">97. \\(\\frac{7}{10}-w\\) when\r\na) \\(w=\\frac{1}{2}\\)\r\nb) \\(w=-\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{2}\\)<\/td>\r\n<td style=\"width: 50%; height: 48px;\">98. \\(\\frac{5}{12}-w\\) when\r\na) \\(w=\\frac{1}{4}\\)\r\nb) \\(w=-\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{4}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"width: 50%; height: 15px;\">99. \\(2{x}^{2}{y}^{3}\\) when \\(x=-\\phantom{\\rule{0.2em}{0ex}}\\frac{2}{3}\\) and \\(y=-\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{2}\\)<\/td>\r\n<td style=\"width: 50%; height: 15px;\">100. \\(8{u}^{2}{v}^{3}\\) when \\(u=-\\phantom{\\rule{0.2em}{0ex}}\\frac{3}{4}\\) and \\(v=-\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{2}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px;\">\r\n<td style=\"width: 50%; height: 15px;\">101. \\(\\frac{a+b}{a-b}\\) when \\(a=-3,b=8\\)<\/td>\r\n<td style=\"width: 50%; height: 15px;\">102. \\(\\frac{r-s}{r+s}\\) when \\(r=10,s=-5\\)<\/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%;\">103. <strong data-effect=\"bold\">Decorating<\/strong> Laronda is making covers for the throw pillows on her sofa. For each pillow cover, she needs \\(\\frac{1}{2}\\) yard of print fabric and \\(\\frac{3}{8}\\) yard of solid fabric. What is the total amount of fabric Laronda needs for each pillow cover?<\/td>\r\n<td style=\"width: 50%;\">104. <strong data-effect=\"bold\">Baking<\/strong> Samuel is baking chocolate chip cookies and oatmeal cookies. He needs \\(\\frac{1}{2}\\) cup of sugar for the chocolate chip cookies and \\(\\frac{1}{4}\\) of sugar for the oatmeal cookies. How much sugar does he need altogether?<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h2>Writing Exercises<\/h2>\r\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 50%;\">105. Why do you need a common denominator to add or subtract fractions? Explain.<\/td>\r\n<td style=\"width: 50%;\">106. How do you find the LCD of 2 fractions?<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h1>Answers:<\/h1>\r\n<table style=\"border-collapse: collapse; width: 100%; height: 255px;\" border=\"0\">\r\n<tbody>\r\n<tr style=\"height: 17px;\">\r\n<td style=\"width: 33.3333%; height: 17px;\">1. \\(\\frac{11}{13}\\)<\/td>\r\n<td style=\"width: 33.3333%; height: 17px;\">3. \\(\\frac{x+3}{4}\\)<\/td>\r\n<td style=\"width: 33.3333%; height: 17px;\">5. \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{5}{8}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 17px;\">\r\n<td style=\"width: 33.3333%; height: 17px;\">7. \\(\\frac{7}{17}\\)<\/td>\r\n<td style=\"width: 33.3333%; height: 17px;\">9. \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{16}{13}\\)<\/td>\r\n<td style=\"width: 33.3333%; height: 17px;\">11. \\(\\frac{4}{15}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 17px;\">\r\n<td style=\"width: 33.3333%; height: 17px;\">13. \\(\\frac{1}{2}\\)<\/td>\r\n<td style=\"width: 33.3333%; height: 17px;\">15. \\(\\frac{5}{7}\\)<\/td>\r\n<td style=\"width: 33.3333%; height: 17px;\">17. \\(\\frac{5y-7}{8}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 17px;\">\r\n<td style=\"width: 33.3333%; height: 17px;\">19. \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{38}{u}\\)<\/td>\r\n<td style=\"width: 33.3333%; height: 17px;\">21. \\(\\frac{1}{5}\\)<\/td>\r\n<td style=\"width: 33.3333%; height: 17px;\">23. \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{2}{9}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 17px;\">\r\n<td style=\"width: 33.3333%; height: 17px;\">25. \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{4}\\)<\/td>\r\n<td style=\"width: 33.3333%; height: 17px;\">27. \\(\\frac{n-4}{5}\\)<\/td>\r\n<td style=\"width: 33.3333%; height: 17px;\">29. \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{5}{24}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 17px;\">\r\n<td style=\"width: 33.3333%; height: 17px;\">31. \\(\\frac{2}{9}\\)<\/td>\r\n<td style=\"width: 33.3333%; height: 17px;\">33. \\(\\frac{9}{14}\\)<\/td>\r\n<td style=\"width: 33.3333%; height: 17px;\">35. \\(\\frac{4}{9}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 17px;\">\r\n<td style=\"width: 33.3333%; height: 17px;\">37. \\(\\frac{29}{24}\\)<\/td>\r\n<td style=\"width: 33.3333%; height: 17px;\">39. \\(\\frac{1}{48}\\)<\/td>\r\n<td style=\"width: 33.3333%; height: 17px;\">41. \\(\\frac{7}{24}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 17px;\">\r\n<td style=\"width: 33.3333%; height: 17px;\">43. \\(\\frac{37}{120}\\)<\/td>\r\n<td style=\"width: 33.3333%; height: 17px;\">45. \\(\\frac{17}{105}\\)<\/td>\r\n<td style=\"width: 33.3333%; height: 17px;\">47. \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{53}{40}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 17px;\">\r\n<td style=\"width: 33.3333%; height: 17px;\">49. \\(\\frac{1}{12}\\)<\/td>\r\n<td style=\"width: 33.3333%; height: 17px;\">51. \\(\\frac{15}{8}\\)<\/td>\r\n<td style=\"width: 33.3333%; height: 17px;\">53. \\(\\frac{4x+3}{12}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 17px;\">\r\n<td style=\"width: 33.3333%; height: 17px;\">55. \\(\\frac{4y-12}{20}\\)<\/td>\r\n<td style=\"width: 33.3333%; height: 17px;\">57. a)\\(\\frac{5}{6}\\)b) 4<\/td>\r\n<td style=\"width: 33.3333%; height: 17px;\">59. a)\\(\\frac{25n}{16}\\)b)\\(\\frac{25n-16}{30}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 17px;\">\r\n<td style=\"width: 33.3333%; height: 17px;\">61. \\(\\frac{5}{4}\\)<\/td>\r\n<td style=\"width: 33.3333%; height: 17px;\">63. \\(\\frac{1}{24}\\)<\/td>\r\n<td style=\"width: 33.3333%; height: 17px;\">65. \\(\\frac{13}{18}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 17px;\">\r\n<td style=\"width: 33.3333%; height: 17px;\">67. \\(\\frac{-28-15y}{60}\\)<\/td>\r\n<td style=\"width: 33.3333%; height: 17px;\">69. \\(\\frac{33}{64}\\)<\/td>\r\n<td style=\"width: 33.3333%; height: 17px;\">71. 54<\/td>\r\n<\/tr>\r\n<tr style=\"height: 17px;\">\r\n<td style=\"width: 33.3333%; height: 17px;\">73. \\(\\frac{49}{25}\\)<\/td>\r\n<td style=\"width: 33.3333%; height: 17px;\">75. \\(\\frac{15}{4}\\)<\/td>\r\n<td style=\"width: 33.3333%; height: 17px;\">77. \\(\\frac{5}{21}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 17px;\">\r\n<td style=\"width: 33.3333%; height: 17px;\">79. \\(\\frac{7}{9}\\)<\/td>\r\n<td style=\"width: 33.3333%; height: 17px;\">81. \\(-5\\)<\/td>\r\n<td style=\"width: 33.3333%; height: 17px;\">83. \\(\\frac{19}{12}\\)<\/td>\r\n<\/tr>\r\n<tr style=\"height: 17px;\">\r\n<td style=\"width: 33.3333%; height: 17px;\">85. \\(\\frac{23}{24}\\)<\/td>\r\n<td style=\"width: 33.3333%; height: 17px;\">87. \\(\\frac{11}{5}\\)<\/td>\r\n<td style=\"width: 33.3333%; height: 17px;\">89. 1<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3333%;\">91. \\(\\frac{13}{3}\\)<\/td>\r\n<td style=\"width: 33.3333%;\">93. a) \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{2}\\) b) \\(-1\\)<\/td>\r\n<td style=\"width: 33.3333%;\">95. a) \\(\\frac{1}{5}\\) b) \\(-1\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3333%;\">97. a) \\(\\frac{1}{5}\\) b) \\(\\frac{6}{5}\\)<\/td>\r\n<td style=\"width: 33.3333%;\">99. \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{1}{9}\\)<\/td>\r\n<td style=\"width: 33.3333%;\">101. \\(-\\phantom{\\rule{0.2em}{0ex}}\\frac{5}{11}\\)<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 33.3333%;\">103. \\(\\frac{7}{8}\\) yard<\/td>\r\n<td style=\"width: 33.3333%;\">105. Answers may vary<\/td>\r\n<td style=\"width: 33.3333%;\"><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h1>Attributions<\/h1>\r\nThis chapter has been adapted from \u201cAdd and Subtract Fractions\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<!-- pb_fixme -->","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>Add or subtract fractions with a common denominator<\/li>\n<li>Add or subtract fractions with different denominators<\/li>\n<li>Use the order of operations to simplify complex fractions<\/li>\n<li>Evaluate variable expressions with fractions<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1>Add or Subtract Fractions with a Common Denominator<\/h1>\n<p id=\"fs-id1170655354165\">When we multiplied fractions, we just multiplied the numerators and multiplied the denominators right straight across. To add or subtract fractions, they must have a common denominator.<\/p>\n<div id=\"fs-id1170654919725\" 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\">Fraction Addition and Subtraction<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1170655188656\">If <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-9267d0977b8d1972f62cc24848f360cf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#44;&#98;&#44;&#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;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"73\" style=\"vertical-align: -4px;\" \/> are numbers where <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-8b5bf141db78347b5c7492b111198fd9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;&#92;&#110;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"40\" style=\"vertical-align: -4px;\" \/>, then<\/p>\n<div id=\"fs-id1170655166745\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-d951d1964ab378bea38dc8fad2829395_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#99;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#98;&#125;&#123;&#99;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#43;&#98;&#125;&#123;&#99;&#125;&#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;&#116;&#101;&#120;&#116;&#123;&#97;&#110;&#100;&#125;&#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;&#97;&#125;&#123;&#99;&#125;&#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;&#98;&#125;&#123;&#99;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#45;&#98;&#125;&#123;&#99;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"249\" style=\"vertical-align: -6px;\" \/><\/p>\n<p>To add or subtract fractions, add or subtract the numerators and place the result over the common denominator.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"manipulative-math\" data-type=\"note\">\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-id1170655202348\" data-type=\"problem\">\n<p id=\"fs-id1170655132751\">Find the sum: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-1e9ac6d47d5e8213bf22dd5c734974cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#120;&#125;&#123;&#51;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"40\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655126354\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-899\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-1e9ac6d47d5e8213bf22dd5c734974cc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#120;&#125;&#123;&#51;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"40\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Add the numerators and place the sum over the common denominator.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-e18bcee1401f8ef03ce214872c4c0e91_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#120;&#43;&#50;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"26\" 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 1.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655171769\" data-type=\"problem\">\n<p id=\"fs-id1170655219838\">Find the sum: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-3621efd76154751f601dc13eb05a11c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#120;&#125;&#123;&#52;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"40\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655063055\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170654965957\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-8e8877de9071556d0e0859d30fee2a1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#120;&#43;&#51;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"26\" 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 1.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655099386\" data-type=\"problem\">\n<p id=\"fs-id1170654914020\">Find the sum: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-3a5785f70d301219cf6dac92cd3ddaf8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#121;&#125;&#123;&#56;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"40\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170654860838\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-5ea1e8027b3575af14e1800d72c68036_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#121;&#43;&#53;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"25\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1170655113498\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1170655174670\" data-type=\"exercise\">\n<div data-type=\"solution\">\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-id1170655083064\" data-type=\"exercise\">\n<div id=\"fs-id1170654878890\" data-type=\"problem\">\n<p id=\"fs-id1170655029152\">Find the difference: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-4f8e3f35ba2b17d85f61b5dd8afaec43_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;&#51;&#125;&#123;&#50;&#52;&#125;&#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;&#51;&#125;&#123;&#50;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"75\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655120820\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<\/div>\n<\/div>\n<table id=\"eip-803\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-4f8e3f35ba2b17d85f61b5dd8afaec43_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;&#51;&#125;&#123;&#50;&#52;&#125;&#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;&#51;&#125;&#123;&#50;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"75\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Subtract the numerators and place the difference over the common denominator.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-ed7463f8ad8e0db24392b1d691f173be_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#45;&#50;&#51;&#45;&#49;&#51;&#125;&#123;&#50;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"50\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-4344d9f623bb527b5c9b960d94d85734_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#45;&#51;&#54;&#125;&#123;&#50;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"25\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify. Remember, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-ca498566175a6f4849f7bb33ac9ec9d4_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;&#97;&#125;&#123;&#98;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#45;&#97;&#125;&#123;&#98;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"72\" style=\"vertical-align: -6px;\" \/>.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-657f8809c69782db10d51fdb7a988819_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;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"25\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\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-id1170655107412\" data-type=\"problem\">\n<p id=\"fs-id1170654982582\">Find the difference: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-37826f2f7b9d28e47cde4f526839bb0f_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;&#57;&#125;&#123;&#50;&#56;&#125;&#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;&#50;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"75\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654984424\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170654977278\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-8b90af50d39b611880c173c3839ffac6_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;&#54;&#125;&#123;&#50;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"32\" 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-id1170655126513\" data-type=\"problem\">\n<p id=\"fs-id1170654943302\">Find the difference: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-6b937c393009f491698f8da7a051916d_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;&#55;&#125;&#123;&#51;&#50;&#125;&#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;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"75\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654925186\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170655000121\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-b136d4040489f2bff3ca8655b26dd117_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;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"25\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1170655117407\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1170654861951\" data-type=\"exercise\">\n<div id=\"fs-id1170654925186\" data-type=\"solution\">\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-id1170654863148\" data-type=\"exercise\">\n<div id=\"fs-id1170655171423\" data-type=\"problem\">\n<p id=\"fs-id1170655151277\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-e036265524ac30fa4687a7daf8edaaff_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;&#120;&#125;&#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;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"69\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655111995\" 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<\/div>\n<\/div>\n<table id=\"eip-689\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-e036265524ac30fa4687a7daf8edaaff_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;&#120;&#125;&#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;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"69\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Subtract the numerators and place the difference over the common denominator.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-d6beb787154cd4a5cbf4a891d1c0053c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#45;&#49;&#52;&#125;&#123;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"25\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Rewrite with the sign in front of the fraction.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-e100ce7329692e98727aa859d0e193ca_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;&#52;&#125;&#123;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"32\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p>Find the difference: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-26fe470400ca6a4cbc6f506670c5d89b_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;&#120;&#125;&#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;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"63\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654983100\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-a0ec465728dca7539fed4b2c7cdeefb8_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;&#54;&#125;&#123;&#120;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"32\" 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 3.