{"id":100,"date":"2020-06-20T11:01:16","date_gmt":"2020-06-20T15:01:16","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/mathfortrades2clone\/chapter\/order-of-operations\/"},"modified":"2022-09-29T14:57:34","modified_gmt":"2022-09-29T18:57:34","slug":"order-of-operations","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/mathfortrades2clone\/chapter\/order-of-operations\/","title":{"raw":"Order of Operations","rendered":"Order of Operations"},"content":{"raw":"&nbsp;\n\nhttps:\/\/media.bccampus.ca\/id\/0_ufkbzxzk?width=608&amp;height=402&amp;playerId=23449753\n\nClick play on the following audio player to listen along as you read this section.\n\nhttps:\/\/media.bccampus.ca\/id\/0_clhe75vh?width=608&amp;height=402&amp;playerId=23449753\n\n<img class=\"alignleft wp-image-95\" src=\"https:\/\/pressbooks.bccampus.ca\/harpsample\/wp-content\/uploads\/sites\/1776\/2020\/06\/help-147419_1280-150x150.png\" alt=\"\" width=\"100\" height=\"100\">\n\nWhat does it mean when we talk about \"order of operations\" in math? Well the order of operations are a set of rules that need to be followed when dealing with math equations. Why do we need rules you ask? If there were no rules then you might end up with two different answers to the same math question.\n\nTake a look at the following equation and calculate what you think the answer would be.\n<p style=\"text-align: center;\">[latex]\\Large 5 + 4 \\times 3 = ? [\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\Large \\begin{array}{lrl}\\text{Option A} &amp; \\text{Start with:} &amp; 5 + 4 = 9 \\\\ &amp; \\text{Then:} &amp; 9 \\times 3 = 27 \\end{array}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\Large \\begin{array}{lrl} \\text{Option B}&amp; \\text{Start with:} &amp; 4 \\times 3 = 12 \\\\ &amp; \\text{Then:} &amp; 12 + 5 = 17 \\end{array} [\/latex]<\/p>\nThe idea here is that you can\u2019t have two answers for the same question. That just won\u2019t work in math. One of the two answers must be correct and in both options the actual math (by that I mean if you plugged the numbers into a calculator) is correct. No mistakes were made. The issue is that the order of operations in one of the options is wrong.\n<p style=\"text-align: left;\">And the correct answer is\u2026 Option B.<\/p>\nThe next question then becomes \"what are the rules to follow when dealing with equations?\"\n\nThis is where the term \"BEDMAS\" comes into play.\n<h1>Bedmas<\/h1>\n<img class=\"alignleft wp-image-96\" src=\"https:\/\/pressbooks.bccampus.ca\/harpsample\/wp-content\/uploads\/sites\/1776\/2022\/09\/business-1754904_1920.jpg\" alt=\"\" width=\"150\" height=\"47\">\n\nBedmas is an acronym used to identify the order of operations when dealing with math. When you have equations that use different operations such as addition, subtraction, multiplication, and division, BEDMAS sets out the order to do those calculations.\n\nThe example above shows us that having these guidelines will make sure that we don\u2019t get the wrong answer when working through math problems.\n\n<span class=\"big\">BEDMAS<\/span>\n<ul>\n \t<li><span class=\"big\">Brackets<\/span><\/li>\n \t<li><span class=\"big\">Exponents<\/span><\/li>\n \t<li><span class=\"big\">Division<\/span><\/li>\n \t<li><span class=\"big\">Multiplication<\/span><\/li>\n \t<li><span class=\"big\">Addition<\/span><\/li>\n \t<li><span class=\"big\">Subtraction<\/span><\/li>\n<\/ul>\nBedmas tells us the order of operations when performing calculations within an equation. For example we multiply before we add which in turn is done before we subtract.\n\nWe should all be familiar with division, multiplication, addition and subtraction at this point but what about dealing with brackets and exponents? What are they and how do they work?