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p>Find the difference: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-7122c2929bb065fa815a4b94f55f2307_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;&#55;&#125;&#123;&#97;&#125;&#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;&#97;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"69\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655006907\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170655111959\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-87cd936f77508d59fe60f52d2bdc1463_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;&#50;&#125;&#123;&#97;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"32\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p>Now we will do an example that has both addition and subtraction.<\/p>\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-id1170654958831\" data-type=\"problem\">\n<p id=\"fs-id1170655132925\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-e9f46d8e3038fd4a9da7f9130ad6e9d6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#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;&#53;&#125;&#123;&#56;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#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;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"109\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655127415\" 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-89\" summary=\".\">\n<tbody>\n<tr>\n<td>Add and subtract fractions\u2014do they have a common denominator? Yes.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-e9f46d8e3038fd4a9da7f9130ad6e9d6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#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;&#53;&#125;&#123;&#56;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#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;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"109\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Add and subtract the numerators and place the difference over the common denominator.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-9e57fefc235bd82fba4d2a82c19519c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#45;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#45;&#49;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"64\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify left to right.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-a89e63d0957038cb401621c0626b2197_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#45;&#50;&#45;&#49;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"36\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-24be3f51da559afa3cc8bdfd3689625d_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;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"25\" 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 4.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655219867\" data-type=\"problem\">\n<p id=\"fs-id1170655197202\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-94a71bd3425b5284ad7ddf946c0f5a2d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#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;&#52;&#125;&#123;&#57;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#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=\"23\" width=\"109\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654972445\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170654981205\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-b80ba2734f70ff584d473cda66662853_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"21\" 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 4.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654986125\" data-type=\"problem\">\n<p id=\"fs-id1170655029206\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-f9f42de9d8af71a963b95e9c70ff880a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#57;&#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;&#52;&#125;&#123;&#57;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#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=\"23\" width=\"109\" style=\"vertical-align: -7px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654957671\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170655117362\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-9e8e6a26f83853fffeb09f3a9f9474ae_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;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"25\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<h1>Add or Subtract Fractions with Different Denominators<\/h1>\n<p id=\"fs-id1170655126325\">As we have seen, to add or subtract fractions, their denominators must be the same. The least common denominator (LCD) of two fractions is the smallest number that can be used as a common <span class=\"no-emphasis\" data-type=\"term\">denominator<\/span> of the fractions. The LCD of the two fractions is the least common multiple (LCM) of their denominators.<\/p>\n<div id=\"fs-id1170655194149\" 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\">Least Common Denominator<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>The least common denominator (LCD) of two fractions is the least common multiple (LCM) of their denominators.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170655061300\">After we find the least common denominator of two fractions, we convert the fractions to equivalent fractions with the LCD. Putting these steps together allows us to add and subtract fractions because their denominators will be the same!<\/p>\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-id1170654983383\" data-type=\"exercise\">\n<div id=\"fs-id1170654938746\" data-type=\"problem\">\n<p id=\"fs-id1170655112854\">Add: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-751675e24431675ff2b4451a549c074a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#49;&#50;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#49;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"53\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655216078\" 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><span id=\"fs-id1170655396298\" data-type=\"media\" data-alt=\"In this figure, we have a table with directions on the left, hints or explanations in the middle, and mathematical statements on the right. On the first line, we have \u201cStep 1. Do they have a common denominator? No \u2013 rewrite each fraction with the LCD (least common denominator).\u201d To the right of this, we have the statement \u201cNo. Find the LCD 12, 18.\u201d To the right of this, we have 12 equals 2 times 2 times 3 and 18 equals 2 times 3 times 3. The LCD is hence 2 times 2 times 3 times 3, which equals 36. As another hint, we have \u201cChange into equivalent fractions with the LCD,. Do not simplify the equivalent fractions! If you do, you\u2019ll get back to the original fractions and lose the common denominator!\u201d To the right of this, we have 7\/12 plus 5\/18, which becomes the quantity (7 times 3) over the quantity (12 times 3) plus the quantity (5 times 2) over the quantity (18 times 2), which becomes 21\/36 plus 10\/36.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_001a_new.jpg\" alt=\"In this figure, we have a table with directions on the left, hints or explanations in the middle, and mathematical statements on the right. On the first line, we have \u201cStep 1. Do they have a common denominator? No \u2013 rewrite each fraction with the LCD (least common denominator).\u201d To the right of this, we have the statement \u201cNo. Find the LCD 12, 18.\u201d To the right of this, we have 12 equals 2 times 2 times 3 and 18 equals 2 times 3 times 3. The LCD is hence 2 times 2 times 3 times 3, which equals 36. As another hint, we have \u201cChange into equivalent fractions with the LCD,. Do not simplify the equivalent fractions! If you do, you\u2019ll get back to the original fractions and lose the common denominator!\u201d To the right of this, we have 7\/12 plus 5\/18, which becomes the quantity (7 times 3) over the quantity (12 times 3) plus the quantity (5 times 2) over the quantity (18 times 2), which becomes 21\/36 plus 10\/36.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1170654914425\" data-type=\"media\" data-alt=\"The next step reads \u201cStep 2. Add or subtract the fractions.\u201d The hint reads \u201cAdd.\u201d And we have 31\/36.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_001b_new.jpg\" alt=\"The next step reads \u201cStep 2. Add or subtract the fractions.\u201d The hint reads \u201cAdd.\u201d And we have 31\/36.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1170654931846\" data-type=\"media\" data-alt=\"The final step reads \u201cStep 3. Simplify, if possible.\u201d The explanation reads \u201cBecause 31 is a prime number, it has no factors in common with 36. The answer is simplified.\u201d\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_001c_new.jpg\" alt=\"The final step reads \u201cStep 3. Simplify, if possible.\u201d The explanation reads \u201cBecause 31 is a prime number, it has no factors in common with 36. The answer is simplified.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\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 5.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655123979\" data-type=\"problem\">\n<p id=\"fs-id1170655123981\">Add: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-c367d141f8ae50a954f67ada2c34cbca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#49;&#50;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#49;&#125;&#123;&#49;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"53\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655223620\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170655108732\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-fa19d1ef3116c82fb7b8ee073c44d90a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#57;&#125;&#123;&#54;&#48;&#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-id1170655194665\" data-type=\"problem\">\n<p id=\"fs-id1170655042204\">Add: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-5a7cb6bdf589245e05594181cfd95398_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#51;&#125;&#123;&#49;&#53;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#55;&#125;&#123;&#50;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"53\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655062834\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170655062836\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-06be4ace88da8d14e4318a0ce652c264_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#48;&#51;&#125;&#123;&#54;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"21\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">HOW TO: Add or Subtract Fractions<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<ol id=\"fs-id1166424871688\" class=\"stepwise\" type=\"1\">\n<li>Do they have a common denominator?\n<ul id=\"fs-id1170655108352\" data-bullet-style=\"open-circle\">\n<li>Yes\u2014go to step 2.<\/li>\n<li>No\u2014rewrite each fraction with the LCD (least common denominator). Find the LCD. Change each fraction into an equivalent fraction with the LCD as its denominator.<\/li>\n<\/ul>\n<\/li>\n<li>Add or subtract the fractions.<\/li>\n<li>Simplify, if possible.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div id=\"fs-id1170655092253\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1170654903279\" data-type=\"exercise\">\n<div id=\"fs-id1170655062834\" data-type=\"solution\">\n<p>When finding the equivalent fractions needed to create the common denominators, there is a quick way to find the number we need to multiply both the numerator and denominator. This method works if we found the LCD by factoring into primes.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170654940613\">Look at the factors of the LCD and then at each column above those factors. The \u201cmissing\u201d factors of each denominator are the numbers we need.<\/p>\n<p><span id=\"fs-id1170655102403\" data-type=\"media\" data-alt=\"The number 12 is factored into 2 times 2 times 3 with an extra space after the 3, and the number 18 is factored into 2 times 3 times 3 with an extra space between the 2 and the first 3. There are arrows pointing to these extra spaces that are marked \u201cmissing factors.\u201d The LCD is marked as 2 times 2 times 3 times 3, which is equal to 36. The numbers that create the LCD are the factors from 12 and 18, with the common factors counted only once (namely, the first 2 and the first 3).\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_002_img_new.jpg\" alt=\"The number 12 is factored into 2 times 2 times 3 with an extra space after the 3, and the number 18 is factored into 2 times 3 times 3 with an extra space between the 2 and the first 3. There are arrows pointing to these extra spaces that are marked \u201cmissing factors.\u201d The LCD is marked as 2 times 2 times 3 times 3, which is equal to 36. The numbers that create the LCD are the factors from 12 and 18, with the common factors counted only once (namely, the first 2 and the first 3).\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1170654967245\">In <a class=\"autogenerated-content\" href=\"#fs-id1170654983383\">(Example 5)<\/a>, the LCD, 36, has two factors of 2 and two factors of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-c7d72a208fb64cc72fdd5ae469d526b5_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;\" \/>.<\/p>\n<p id=\"fs-id1170655175041\">The numerator 12 has two factors of 2 but only one of 3\u2014so it is \u201cmissing\u201d one 3\u2014we multiply the numerator and denominator by 3<\/p>\n<p id=\"fs-id1170655175044\">The numerator 18 is missing one factor of 2\u2014so we multiply the numerator and denominator by 2<\/p>\n<p id=\"fs-id1170654972409\">We will apply this method as we subtract the fractions in <a class=\"autogenerated-content\" href=\"#fs-id1170655000686\">(Example 6)<\/a>.<\/p>\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-id1170655000686\" data-type=\"problem\">\n<p id=\"fs-id1170655081926\">Subtract: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-71c0b62e23e9b0883f9e418372202632_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#49;&#53;&#125;&#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;&#57;&#125;&#123;&#50;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"57\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655200456\" 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-id1170655150350\">Do the fractions have a common denominator? No, so we need to find the LCD.<\/p>\n<table id=\"eip-id1169754059819\" class=\"unnumbered unstyled can-break has-images\" summary=\"In the first line of this problem, the expression 7\/15 minus 19\/24 is given. On the following line, we have the direction \u201cFind the LCD.\u201d The number 15 is factored into 3 times 5 with three extra spaces before the 3, and the number 24 is factored into 2 times 2 times 2 times 3 with an extra space after the 3. The LCD is marked as 2 times 2 times 2 times 3 times 5, which is equal to 120. On the following line, we have the direction \u201cMultiply 8 in the first fraction and 5 in the second fraction to get the LCD.\u201d Under this reads, Rewrite as equivalent fractions with the LCD.\u201d We have the quantity (7 times 8) divided by the quantity (15 times 8) minus the fraction with (19 times 5) as the numerator and (24 times 5) as the denominator. The following line tells us to \u201cSimplify each numerator and denominator.\u201d Hence, we have 56\/120 minus 95\/120. The next lines tells us to \u201cSubtract.\u201d Hence, we have negative 39\/120. The next line tells us to \u201cRewrite showing the common factor of 3.\u201d We have negative (13 times 3) divided by the quantity (40 times 3). We are then instructed to \u201cRemove the common factor to simplify.\u201d We obtain negative 13\/40.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Find the LCD.<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-8582043f7443f08d411e7bf6544f3f04_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#53;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"1\" width=\"1\" style=\"vertical-align: 0px;\" \/><span id=\"eip-id1169754362252\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_003a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Notice, 15 is \u201cmissing\u201d three factors of 2 and 24 is \u201cmissing\u201d the 5 from the factors of the LCD. So we multiply 8 in the first fraction and 5 in the second fraction to get the LCD.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Rewrite as equivalent fractions with the LCD.<\/td>\n<td><span id=\"eip-id1169754058803\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_003b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1169754058820\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_003c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-2bce5e9732ebba43664bb2f60d2d91fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#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;&#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;&#57;&#125;&#123;&#49;&#50;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"44\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Check to see if the answer can be simplified.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-9383ed41ca5af3621303711c34848e63_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#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;&#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;&#51;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#125;&#123;&#52;&#48;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"48\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Both 39 and 120 have a factor of 3.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-b915c9c25c29d6d5b8069091230a10f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#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;&#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;&#51;&#125;&#123;&#52;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"37\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Do not simplify the equivalent fractions! If you do, you\u2019ll get back to the original fractions and lose the common denominator!<\/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 6.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654968270\" data-type=\"problem\">\n<p id=\"fs-id1170655175417\">Subtract: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-ae1c41046c30aa07beed4b0de8047221_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#51;&#125;&#123;&#50;&#52;&#125;&#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;&#55;&#125;&#123;&#51;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"57\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655164359\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170655164361\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-30f616b836b825be7e35cba9f794227e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#57;&#54;&#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 6.