\n\nBrackets are the first order of business in Bedmas and look like the following:\n\n<img class=\"aligncenter wp-image-97 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/harpsample\/wp-content\/uploads\/sites\/1776\/2022\/09\/picture-3-e1611611514718.png\" alt=\"A left square bracket and a right square bracket.\" width=\"128\" height=\"67\">\n\nSometimes brackets can also be referred to as \"parenthesis\" and you may see the acronym PEDMAS used instead of BEDMAS. It means the same thing, and the symbol for parenthesis looks like the following:\n\n<img class=\" aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/harpsample\/wp-content\/uploads\/sites\/1776\/2022\/09\/picture-4-e1611611558394.png\" width=\"127\" height=\"72\">\n\nYou can look at brackets as a mechanism that is used to group numbers or symbols together. The calculations within the brackets (or parenthesis) are then the first to be done.\n\nFor example:\n<p style=\"text-align: center;\">[latex]\\Large \\text{Z} = 4 \\times 2 \\times (5 \\times 9) [\/latex]<\/p>\nThis situation would indicate the first calculation we perform is 5 \u00d7 9. Then we would work through the rest of the equation.\n\nExponents are the second order of operation in Bedmas. Have you ever looked at a math problem and seen the following?\n<p style=\"text-align: center;\">[latex]\\Large \\text{D} = 4 + 8 \\times 5 - 3 + {9}^{3} [\/latex]<\/p>\nWell the 9<sup>3<\/sup> is what we are talking about when dealing with exponents. Specifically we are dealing with the 3 portion.\n\nExponents tell you how many times you multiply a number by itself within an equation. In this case the 3 indicates that we multiply the 9 three times.\n<p style=\"text-align: center;\">[latex]\\Large {9}^{3} = 9 \\times 9 \\times 9 [\/latex]<\/p>\nWe can look at another example to see how exponents work.\n<p style=\"text-align: center;\">[latex]\\Large {5}^{6} = 5 \\times 5 \\times 5 \\times 5 \\times 5 \\times 5[\/latex]<\/p>\nAfter brackets and exponents we move onto dividing, multiplying, adding and subtracting.\n\nLet\u2019s we go through a couple of examples to see if you get the idea.\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Example<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<p style=\"text-align: center;\">[latex]\\Large\\text{A}=1+2\\times 6\\div 3[\/latex]<\/p>\nAlthough we won\u2019t include this in the steps to answer the question, the first thing you might want to do is write down Bedmas so you can refer to it visually.\n<ul>\n \t<li><strong>B<\/strong>rackets<\/li>\n \t<li><strong>E<\/strong>xponents<\/li>\n \t<li><strong>D<\/strong>ivision<\/li>\n \t<li><strong>M<\/strong>ultiplication<\/li>\n \t<li><strong>A<\/strong>ddition<\/li>\n \t<li><strong>S<\/strong>ubtraction<\/li>\n<\/ul>\n<strong>Step 1: <\/strong>There are no brackets in this equation and no exponents either. The first calculation we come to is division.\n<p style=\"text-align: center;\">[latex]\\Large \\begin{array}{c}\\text{A}=1+2\\times \\mathbf{6 \\div 3} \\\\ 6 \\div 3 = 2 \\\\ \\text{So now we have:} \\\\ \\text{A}=1+2 \\times 2 \\end{array}[\/latex]<\/p>\n<strong>Step 2: <\/strong>Move on to the next step in Bedmas which is multiplication.\n<p style=\"text-align: center;\">[latex]\\Large\\begin{array}{c} \\text{A} = 1+ \\mathbf{2\\times 2} \\\\ 2 \\times 2 = 4 \\\\ \\text{So now we have:} \\\\ \\text{A} = 1 + 4 \\end{array} [\/latex]<\/p>\n<strong>Step 3: <\/strong>We only have one more operation to go so we are nearing the end. Just add the one and four and we have our answer.