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655098048\" data-type=\"problem\">\n<p id=\"fs-id1170655098050\">Subtract: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-44b260ff9355ecbb78674320bfd8291e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#49;&#125;&#123;&#51;&#50;&#125;&#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;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"57\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655111921\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170655111923\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-3698a030d09fd72b7ad5b6406ae2ff23_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#53;&#125;&#123;&#50;&#50;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"21\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170655129917\">In the next example, one of the fractions has a variable in its numerator. Notice that we do the same steps as when both numerators are numbers.<\/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-id1170655201164\" data-type=\"problem\">\n<p id=\"fs-id1170655201167\">Add: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-f36ee1497be9eecbc065aa6d95b6af9f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#53;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#120;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"40\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655114432\" 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-id1170655120660\">The fractions have different denominators.<\/p>\n<table id=\"eip-id1169752964735\" class=\"unnumbered unstyled can-break\" summary=\"In the first line of this problem, the expression 3\/5 plus x\/8 is given. On the following line, we have the direction \u201cFind the LCD.\u201d The number 5 is factored into 5 with three extra spaces before the 5, and the number 8 is factored into 2 times 2 times 2 with an extra space after the 2. The LCD is marked as 2 times 2 times 2 times 5, which is equal to 40. On the following line, we have the direction \u201cRewrite as equivalent fractions with the LCD.\u201d We have the quantity (3 times 8) divided by the quantity (5 times 8) plus the fraction with (x times 5) as the numerator and (8 times 5) as the denominator. The following line tells us to \u201cSimplify.\u201d Hence, we have 24\/40 plus 5x\/40. The next line tells us to \u201cAdd.\u201d Hence, we have the quantity (24 + 5x) divided by 40.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-fda1231336b1197ef1bfd5e0b55f0c5b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#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;\" title=\"Rendered by QuickLaTeX.com\" height=\"1\" width=\"1\" style=\"vertical-align: 0px;\" \/><span id=\"eip-id1169752980194\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_004a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Find the LCD.<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-bdfd74f7de57b83ccc3516ecc88e2986_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#52;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"1\" width=\"1\" style=\"vertical-align: 0px;\" \/><span id=\"eip-id1169752827456\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_004b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Rewrite as equivalent fractions with the LCD.<\/td>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-fda1231336b1197ef1bfd5e0b55f0c5b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#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;\" title=\"Rendered by QuickLaTeX.com\" height=\"1\" width=\"1\" style=\"vertical-align: 0px;\" \/><span id=\"eip-id1169753158504\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_004c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-fda1231336b1197ef1bfd5e0b55f0c5b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#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;\" title=\"Rendered by QuickLaTeX.com\" height=\"1\" width=\"1\" style=\"vertical-align: 0px;\" \/><span id=\"eip-id1169753130877\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_004d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-fda1231336b1197ef1bfd5e0b55f0c5b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#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;\" title=\"Rendered by QuickLaTeX.com\" height=\"1\" width=\"1\" style=\"vertical-align: 0px;\" \/><span id=\"eip-id1169753130893\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_004e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/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 7.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655226887\" data-type=\"problem\">\n<p id=\"fs-id1170654954496\">Add: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-cc46d5ca2c62a1e356949c29261b31f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#121;&#125;&#123;&#54;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"40\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655224317\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170655224319\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-906b8a8e842ce4d3b7997fae9c187ced_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#121;&#43;&#52;&#50;&#125;&#123;&#53;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"39\" 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 7.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655111439\" data-type=\"problem\">\n<p>Add: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-45f0d1a3dd6fa79bce1a17ff24cdcdb5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#120;&#125;&#123;&#54;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#49;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"47\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654990354\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170655150393\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-d37172e18d6d941d5df9579b44de9cc9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#53;&#120;&#43;&#52;&#50;&#125;&#123;&#49;&#51;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"47\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170655189510\">We now have all four operations for fractions. The table below summarizes <span class=\"no-emphasis\" data-type=\"term\">fraction operations<\/span>.<\/p>\n<div class=\"textbox shaded\">\n<table>\n<caption>Summary of Fraction Operations<\/caption>\n<tbody>\n<tr>\n<th scope=\"col\">Fraction Operation<\/th>\n<th scope=\"col\">Sample Equation<\/th>\n<th scope=\"col\">What to Do<\/th>\n<\/tr>\n<tr>\n<td>Fraction multiplication<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-1ed79ec8404620993550124c8de79c90_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#98;&#125;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#99;&#125;&#123;&#100;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#99;&#125;&#123;&#98;&#100;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"73\" style=\"vertical-align: -6px;\" \/><\/td>\n<td>Multiply the numerators and multiply the denominators<\/td>\n<\/tr>\n<tr>\n<td>Fraction division<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-239d75afec64f511ba1307bc4e0abe98_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#98;&#125;&#32;&#92;&#100;&#105;&#118;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#99;&#125;&#123;&#100;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#98;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#100;&#125;&#123;&#99;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"99\" style=\"vertical-align: -6px;\" \/><\/td>\n<td>Multiply the first fraction by the reciprocal of the second.<\/td>\n<\/tr>\n<tr>\n<td>Fraction addition<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-a09139f49d460f9076afe2ff290d57f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#99;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#98;&#125;&#123;&#99;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#43;&#98;&#125;&#123;&#99;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"90\" style=\"vertical-align: -6px;\" \/><\/td>\n<td>Add the numerators and place the sum over the common denominator.<\/td>\n<\/tr>\n<tr>\n<td>Fraction subtraction<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-d13951b27524ed5b5be4d8d4fcda4ed8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#99;&#125;&#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;&#98;&#125;&#123;&#99;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#45;&#98;&#125;&#123;&#99;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"94\" style=\"vertical-align: -6px;\" \/><\/td>\n<td>Subtract the numerators and place the difference over the common denominator.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>To multiply or divide fractions, an LCD is NOT needed. To add or subtract fractions, an LCD is needed.<\/p>\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-id1170655061519\" data-type=\"exercise\">\n<div id=\"fs-id1170655061521\" data-type=\"problem\">\n<p id=\"fs-id1170655061523\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-b2414ae6582d2594c813884b3a9b36ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#120;&#125;&#123;&#54;&#125;&#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;&#49;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"58\" style=\"vertical-align: -6px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-0ca9fc0e8d5ce3ec455e3b43201c67bc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#120;&#125;&#123;&#54;&#125;&#92;&#99;&#100;&#111;&#116;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#49;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"45\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654944167\" data-type=\"solution\">\n<div data-type=\"title\"><strong><br \/>\nSolution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1170654936746\">First ask, \u201cWhat is the operation?\u201d Once we identify the operation that will determine whether we need a common denominator. Remember, we need a common denominator to add or subtract, but not to multiply or divide.<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 70px;\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">a) <strong>What is the operation? The operation is subtraction.<\/strong><\/td>\n<td style=\"width: 50%; height: 14px;\"><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">Do the fractions have a common denominator? No.<\/td>\n<td style=\"width: 50%; height: 14px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-5d1f37f5b2d3f1b3b73612ceed7e31da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#120;&#125;&#123;&#54;&#125;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#49;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"54\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">Rewrite each fraction as an equivalent fraction with the LCD.<\/td>\n<td style=\"width: 50%; height: 14px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-25464b99cdff24a55dd04e0703ba65dd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#120;&#92;&#99;&#100;&#111;&#116;&#53;&#125;&#123;&#54;&#92;&#99;&#100;&#111;&#116;&#53;&#125;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#92;&#99;&#100;&#111;&#116;&#51;&#125;&#123;&#49;&#48;&#92;&#99;&#100;&#111;&#116;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"76\" style=\"vertical-align: -6px;\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-c0ea80830fb7d5fa943f7ee4ec82b76e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#53;&#120;&#125;&#123;&#51;&#48;&#125;&#45;&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#125;&#123;&#51;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"61\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">Subtract the numerators and place the difference over the common denominators.<\/td>\n<td style=\"width: 50%; height: 14px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-671e377b1c56c603e31e061747810362_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#53;&#120;&#45;&#57;&#125;&#123;&#51;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"40\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">Simplify, if possible.<\/td>\n<td style=\"width: 50%; height: 14px;\">There are no common factors. The fraction is simplified.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">b) <strong>What is the operation? Multiplication.<\/strong><\/td>\n<td style=\"width: 50%; height: 14px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-0ca9fc0e8d5ce3ec455e3b43201c67bc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#120;&#125;&#123;&#54;&#125;&#92;&#99;&#100;&#111;&#116;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#49;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"45\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">To multiply fractions, multiply the numerators and multiply the denominators.<\/td>\n<td style=\"width: 50%; height: 14px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-f95c3b7a39229704011187156977ef48_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#120;&#92;&#99;&#100;&#111;&#116;&#51;&#125;&#123;&#54;&#92;&#99;&#100;&#111;&#116;&#49;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"26\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">Rewrite, showing common factors. Remove common factors.<\/td>\n<td style=\"width: 50%; height: 14px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-203f2042d82b546338180dff3f799e9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#41;&#53;&#125;&#120;&#32;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#41;&#51;&#125;&#125;&#123;&#50;&#92;&#99;&#100;&#111;&#116;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#41;&#51;&#125;&#92;&#99;&#100;&#111;&#116;&#50;&#92;&#99;&#100;&#111;&#116;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#41;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"34\" width=\"51\" style=\"vertical-align: -13px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">Simplify.<\/td>\n<td style=\"width: 50%; height: 14px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-d3685b862bc3abb6d3ac926dbdd6429a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#120;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"8\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><span style=\"orphans: 1; text-align: initial; font-size: 0.9em; word-spacing: normal;\">Notice we needed an LCD to add <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-b2414ae6582d2594c813884b3a9b36ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#120;&#125;&#123;&#54;&#125;&#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;&#49;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"58\" style=\"vertical-align: -6px;\" \/>, but not to multiply <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-0ca9fc0e8d5ce3ec455e3b43201c67bc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#120;&#125;&#123;&#54;&#125;&#92;&#99;&#100;&#111;&#116;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#49;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"45\" style=\"vertical-align: -6px;\" \/>.<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1170655104899\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1170655195238\" data-type=\"exercise\">\n<div id=\"fs-id1170655199104\" data-type=\"solution\">\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<p>Simplify. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-d40d3220f9423bd0602cd111dd31a9e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#55;&#97;&#45;&#51;&#50;&#125;&#123;&#51;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"46\" style=\"vertical-align: -6px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-4f1ec16a38ab988e9c6f908885be1530_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#97;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"15\" style=\"vertical-align: -6px;\" \/><\/p>\n<div id=\"fs-id1170655132961\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p>a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-d40d3220f9423bd0602cd111dd31a9e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#55;&#97;&#45;&#51;&#50;&#125;&#123;&#51;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"46\" style=\"vertical-align: -6px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-4f1ec16a38ab988e9c6f908885be1530_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#97;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"15\" 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 8.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655165629\" data-type=\"problem\">\n<p id=\"fs-id1170655165632\">Simplify: a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-55985fc38a6aa7ce2f664718afcdf4dd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#107;&#125;&#123;&#53;&#125;&#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;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"50\" style=\"vertical-align: -6px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-4d163c0d1cf28b9d818adc57a6504635_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#107;&#125;&#123;&#53;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"38\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655132961\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170655132963\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-3613cc4df86bb5c851fb55319e862c16_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#52;&#107;&#45;&#53;&#125;&#123;&#51;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"39\" style=\"vertical-align: -6px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-3cc0842b5ad57a25161a3730f7268010_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#107;&#125;&#123;&#49;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"15\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Use the Order of Operations to Simplify Complex Fractions<\/h1>\n<p id=\"fs-id1170654969636\">We have seen that a complex fraction is a fraction in which the numerator or denominator contains a fraction. The fraction bar indicates <span class=\"no-emphasis\" data-type=\"term\">division<\/span>. We simplified the complex fraction <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-66597eaef9b923152585c4c439a98ac0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#125;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#56;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"10\" style=\"vertical-align: -13px;\" \/> by dividing <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-b5c8c9a183cece3e98b7b8975d3b4938_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/> by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-ea9c485ae4d513e2d9c404272f21d5e6_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;\" \/>.<\/p>\n<p id=\"fs-id1170655111615\">Now we\u2019ll look at complex fractions where the numerator or denominator contains an expression that can be simplified. So we first must completely simplify the numerator and denominator separately using the order of operations. Then we divide the numerator by the denominator.<\/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-id1170655189464\" data-type=\"exercise\">\n<div id=\"fs-id1170655189466\" data-type=\"problem\">\n<p id=\"fs-id1170654962386\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-b34038f61ffa7041cf60b8fb8b1756cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#125;&#123;&#52;&#43;&#123;&#51;&#125;&#94;&#123;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"35\" width=\"32\" style=\"vertical-align: -9px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654953233\" 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><span id=\"fs-id1170654968903\" data-type=\"media\" data-alt=\"In this figure, we have a table with directions on the left and mathematical statements on the right. On the first line, we have \u201cStep 1. Simplify the numerator. Remember one half squared means one half times one half.\u201d To the right of this, we have the quantity (1\/2) squared all over the quantity (4 plus 3 squared). Then, we have 1\/4 over the quantity (4 plus 3 squared).\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_010a_new.jpg\" alt=\"In this figure, we have a table with directions on the left and mathematical statements on the right. On the first line, we have \u201cStep 1. Simplify the numerator. Remember one half squared means one half times one half.\u201d To the right of this, we have the quantity (1\/2) squared all over the quantity (4 plus 3 squared). Then, we have 1\/4 over the quantity (4 plus 3 squared).\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1170655096686\" data-type=\"media\" data-alt=\"The next line\u2019s direction reads \u201cStep 2. Simplify the denominator.\u201d To the right of this, we have 1\/4 over the quantity (4 plus 9), under which we have 1\/4 over 13.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_010b_new.jpg\" alt=\"The next line\u2019s direction reads \u201cStep 2. Simplify the denominator.\u201d To the right of this, we have 1\/4 over the quantity (4 plus 9), under which we have 1\/4 over 13.\" data-media-type=\"image\/jpeg\" \/><\/span><span id=\"fs-id1170655090064\" data-type=\"media\" data-alt=\"The final step is \u201cStep 3. Divide the numerator by the denominator. Simplify if possible. Remember, thirteen equals thirteen over 1.\u201d To the right we have 1\/4 divided by 13. Then we have 1\/4 times 1\/13, which equals 1\/52.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_010c_new.jpg\" alt=\"The final step is \u201cStep 3. Divide the numerator by the denominator. Simplify if possible. Remember, thirteen equals thirteen over 1.\u201d To the right we have 1\/4 divided by 13. Then we have 1\/4 times 1\/13, which equals 1\/52.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\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 9.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655029722\" data-type=\"problem\">\n<p id=\"fs-id1170655029724\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-8129671c8e75616c5ae8013d041009d0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#125;&#123;&#123;&#50;&#125;&#94;&#123;&#51;&#125;&#43;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"35\" width=\"32\" style=\"vertical-align: -9px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655178937\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170655178939\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-8c25a6704f9cecfa1b13e2803121a11d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#57;&#48;&#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 9.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654943859\" data-type=\"problem\">\n<p>Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-f22dad97ed2753f00d863fe635d80ec1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#43;&#123;&#52;&#125;&#94;&#123;&#50;&#125;&#125;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"32\" style=\"vertical-align: -17px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655354060\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170655213977\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-2785dd888eb2d9578ff504105e78f96b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#55;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"26\" style=\"vertical-align: 0px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">HOW TO: Simplify Complex Fractions<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<ol id=\"fs-id1166424845977\" class=\"stepwise\" type=\"1\">\n<li>Simplify the numerator.<\/li>\n<li>Simplify the denominator.<\/li>\n<li>Divide the numerator by the denominator. Simplify if possible.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div id=\"fs-id1170654962204\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1170654962207\" data-type=\"exercise\">\n<div id=\"fs-id1170655029722\" 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-id1170654968376\" data-type=\"problem\">\n<p id=\"fs-id1170655021220\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-8298a634b03202aaaf684588ab5a1f52_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;&#50;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#125;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#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;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"34\" style=\"vertical-align: -13px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655102612\" 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-id1170655102617\">It may help to put parentheses around the numerator and the denominator.<\/p>\n<table id=\"eip-20\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-e3191c08f8be435f43de4a0f4d9ed41c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#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;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"48\" style=\"vertical-align: -15px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify the numerator (LCD = 6) and simplify the denominator (LCD = 12).<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-92359da9c3b8bc32353f03b46adcd9aa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#54;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#54;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#125;&#123;&#49;&#50;&#125;&#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;&#49;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"60\" style=\"vertical-align: -15px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-3cc578a8198b3cedb6ff0070dee9baea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#54;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#49;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"30\" style=\"vertical-align: -15px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Divide the numerator by the denominator.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-7422c164aca6dd03fd4135dbbccdd129_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#54;&#125;&#92;&#100;&#105;&#118;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#49;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"46\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-b0c4f415315c68bbdb7e83be4f14eb33_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#54;&#125;&#92;&#99;&#100;&#111;&#116;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#50;&#125;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"38\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Divide out common factors.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-537d1b513a9adadf1c2900f413bc1a26_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#92;&#99;&#100;&#111;&#116;&#54;&#92;&#99;&#100;&#111;&#116;&#50;&#125;&#123;&#54;&#92;&#99;&#100;&#111;&#116;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"29\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-174a3104a2b53e14a44efe68804d55a4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/><\/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-id1170655213970\" data-type=\"problem\">\n<p id=\"fs-id1170655213972\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-1db92d1c79fbae7967609fa95f765a75_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;&#51;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#125;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#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;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"34\" style=\"vertical-align: -13px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655166560\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170655166563\">2<\/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-id1170655027368\" data-type=\"problem\">\n<p id=\"fs-id1170655232373\">Simplify: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-75b35c636f58aaeb3c019670873343f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#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;&#125;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"34\" style=\"vertical-align: -13px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655224374\" data-type=\"solution\">\n<details>\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170655154600\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-92f3bc96ea4492d6751c552ba095b410_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#55;&#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>\n<\/div>\n<h1>Evaluate Variable Expressions with Fractions<\/h1>\n<p id=\"fs-id1170654943331\">We have evaluated expressions before, but now we can evaluate expressions with fractions. Remember, to evaluate an expression, we substitute the value of the variable into the expression and then simplify.<\/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-id1170654920102\" data-type=\"problem\">\n<p id=\"fs-id1170655151128\">Evaluate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-0885e848d8cd5debdc4ee6c0434971b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"41\" style=\"vertical-align: -6px;\" \/> when a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-25efd8c8f5c15a396baa7650b0931b6e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#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;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"60\" style=\"vertical-align: -6px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-d94f572c8f8a94b98d6c47791d8bdc33_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#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=\"60\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655151791\" 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<ol id=\"fs-id1166425002264\" class=\"circled\" type=\"a\">\n<li>To evaluate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-0885e848d8cd5debdc4ee6c0434971b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"41\" style=\"vertical-align: -6px;\" \/> when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-25efd8c8f5c15a396baa7650b0931b6e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#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;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"60\" style=\"vertical-align: -6px;\" \/>, substitute <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-d9bcfe523a6807d6935b0b4e8c98978d_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;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"25\" style=\"vertical-align: -6px;\" \/> for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-120313500a6d2b83018c96e99a915cf1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\" \/> in the expression.<br \/>\n<table id=\"eip-id1169754119484\" style=\"width: 100%;\" summary=\"In the first line of this problem, the expression x plus 1\/3 is given. On the following line, we have the direction \u201cSubstitute negative 1\/3 for x.\u201d Then our expression reads as negative 1\/3 plus 1\/3. The following line tells us to \u201cSimplify.\u201d Hence, we have 0.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1169754119503\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_005b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1169754119516\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_005a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td><span id=\"eip-id1169754060494\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_005c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-429d483db191dfd66f8f05c2a4f86209_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#56;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"1\" width=\"1\" style=\"vertical-align: 0px;\" \/><\/td>\n<td data-align=\"center\">0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/li>\n<li>To evaluate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-0885e848d8cd5debdc4ee6c0434971b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"41\" style=\"vertical-align: -6px;\" \/> when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-d94f572c8f8a94b98d6c47791d8bdc33_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#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=\"60\" style=\"vertical-align: -6px;\" \/>, we substitute <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-03040e7d19fe63a3dcd77ae9a7273f3f_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;\" \/> for <em data-effect=\"italics\">x<\/em> in the expression.<br \/>\n<table id=\"eip-id1169752950666\" style=\"width: 100%;\" summary=\"In the first line of this problem, the expression x plus 1\/3 is given. On the following line, we have the direction \u201cSubstitute negative 3\/4 for x.\u201d Then our expression reads as negative 3\/4 plus 1\/3. The following line instructs us to \u201cRewrite as equivalent fractions with the LCD, 12.\u201d Our expression thus reads as negative (3 times 3) divided by (4 times 3) plus the quantity (1 times 4) divided by (3 times 4). The following line tells us to \u201cSimplify.\u201d Hence, we have negative 9\/12 + 4\/12. The last line tells us to \u201cAdd.\u201d Hence, we have negative 5\/12.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1169750875592\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_006b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1169750875606\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_006a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td><span id=\"eip-id1169750580487\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_006c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Rewrite as equivalent fractions with the LCD, 12.<\/td>\n<td><span id=\"eip-id1169750580506\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_006d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><span id=\"eip-id1169752933600\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_006e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-eef728e70d8e7bb515df3b5640aa1a7e_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;&#49;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"32\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/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 11.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655029358\" data-type=\"problem\">\n<p id=\"fs-id1170655029360\">Evaluate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-a9901d7f4360bd8becb26acb31b8164f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"41\" style=\"vertical-align: -6px;\" \/> when a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-2415977b8bc15bfed0909b116a158550_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#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;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"60\" style=\"vertical-align: -6px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-656c6e31926110186ff8d5343b2d407f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#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=\"60\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655081366\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170655081368\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-b80ba2734f70ff584d473cda66662853_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"21\" style=\"vertical-align: 0px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-7c4a20df0a2e71b64a6e7dac3f4026e0_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;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"25\" 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 11.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170654905739\" data-type=\"problem\">\n<p id=\"fs-id1170654905741\">Evaluate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-b110cdba162477112f4e32880ecc1ceb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"40\" style=\"vertical-align: -6px;\" \/> when a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-9a41cc459b753429c077364ad40e9ceb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"42\" style=\"vertical-align: -6px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-23966be56b51a709518e95698ad5db12_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#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=\"59\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655174530\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170654953613\">a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-e8754864f13d01c34ce94df9b50c1b44_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) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-c86d4c8226654e45d579060abaad2f2f_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;&#49;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"32\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1170654937339\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1170654937342\" data-type=\"exercise\">\n<div id=\"fs-id1170654905739\" data-type=\"problem\">\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-id1170655348076\" data-type=\"problem\">\n<p>Evaluate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-6fcbfa01d0c891bb5b0b04de1f323679_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;&#54;&#125;&#45;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"58\" style=\"vertical-align: -6px;\" \/> when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-86ec9ebb5944a07957cb61b462b1177f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#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;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"59\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655029899\" 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-id1169750824026\" class=\"unnumbered unstyled\" summary=\"In the first line of this problem, the expression negative 5\/6 minus y is given. On the following line, we have the direction \u201cSubstitute negative 2\/3 for y.\u201d Then our expression reads as negative 5\/6 minus negative 2\/3. The following line instructs us to \u201cRewrite as equivalent fractions with the LCD, 6.\u201d Our expression thus reads as negative 5\/6 minus negative 4\/6. The following line tells us to \u201cSubtract.\u201d Hence, we have the quantity (negative 5 minus negative 4) divided by 6. The following line instructs us to \u201cSimplify\u201d, which becomes one sixth.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td><span id=\"eip-id1169750785591\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_007b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1169750785605\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_007a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td><span id=\"eip-id1169750785615\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_007c_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Rewrite as equivalent fractions with the LCD, 6.<\/td>\n<td><span id=\"eip-id1169750995278\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_007d_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Subtract.<\/td>\n<td><span id=\"eip-id1169750995294\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_007e_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-82d5903ba5f3e2e15b282efec9f1f988_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;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"25\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1170655174530\" data-type=\"solution\">\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 data-type=\"problem\">\n<p id=\"fs-id1170655166336\">Evaluate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-569d11317d114921b0922ace3fe63a14_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;&#50;&#125;&#45;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"58\" style=\"vertical-align: -6px;\" \/> when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-852c6a87ace26633472a2bd3b3d42084_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#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=\"59\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655189969\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170655189972\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-83504ded5ac8506e78eb50b2932e3822_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;\" \/><\/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-id1170655112594\" data-type=\"problem\">\n<p id=\"fs-id1170655112596\">Evaluate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-9d02f2ada4e5730ed82c515aa6fce95e_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;&#56;&#125;&#45;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"58\" style=\"vertical-align: -6px;\" \/> when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-e4b3ed979a30062c142c9e76f0f84f78_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#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=\"60\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654972309\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170654972312\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-b6e42d89c521dace7c13295068349796_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;&#55;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"32\" style=\"vertical-align: -6px;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1170655232453\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1170655112591\" data-type=\"exercise\">\n<div id=\"fs-id1170654972309\" data-type=\"solution\">\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-id1170655120764\" data-type=\"problem\">\n<p id=\"fs-id1170655108542\">Evaluate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-b6ee95b9d6aa1845bcd26e05c36172cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"36\" style=\"vertical-align: -4px;\" \/> when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-f698a7d492c99f1ef04be177ff19c562_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"43\" style=\"vertical-align: -6px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-86ec9ebb5944a07957cb61b462b1177f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#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;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"59\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654969427\" 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-id1170655193059\">Substitute the values into the expression.<\/p>\n<table id=\"eip-id1169751865150\" class=\"unnumbered unstyled\" summary=\"In the first line of this problem, the expression 2 times (x squared) times y is given. On the following line, we have the direction \u201cSubstitute 1\/4 for x and negative 2\/3 for y.\u201d Then our expression reads as 2 times (the quantity (1\/4) squared) times (negative 2\/3). The following line instructs us to \u201cSimplify exponents first.\u201d Our expression thus reads as 2 times (1\/16) times (negative 2\/3). The following line tells us to \u201cMultiply. Divide out the common factors.\u201d The common factors are crossed out. The following line instructs us to \u201cSimplify.\u201d We further simplify on the last line to obtain negative one twelfth.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-b6ee95b9d6aa1845bcd26e05c36172cb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#121;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"36\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1169754068123\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_008a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td data-align=\"center\"><span id=\"eip-id1169754138748\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_008b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Simplify exponents first.<\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-bece1cffde51b4169ee8763cb9da1940_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#54;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#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;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"91\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Multiply. Divide out the common factors. Notice we write 16 as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-4d9d0c2b45fc932025dc78de72679f75_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#50;&#92;&#99;&#100;&#111;&#116;&#32;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"52\" style=\"vertical-align: 0px;\" \/> to make it easy to remove common factors.<\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-2342b0fc8651870196f943251f46496b_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;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#41;&#50;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#49;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#41;&#50;&#125;&#125;&#123;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#41;&#50;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#111;&#118;&#101;&#114;&#108;&#105;&#110;&#101;&#123;&#41;&#50;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#52;&#92;&#99;&#100;&#111;&#116;&#32;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"34\" width=\"69\" style=\"vertical-align: -13px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-c86d4c8226654e45d579060abaad2f2f_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;&#49;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"32\" 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 13.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655202092\" data-type=\"problem\">\n<p id=\"fs-id1170655202094\">Evaluate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-80120d7d74f4ecf921ff7a875942ef19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#97;&#123;&#98;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"33\" style=\"vertical-align: 0px;\" \/> when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-112605e27c9e07ffafcb90faecddae3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#61;&#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;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"59\" style=\"vertical-align: -6px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-2e7bbffbff742b60391fcf8c78a00d62_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#98;&#61;&#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;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"58\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655189288\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170655189290\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-7c4a20df0a2e71b64a6e7dac3f4026e0_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;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"25\" 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 13.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1170655205665\" data-type=\"problem\">\n<p id=\"fs-id1170655090914\">Evaluate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-4f828b60dcee3c8a23a0c4ad60e3d5db_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#123;&#99;&#125;&#94;&#123;&#51;&#125;&#100;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"34\" style=\"vertical-align: 0px;\" \/> when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-7f4e59cfec06171784ff5f73b2d2e5e1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;&#61;&#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;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"58\" style=\"vertical-align: -6px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-77419902e3a19a3356c1f68f6b63aa7f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#100;&#61;&#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=\"59\" style=\"vertical-align: -6px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655170246\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170654939677\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-4f857ffb35ec6d7843234fa5beb2b4e2_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;\" \/><\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p id=\"fs-id1170654904864\">The next example will have only variables, no constants.<\/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-id1170655121184\" data-type=\"problem\">\n<p id=\"fs-id1170655121186\">Evaluate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-95f1cb15a2b8e36c42cc412c7bcc6f1b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#112;&#43;&#113;&#125;&#123;&#114;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"26\" style=\"vertical-align: -6px;\" \/> when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-7eb56f4f7e7f87ae52db8fd04179bec9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#61;&#45;&#52;&#44;&#113;&#61;&#45;&#50;&#44;&#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;&#114;&#61;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"201\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655112870\" 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-id1170655189822\">To evaluate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-95f1cb15a2b8e36c42cc412c7bcc6f1b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#112;&#43;&#113;&#125;&#123;&#114;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"26\" style=\"vertical-align: -6px;\" \/> when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-7eb56f4f7e7f87ae52db8fd04179bec9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#112;&#61;&#45;&#52;&#44;&#113;&#61;&#45;&#50;&#44;&#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;&#114;&#61;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"201\" style=\"vertical-align: -4px;\" \/>, we substitute the values into the expression.<\/p>\n<table id=\"eip-id1169753258394\" class=\"unnumbered unstyled\" summary=\"In the first line of this problem, the quantity (p plus q) divided by r is given. On the following line, we have the direction \u201cSubstitute negative 4 for p, negative 2 for q and 8 for r.\u201d Then our expression reads as the quantity negative 4 plus negative 2 divided by 8. The following line instructs us to \u201cAdd in the numerator first.\u201d Our expression thus reads as negative 6\/8. The following line tells us to \u201cSimplify.\u201d Hence, we have the quantity negative three fourths.\" data-label=\"\">\n<tbody>\n<tr>\n<td><\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-95f1cb15a2b8e36c42cc412c7bcc6f1b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#112;&#43;&#113;&#125;&#123;&#114;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"26\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td><span id=\"eip-id1169750995237\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_009a_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<td data-align=\"center\"><span id=\"eip-id1169750995249\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/uploads\/sites\/688\/2020\/08\/CNX_ElemAlg_Figure_01_06_009b_img_new.jpg\" alt=\".\" data-media-type=\"image\/png\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Add in the numerator first.<\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-a6d483b8a11c5443472528c17a587139_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#45;&#54;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"18\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td data-align=\"center\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-03040e7d19fe63a3dcd77ae9a7273f3f_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;\" \/><\/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-id1170655121362\" data-type=\"problem\">\n<p id=\"fs-id1170655121364\">Evaluate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-fb8dbc80967e1908c44c133c3f2f52e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#43;&#98;&#125;&#123;&#99;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"24\" style=\"vertical-align: -6px;\" \/> when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-dd65832e14bbc636ea14c576ebedaa24_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#61;&#45;&#56;&#44;&#98;&#61;&#45;&#55;&#44;&#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;&#99;&#61;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"198\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170654940661\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170654977155\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-4602b52ab64a3d0abb450b3685b99fb5_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<\/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-id1170654966036\" data-type=\"problem\">\n<p id=\"fs-id1170654966038\">Evaluate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-f85fb6a0e4bd634b63c8dfad01989a86_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#120;&#43;&#121;&#125;&#123;&#122;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"26\" style=\"vertical-align: -6px;\" \/> when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-d0ef93319c886c58082ebfe202b44d45_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#57;&#44;&#121;&#61;&#45;&#49;&#56;&#44;&#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;&#122;&#61;&#45;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"211\" style=\"vertical-align: -4px;\" \/>.<\/p>\n<\/div>\n<div id=\"fs-id1170655083076\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1170655083078\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-f70a0d5912d2c8626a94447268050570_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#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<h1>Key Concepts<\/h1>\n<ul id=\"fs-id1170655194091\" data-bullet-style=\"bullet\">\n<li><strong data-effect=\"bold\">Fraction Addition and Subtraction:<\/strong> If <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-9267d0977b8d1972f62cc24848f360cf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#44;&#98;&#44;&#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;&#99;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"73\" style=\"vertical-align: -4px;\" \/> are numbers where <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-8b5bf141db78347b5c7492b111198fd9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#99;&#92;&#110;&#101;&#32;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"40\" style=\"vertical-align: -4px;\" \/>, then<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-a09139f49d460f9076afe2ff290d57f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#99;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#98;&#125;&#123;&#99;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#43;&#98;&#125;&#123;&#99;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"90\" style=\"vertical-align: -6px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-d13951b27524ed5b5be4d8d4fcda4ed8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#125;&#123;&#99;&#125;&#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;&#98;&#125;&#123;&#99;&#125;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#45;&#98;&#125;&#123;&#99;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"94\" style=\"vertical-align: -6px;\" \/>.<br \/>\nTo add or subtract fractions, add or subtract the numerators and place the result over the common denominator.<\/li>\n<li><strong data-effect=\"bold\">Strategy for Adding or Subtracting Fractions<\/strong>\n<ol id=\"fs-id1170654966823\" class=\"stepwise\" type=\"1\">\n<li>Do they have a common denominator?<br \/>\nYes\u2014go to step 2.<br \/>\nNo\u2014Rewrite each fraction with the LCD (Least Common Denominator). Find the LCD. Change each fraction into an equivalent fraction with the LCD as its denominator.<\/li>\n<li>Add or subtract the fractions.<\/li>\n<li>Simplify, if possible. To multiply or divide fractions, an LCD IS NOT needed. To add or subtract fractions, an LCD IS needed.<\/li>\n<\/ol>\n<\/li>\n<li><strong data-effect=\"bold\">Simplify Complex Fractions<\/strong>\n<ol id=\"fs-id1170655260316\" class=\"stepwise\" type=\"1\">\n<li>Simplify the numerator.<\/li>\n<li>Simplify the denominator.<\/li>\n<li>Divide the numerator by the denominator. Simplify if possible.<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<h1>Glossary<\/h1>\n<div class=\"textbox shaded\">\n<dl id=\"fs-id1166424922293\">\n<dt>least common denominator<\/dt>\n<dd id=\"fs-id1166424922299\">The least common denominator (LCD) of two fractions is the Least common multiple (LCM) of their denominators.<\/dd>\n<\/dl>\n<\/div>\n<h1>Practice Makes Perfect<\/h1>\n<h2>Add and Subtract Fractions with a Common Denominator<\/h2>\n<p id=\"fs-id1166425099458\">In the following exercises, add.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">1. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-2963e197227126f3618a2c73aaaf8b2d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#54;&#125;&#123;&#49;&#51;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#49;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"53\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%;\">2. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-477503ded04f12cd8af46cd9d842d9dc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#49;&#53;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#49;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"53\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">3. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-3621efd76154751f601dc13eb05a11c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#120;&#125;&#123;&#52;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"40\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%;\">4. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-ea7e56af4bb949902490665a43b750f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#56;&#125;&#123;&#113;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#54;&#125;&#123;&#113;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"25\" width=\"40\" style=\"vertical-align: -9px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">5. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-399dc6a01f9d0baf3c2d01473f515698_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;&#49;&#54;&#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;&#55;&#125;&#123;&#49;&#54;&#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%;\">6. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-28844c3589ff8be1a46a04bf2af7e4fc_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;&#49;&#54;&#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;&#57;&#125;&#123;&#49;&#54;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"105\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">7. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-bba43eb08b9130bb8d92714248dbe9dc_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;&#49;&#55;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#53;&#125;&#123;&#49;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"72\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%;\">8. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-55c0780f807aada08e42fa0cf65ea86c_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;&#49;&#57;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#55;&#125;&#123;&#49;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"72\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">9. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-53bf73bd9a7c3b90db30be508e4eacb3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#54;&#125;&#123;&#49;&#51;&#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;&#48;&#125;&#123;&#49;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#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;&#50;&#125;&#123;&#49;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"159\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%;\">10. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-408c29903341bf5ea3171dbdc0b87de5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#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;&#55;&#125;&#123;&#49;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#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;&#49;&#125;&#123;&#49;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"159\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div id=\"fs-id1170655121728\" data-type=\"exercise\">\n<div id=\"fs-id1170655121730\" data-type=\"problem\">In the following exercises, subtract.<\/div>\n<\/div>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">11. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-e2612a2da061520f523ec2551ca2e1d1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#49;&#125;&#123;&#49;&#53;&#125;&#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;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"57\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%;\">12. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-dc1138dd7fd31cbd3f29b742ecb7365b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#125;&#123;&#49;&#51;&#125;&#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;&#49;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"57\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">13. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-2eeddba8396cb2276e1529731f98b71f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#49;&#125;&#123;&#49;&#50;&#125;&#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;&#49;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"57\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%;\">14. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-52fdb3a82516e307054f6c023e5519c7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#49;&#50;&#125;&#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;&#49;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"57\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">15. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-663e5786fc5dcfff13544eaa3b4cd8f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#57;&#125;&#123;&#50;&#49;&#125;&#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;&#50;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"57\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%;\">16. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-793e70af3200b7506f00af56611e486c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#55;&#125;&#123;&#50;&#49;&#125;&#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;&#50;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"57\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">17. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-1f524c9b3923fe70a669eb46b9d67b4c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#121;&#125;&#123;&#56;&#125;&#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;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"50\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%;\">18. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-8922b22ec882bbd8212d2dd28e1c6e73_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#49;&#122;&#125;&#123;&#49;&#51;&#125;&#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;&#49;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"64\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">19. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-521a9a599b193414091c3c9e7455b316_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;&#51;&#125;&#123;&#117;&#125;&#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;&#53;&#125;&#123;&#117;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"75\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%;\">20. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-2a8f66c0a8f0877becce72ba328f9446_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;&#57;&#125;&#123;&#118;&#125;&#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;&#54;&#125;&#123;&#118;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"75\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">21. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-1c652d04f99722ea68af891785be0c4e_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;&#53;&#125;&#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;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"91\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%;\">22. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-0c96d07658c305748eeda23ad59b3ee0_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;&#55;&#125;&#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;&#53;&#125;&#123;&#55;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"91\" 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\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-9fe5eb8af7bc8da04db6960ae1711c1b_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;&#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;&#53;&#125;&#123;&#57;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"91\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%;\">24. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-6fb5bf4e3a8594963fe29ba1d6f31e33_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;&#49;&#49;&#125;&#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;&#53;&#125;&#123;&#49;&#49;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"105\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Mixed Practice<\/h2>\n<p id=\"fs-id1166422823760\">In the following exercises, simplify.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">25. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-9cfe8a5c5ae68e5769029e02e88e7575_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;&#49;&#56;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#125;&#123;&#49;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"63\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%;\">26. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-c1148287879b7e76d03db872e3f577b6_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;&#49;&#52;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#49;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"63\" 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\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-cb11a7fbdaf8bf56bb490bbb993001a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#110;&#125;&#123;&#53;&#125;&#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=\"44\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%;\">28. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-b92c9d8337098255b15f845a6d83595c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#54;&#125;&#123;&#49;&#49;&#125;&#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;&#115;&#125;&#123;&#49;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"57\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">29. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-6e0ac59aad8d26563fce805b6210d786_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;&#50;&#52;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#50;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"72\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%;\">30. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-62d678bb8a57b5f26e2af74afef71764_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;&#49;&#56;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"72\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">31. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-688b53057381fdcb59e99f186cb5db4c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#56;&#125;&#123;&#49;&#53;&#125;&#92;&#100;&#105;&#118;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#50;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"53\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%;\">32. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-166e6e5d780d07143f3fe7a6e3d08197_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#49;&#50;&#125;&#92;&#100;&#105;&#118;&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#125;&#123;&#50;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"53\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Add or Subtract Fractions with Different Denominators<\/h2>\n<p id=\"fs-id1166422823699\">In the following exercises, add or subtract.<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 150px;\">\n<tbody>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">33. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-6f71038e1b7347ea04c72aa182593083_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;&#49;&#125;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"39\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">34. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-3a225f935d6ec3a01b21a540047d115c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"39\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">35. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-72db3c4e0dc507f57f23a4dbe30e587c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#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;&#49;&#125;&#123;&#57;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"73\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">36. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-17e6f18e0ef6ff36b24dac2a544acf99_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;&#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;&#49;&#125;&#123;&#56;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"73\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">37. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-3761fc84ed28bb37dd579629ebd40fa4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#49;&#50;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"46\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">38. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-fbeeb02dacde6a73cf793ac40500ed4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#49;&#50;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"46\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">39. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-fd65e6823ae3da23a8cd930d5a34929f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#49;&#50;&#125;&#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;&#49;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"57\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">40. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-db5941f5f3b56452b3491409efd88c49_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#49;&#54;&#125;&#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;&#49;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"57\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">41. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-52db211ccf24fb11fea74d224b5af97b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#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;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"43\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">42. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-d736eabaefd161a4158993f955266ac4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#54;&#125;&#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=\"43\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">43. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-163961d1e2dec65d4228878e48440021_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;&#49;&#125;&#123;&#51;&#48;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#55;&#125;&#123;&#52;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"72\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">44. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-6a75a03bb1572b2449017f13c3318588_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;&#48;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#55;&#125;&#123;&#51;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"72\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">45. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-afb3d588a419fccab61a8b4001d601ff_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;&#51;&#125;&#123;&#51;&#48;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#53;&#125;&#123;&#52;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"72\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">46. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-9b98064765a3fce5ba105b55b4dbd14d_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;&#51;&#125;&#123;&#51;&#48;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#52;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"72\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">47. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-0fd8e550425302dde5b84628dfdc7051_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;&#57;&#125;&#123;&#53;&#54;&#125;&#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;&#50;&#125;&#123;&#51;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"75\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">48. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-438a45b321272b92e4990fc7fd6b4361_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;&#51;&#125;&#123;&#52;&#57;&#125;&#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;&#56;&#125;&#123;&#51;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"75\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">49. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-4d12e3a377a05d612f94e379f9ab40d0_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;&#51;&#125;&#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;&#51;&#125;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"91\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">50. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-73be90179871970237e1805390ea52b2_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;&#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;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"91\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">51. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-d77f7c554d17d4df5063343153bf9c29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"38\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">52. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-ef8a32be6da92c1167e9f44b8b5d6b8a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#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;&#49;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"49\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">53. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-547878c7cc5378d93ad48fbd76d1128a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#120;&#125;&#123;&#51;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"40\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%;\">54. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-92ad8da1cf400f614e5c8720ae252515_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#121;&#125;&#123;&#50;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"40\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">55. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-795f4bf82424c4a51b7d1f54d7bb5431_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#121;&#125;&#123;&#52;&#125;&#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;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"43\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%;\">56. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-3e1b5ff99e3240d16ac68d62d22431c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#120;&#125;&#123;&#53;&#125;&#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=\"44\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Mixed Practice<\/h2>\n<p id=\"fs-id1166424777198\">In the following exercises, simplify.<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 136px;\">\n<tbody>\n<tr style=\"height: 31px;\">\n<td style=\"width: 50%; height: 31px;\">57. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-228b83f448836f295fa47aa09cad5c0c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"39\" style=\"vertical-align: -6px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-3209d2cdbb8a25550387e6786b2ab517_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#92;&#100;&#105;&#118;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"39\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%; height: 31px;\">58. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-ffa35961232357a9db846ba9d0a2ec00_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;&#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;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"61\" style=\"vertical-align: -6px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-8270fc02ae770146adddd449518d328f_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;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"49\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">59. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-93272737435c202711051be0be6d2236_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#110;&#125;&#123;&#54;&#125;&#92;&#100;&#105;&#118;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#56;&#125;&#123;&#49;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"55\" style=\"vertical-align: -6px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-f3d155308843f8e8a77f0791c17542a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#110;&#125;&#123;&#54;&#125;&#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;&#49;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"58\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">60. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-85aa9ceebbdb92c8e6353c32b487865a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#97;&#125;&#123;&#56;&#125;&#92;&#100;&#105;&#118;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#49;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"54\" style=\"vertical-align: -6px;\" \/> b) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-1d0b14f5b2eb6fd2c3458f653ad84ae6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#97;&#125;&#123;&#56;&#125;&#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;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"57\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">61. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-a3d8a27b9820cdb0bfe6c6ea41da6b89_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;&#56;&#125;&#92;&#100;&#105;&#118;&#32;&#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;&#51;&#125;&#123;&#49;&#48;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"98\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">62. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-89babdf702f01c98910e75111fd65831_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;&#49;&#50;&#125;&#92;&#100;&#105;&#118;&#32;&#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;&#53;&#125;&#123;&#57;&#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: 15px;\">\n<td style=\"width: 50%; height: 15px;\">63. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-d3f00ca50aa8d8e557ce9cd97fbf6ff5_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;&#56;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#49;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"65\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">64. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-08e36c1195453adcaf62eaac2d3b1ead_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;&#56;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#49;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"65\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">65. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-6a7666787e132466dd90368e7893cdd1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#54;&#125;&#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=\"43\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">66. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-63cedad922064e8ece50d4844d590762_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#57;&#125;&#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;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"43\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">67. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-f4e1d7b93f8daa8ce6d23edd69aadbd1_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;&#53;&#125;&#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;&#121;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"69\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">68. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-4dfb33dd1229cc11fba573ef31d70dbf_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;&#56;&#125;&#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;&#120;&#125;&#123;&#49;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"68\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">69. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-c93a957b90f8cec9123331f418957ab3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#49;&#125;&#123;&#49;&#50;&#97;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#97;&#125;&#123;&#49;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"53\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">70. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-cfa4a0098df756dc32ef2349aafb3a9f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#48;&#121;&#125;&#123;&#49;&#51;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#56;&#125;&#123;&#49;&#53;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"60\" style=\"vertical-align: -9px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div id=\"fs-id1170655105139\" data-type=\"exercise\">\n<h2>Use the Order of Operations to Simplify Complex Fractions<\/h2>\n<\/div>\n<p id=\"fs-id1166422535949\">In the following exercises, simplify.<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 135px;\">\n<tbody>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">71. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-be1026aca9c967c5cce21f485d31d43d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#50;&#125;&#94;&#123;&#51;&#125;&#43;&#123;&#52;&#125;&#94;&#123;&#50;&#125;&#125;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"38\" style=\"vertical-align: -17px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">72. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-b3d2c10af421c49ebb0b11e467bd2e44_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#51;&#125;&#94;&#123;&#51;&#125;&#45;&#123;&#51;&#125;&#94;&#123;&#50;&#125;&#125;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"38\" style=\"vertical-align: -17px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">73. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-c80ff79eaef92b28562ef658b96d519b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#125;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#55;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"31\" style=\"vertical-align: -17px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">74. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-92e891f77c7c26627f9af22a3a0660a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#125;&#123;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#56;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"43\" width=\"31\" style=\"vertical-align: -17px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">75. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-b3d97431c15fa015de7875b69677834a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"29\" width=\"31\" style=\"vertical-align: -13px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">76. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-3e2ac128f1a01bb0d57829bc7582c6da_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"29\" width=\"31\" style=\"vertical-align: -13px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">77. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-8acfa9306f6dc0e2c39909306238d67a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#56;&#125;&#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;&#51;&#125;&#125;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#56;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"34\" style=\"vertical-align: -13px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">78. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-77163b63aaee2d58de839f00467b01e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;&#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;&#53;&#125;&#125;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"34\" style=\"vertical-align: -13px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">79. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-fdf9e95f8653239f867c4b343e3f3889_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;&#50;&#125;&#123;&#51;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#49;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"70\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">80. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-39149defd1b7e6cf6ccbda0c5af2843a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#53;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"63\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">81. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-faf6722c5cc03ef51b6d813ccca6a02d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#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;&#53;&#125;&#92;&#100;&#105;&#118;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"81\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">82. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-62b6183d5e36f5ca92c3df3cfecace56_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#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;&#54;&#125;&#92;&#100;&#105;&#118;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"81\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">83. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-23eda9abb58c147517078a2d7f3330ca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#54;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"72\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">84. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-724c93d116e5e8016600019d8afad394_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"72\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">85. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-dd74590c155c710f3c6db2b4eb1ee083_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#56;&#125;&#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;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"75\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">86. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-df718ab7ea367b157b071fc152a9b773_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;&#56;&#125;&#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=\"75\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">87. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-0ac4942bc7e23f73ec46dcd7f9552458_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;&#57;&#125;&#123;&#50;&#48;&#125;&#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;&#49;&#53;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"94\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">88. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-c30f4da353e19a6fdb4e18bca62f9cc3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#53;&#125;&#123;&#49;&#54;&#125;&#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;&#54;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"80\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">89. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-9b455bd988d2cf00c93ebac991eddac2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#56;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#54;&#125;&#125;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#57;&#125;&#123;&#50;&#52;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"31\" style=\"vertical-align: -13px;\" \/><\/td>\n<td style=\"width: 50%;\">90. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-bcc9b4f7ba149db2b611849dbbb547aa_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;&#54;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#49;&#48;&#125;&#125;&#123;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#52;&#125;&#123;&#51;&#48;&#125;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"36\" width=\"37\" style=\"vertical-align: -13px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">91. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-17683a21083f694f33b21ab106c9714e_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;&#57;&#125;&#43;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#54;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#100;&#105;&#118;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;&#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=\"140\" style=\"vertical-align: -7px;\" \/><\/td>\n<td style=\"width: 50%;\">92. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-e5c3f0821d638ff24543584d6b465776_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;&#49;&#125;&#123;&#54;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#100;&#105;&#118;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#56;&#125;&#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=\"140\" style=\"vertical-align: -7px;\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div id=\"fs-id1170654962656\" data-type=\"exercise\">\n<h2>Evaluate Variable Expressions with Fractions<\/h2>\n<\/div>\n<p id=\"fs-id1166422832732\">In the following exercises, evaluate.<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 219px;\">\n<tbody>\n<tr style=\"height: 48px;\">\n<td style=\"width: 50%; height: 48px;\">93. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-96121496c1e69f7bb3be04437b6cf607_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#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;&#53;&#125;&#123;&#54;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"74\" style=\"vertical-align: -7px;\" \/> when<br \/>\na) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-78514cf19a88f6aa082b1691d66a1231_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"43\" style=\"vertical-align: -6px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-9bc1d16d9b1189bc83db1d1760dba398_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#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;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"60\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%; height: 48px;\">94. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-4f9de4306e3a9f5f93916971d1f14bde_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#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;&#49;&#125;&#123;&#49;&#50;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"81\" style=\"vertical-align: -7px;\" \/> when<br \/>\na) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-0e02e7fa8612df4f67bf18ee80369d42_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#49;&#125;&#123;&#49;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"50\" style=\"vertical-align: -6px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-4de0fe3714bba39f8c20c2f945369943_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"43\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 48px;\">\n<td style=\"width: 50%; height: 48px;\">95. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-ef97404372a1a5573f2e96e7f9cd5d01_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#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;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"44\" style=\"vertical-align: -6px;\" \/> when<br \/>\na) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-67489634248f2cd552ca3488a887c362_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"43\" style=\"vertical-align: -6px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-2e6256d2c3c4c7687f73dc63871d4e82_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#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;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"60\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%; height: 48px;\">96. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-4601ee656abf02c2b7fbd061d593a6d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#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;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"44\" style=\"vertical-align: -6px;\" \/> when<br \/>\na) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-e7855c05ce046d42cda6e99414761b9a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"43\" style=\"vertical-align: -6px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-c429e70b63ebf7552b5041ced24666d7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#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;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"60\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 48px;\">\n<td style=\"width: 50%; height: 48px;\">97. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-9b4d135858ae87202d2269564f564832_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#49;&#48;&#125;&#45;&#119;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"50\" style=\"vertical-align: -6px;\" \/> when<br \/>\na) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-c732109d5af67df1bb4a044c7e3d95b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#119;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"46\" style=\"vertical-align: -6px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-ce1a37d470944a1ad450387255b7e680_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#119;&#61;&#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;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"63\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%; height: 48px;\">98. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-524f7b7fe40018e25a513759202e0b72_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#49;&#50;&#125;&#45;&#119;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"50\" style=\"vertical-align: -6px;\" \/> when<br \/>\na) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-c6298d40e01de695946009dce8e0bd69_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#119;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"46\" style=\"vertical-align: -6px;\" \/><br \/>\nb) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-f106124dd9f351804c6d071915c0cea9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#119;&#61;&#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=\"63\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">99. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-5aae01cf511166b0e9702f54647bd575_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#123;&#120;&#125;&#94;&#123;&#50;&#125;&#123;&#121;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"43\" style=\"vertical-align: -4px;\" \/> when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-c429e70b63ebf7552b5041ced24666d7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;&#61;&#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;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"60\" style=\"vertical-align: -6px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-d86a31f87a08bdc4a51d7f150fbe3e33_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#121;&#61;&#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;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"59\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">100. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-3dfcec1a529ef20cfab3eaae47c5dc09_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#123;&#117;&#125;&#94;&#123;&#50;&#125;&#123;&#118;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"43\" style=\"vertical-align: 0px;\" \/> when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-3e7ad654e605791a3fd342b661c975d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#117;&#61;&#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=\"60\" style=\"vertical-align: -6px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-0122aeea664332f7a2fec7019974a916_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#118;&#61;&#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;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"59\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 15px;\">\n<td style=\"width: 50%; height: 15px;\">101. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-e89c61017117ec31ffa3c69b9f841ec8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#97;&#43;&#98;&#125;&#123;&#97;&#45;&#98;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"24\" style=\"vertical-align: -6px;\" \/> when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-83cf3457f730315f4c8700333c6bfaa3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#61;&#45;&#51;&#44;&#98;&#61;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"104\" style=\"vertical-align: -4px;\" \/><\/td>\n<td style=\"width: 50%; height: 15px;\">102. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-a28f836f3fe0753f0387c941b9cef606_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#114;&#45;&#115;&#125;&#123;&#114;&#43;&#115;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"24\" style=\"vertical-align: -8px;\" \/> when <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-2b0b6f159c184a47ea8bef677c57287b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;&#61;&#49;&#48;&#44;&#115;&#61;&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"112\" style=\"vertical-align: -4px;\" \/><\/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%;\">103. <strong data-effect=\"bold\">Decorating<\/strong> Laronda is making covers for the throw pillows on her sofa. For each pillow cover, she needs <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-f195e065543a0409dc26688061a95dfa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/> yard of print fabric and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-ba508161ffc38329f850dc9bd0734378_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/> yard of solid fabric. What is the total amount of fabric Laronda needs for each pillow cover?<\/td>\n<td style=\"width: 50%;\">104. <strong data-effect=\"bold\">Baking<\/strong> Samuel is baking chocolate chip cookies and oatmeal cookies. He needs <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-f195e065543a0409dc26688061a95dfa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/> cup of sugar for the chocolate chip cookies and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-524177610787b79d047426c5a01dd7c3_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;\" \/> of sugar for the oatmeal cookies. How much sugar does he need altogether?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Writing Exercises<\/h2>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">105. Why do you need a common denominator to add or subtract fractions? Explain.<\/td>\n<td style=\"width: 50%;\">106. How do you find the LCD of 2 fractions?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Answers:<\/h1>\n<table style=\"border-collapse: collapse; width: 100%; height: 255px;\">\n<tbody>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">1. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-3e2aef6091484c1a8e06a67997e0c8d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#49;&#125;&#123;&#49;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">3. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-8e8877de9071556d0e0859d30fee2a1f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#120;&#43;&#51;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"26\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">5. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-8bdd6017748466e9440e612d6eec7ec7_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;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">7. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-9b7bdfde796a29fd9150b021daa33612_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#49;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">9. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-2440b473db4e27c64fb3c55be69167c0_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;&#54;&#125;&#123;&#49;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"32\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">11. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-a4bbf576235d6f9ccb84d33b574c568a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#49;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">13. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-f195e065543a0409dc26688061a95dfa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">15. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-8261427e8542bfcd4b3ebe85fe624c98_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#55;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">17. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-4510629edb5312c71741708b16753571_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#121;&#45;&#55;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"32\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">19. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-95853ee456fa1f35009bd2034116b6b7_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;&#56;&#125;&#123;&#117;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"32\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">21. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-992211796ad85ddc4478983254f98dc3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">23. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-c29c1f1a84b20e2ee85d1226d3a71089_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;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"25\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">25. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-83504ded5ac8506e78eb50b2932e3822_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: 17px;\">27. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-d06122287dbca63249f16b539be8c53d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#110;&#45;&#52;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"26\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">29. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-64379e2fedd4157bfbeb3a6ce9ebbff2_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;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"32\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">31. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-30612f4e21b12bf1cac746a6f6611661_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#125;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">33. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-53569a5705b84dbafe83c8325eaf351d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#57;&#125;&#123;&#49;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">35. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-dcd5e483b3d567469c35395f262fabbf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#57;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">37. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-0dbdb290c4e07f8239d35d8d38b80f1b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#57;&#125;&#123;&#50;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">39. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-1d3eadaab8726d2986ad44f18a1a2747_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#52;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">41. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-f434b117c3e415f3c807df8e594aaa8e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#55;&#125;&#123;&#50;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">43. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-6fde41ab3f1b69d827a8853447ea1d2c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#55;&#125;&#123;&#49;&#50;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"21\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">45. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-a156de99b3581e89fa9d1f10d71353bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#55;&#125;&#123;&#49;&#48;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"21\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">47. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-08e8d230d48b3fcbe8d2815abec694a6_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;&#51;&#125;&#123;&#52;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"32\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">49. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-d164b40fad118f8774d4392110f2054a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#49;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">51. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-ca1205384ec67c10b8948e40ed14afcf_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#53;&#125;&#123;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">53. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-98a1aff668d7b00c2efe85d6a62517f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#120;&#43;&#51;&#125;&#123;&#49;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"33\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">55. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-71cc335b71d3fbeff331b1d4bc389ba8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#121;&#45;&#49;&#50;&#125;&#123;&#50;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"39\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">57. a)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-eba721ca6ffb58e7f25dd63b694886c6_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;\" \/>b) 4<\/td>\n<td style=\"width: 33.3333%; height: 17px;\">59. a)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-32c10d6c582bf4911cf20258417acac3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#53;&#110;&#125;&#123;&#49;&#54;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"23\" style=\"vertical-align: -6px;\" \/>b)<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-d5c77d1d840ffbcf3dda4fcd364ba305_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#53;&#110;&#45;&#49;&#54;&#125;&#123;&#51;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"47\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">61. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-da74a1bbe23c0e74bbcc63f82354d2ac_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">63. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-9bc28dd62d72933aa04468d117f8daad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#50;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">65. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-f58173e9f19e58637f1a8694b2c40c5a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#51;&#125;&#123;&#49;&#56;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">67. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-4eeaa0e40d0de994865389511ab8dcc5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#45;&#50;&#56;&#45;&#49;&#53;&#121;&#125;&#123;&#54;&#48;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"57\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">69. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-83d557cd7db42ab15517ac0c7ddfa72a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#51;&#51;&#125;&#123;&#54;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">71. 54<\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">73. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-70ac00d181a1ee76735432d6be64f468_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#57;&#125;&#123;&#50;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">75. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-1c10f01382705f327d8fdae72557a8d2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#53;&#125;&#123;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">77. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-12002bf3dcd3499c4979526a868c1000_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#53;&#125;&#123;&#50;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">79. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-069db88dc7641b704d71298cca9e099e_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;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">81. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-efe76bc57eb5e3ea989b840f9ca70719_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">83. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-aefce555fab7e188388f632d9b42bfb9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#57;&#125;&#123;&#49;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 17px;\">\n<td style=\"width: 33.3333%; height: 17px;\">85. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-c2e0b498ed46ac4017c3c8794d40955d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#50;&#51;&#125;&#123;&#50;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">87. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-a1c169f4db364f2c46d6c0d8f50a0631_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#49;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 33.3333%; height: 17px;\">89. 1<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">91. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-318e671832d58a46b1209d6965edefd7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#51;&#125;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"14\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 33.3333%;\">93. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-7c4a20df0a2e71b64a6e7dac3f4026e0_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;&#50;&#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\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-b80ba2734f70ff584d473cda66662853_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"21\" style=\"vertical-align: 0px;\" \/><\/td>\n<td style=\"width: 33.3333%;\">95. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-992211796ad85ddc4478983254f98dc3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#53;&#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\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-b80ba2734f70ff584d473cda66662853_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#45;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"21\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">97. a) <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-992211796ad85ddc4478983254f98dc3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#53;&#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\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-bdb98d4c50220cddc57f00add89fed87_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#102;&#114;&#97;&#99;&#123;&#54;&#125;&#123;&#53;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"7\" style=\"vertical-align: -6px;\" \/><\/td>\n<td style=\"width: 33.3333%;\">99. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-936d26e6a330cf408768682d14b56b85_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;\" \/><\/td>\n<td style=\"width: 33.3333%;\">101. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-5c8c58020fd4ce2e58e7b19c9d70f471_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;&#49;&#49;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"32\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 33.3333%;\">103. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-content\/ql-cache\/quicklatex.com-b80f1521ca2c098d3abf48ab21184644_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;\" \/> yard<\/td>\n<td style=\"width: 33.3333%;\">105. Answers may vary<\/td>\n<td style=\"width: 33.3333%;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Attributions<\/h1>\n<p>This chapter has been adapted from \u201cAdd and Subtract Fractions\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<p><!-- pb_fixme --><\/p>\n","protected":false},"author":103,"menu_order":2,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[60],"license":[],"class_list":["post-13043","chapter","type-chapter","status-publish","hentry","contributor-lynn-marecek"],"part":12991,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-json\/pressbooks\/v2\/chapters\/13043","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-json\/wp\/v2\/users\/103"}],"version-history":[{"count":9,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-json\/pressbooks\/v2\/chapters\/13043\/revisions"}],"predecessor-version":[{"id":13488,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-json\/pressbooks\/v2\/chapters\/13043\/revisions\/13488"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-json\/pressbooks\/v2\/parts\/12991"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-json\/pressbooks\/v2\/chapters\/13043\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-json\/wp\/v2\/media?parent=13043"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-json\/pressbooks\/v2\/chapter-type?post=13043"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-json\/wp\/v2\/contributor?post=13043"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/intermediatedevelopmentalmath\/wp-json\/wp\/v2\/license?post=13043"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}