\n<p style=\"text-align: center;\">[latex]\\Large \\begin{array}{c} \\text{A} = 1 + 4 \\\\ \\text{A} = 5 \\end{array} [\/latex]<\/p>\n\n<\/div>\n<\/div>\n<img class=\"alignleft\" style=\"font-size: 18.6667px; orphans: 1;\" src=\"https:\/\/pressbooks.bccampus.ca\/harpsample\/wp-content\/uploads\/sites\/1776\/2022\/09\/math-work-4711302_1920-e1619713950146.jpg\" width=\"150\" height=\"150\">\n\nYou can now see that if you didn\u2019t follow the rules for order of operations, things could get a little fuzzy. There might be a few different answers you could come up with. Could you imagine writing a multiple-choice math exam where every answer seems to be right depending on how you did the math?\n\nThis is the importance of BEDMAS!\n\nWe\u2019re probably at the point now where a few more examples are in order.\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Example<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nSolve for Y.\n<p style=\"text-align: center;\">[latex] \\Large \\text{Y} = (24+36) \\times 2 + {4}^{2} [\/latex]<\/p>\n<strong>Step 1:<\/strong> Refer to BEDMAS. Work through the brackets first.\n<p style=\"text-align: center;\">[latex]\\Large \\begin{array}{c} \\text{Y}=\\mathbf{(24+36)} \\times 2 + {4}^{2} \\\\ 24 + 36 = 60 \\\\ \\text{Y} = 60 \\times 2 +{4}^{2} \\end{array} [\/latex]<\/p>\n<strong>Step 2: <\/strong>Deal with the exponents next.\n<p style=\"text-align: center;\">[latex]\\Large \\begin{array}{c} \\text{Y} = 60 \\times 2 + \\mathbf{{4}^{2}} \\\\ {4}^{2} = 4 \\times 4 = 16 \\\\ \\text{Y} = 60 \\times 2 + 16 \\end{array}[\/latex]<\/p>\n<strong>Step 3: <\/strong>Work through the multiplying.\n<p style=\"text-align: center;\">[latex]\\Large \\begin{array}{c} \\text{Y}= \\mathbf{60 \\times 2} + 16 \\\\ 60 \\times 2 = 120 \\\\ \\text{Y} = 120 + 16 \\end{array}[\/latex]<\/p>\n<strong>Step 4: <\/strong>The last step in this question is to do the addition.\n<p style=\"text-align: center;\">[latex]\\Large \\begin{array}{c} \\text{Y} = 120 + 16 \\\\ \\text{Y} = 136 \\\\ \\text{Final Answer: Y} = 36 \\end{array} [\/latex]<\/p>\n\n<\/div>\n<\/div>\nOnce you go through a few questions and learn to work things out using Bedmas, working through any math equation or formula becomes routine. After a while, you will just naturally know the steps to take.\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Example<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nSolve for M.\n<p style=\"text-align: center;\">[latex]\\Large \\text{M} = {17}^{2} \\times 24 + 13 + 7 \\times (45 \\div 5)[\/latex]<\/p>\n<strong>Step 1: <\/strong>Work through the brackets first.\n<p style=\"text-align: center;\">[latex]\\Large \\begin{array}{c} \\text{M} = {17}^{2} \\times 24 + 13 + 7 \\times \\mathbf{(45 \\div 5) }\\\\ 45 \\div 5 = 9 \\\\ \\text{M} = {17}^{2} \\times 24 + 13 + 7 \\times 9 \\end{array} [\/latex]<\/p>\n<strong>Step 2: <\/strong>Deal with the exponents next.\n<p style=\"text-align: center;\">[latex]\\Large \\begin{array}{c} \\text{M} = \\mathbf{{17}^{2}} \\times 24 + 13 + 7 \\times (45 \\div 5) \\\\ {17}^{2} = 17 \\times 17 = 289 \\\\ \\text{M} = 289 \\times 24 + 13 + 7 \\times 9 \\end{array} [\/latex]<\/p>\n<strong>Step 3: <\/strong>Work through the multiplying.\n<p style=\"text-align: center;\">[latex]\\Large \\begin{array}{c} \\text{M} = \\mathbf{289 \\times 24} + 13 + \\mathbf{7 \\times 9} \\\\ 289 \\times 24 = 6936 \\\\ 7 \\times 9 = 63 \\\\ \\text{M} = 6939 + 13 + 63 \\end{array} [\/latex]<\/p>\n<strong>Step 4: <\/strong>Complete the addition.\n<p style=\"text-align: center;\">[latex]\\Large \\begin{array}{c} \\text{M} = 6939 + 13 + 63 \\\\ \\text{M} = 7012 \\\\ \\text{Final Answer: M} = 7012 \\end{array}[\/latex]<\/p>\n\n<\/div>\n<\/div>\n<h1>Practice Questions<\/h1>\nTry a couple practice questions for yourself and check the video answers to see how you did.\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Question 1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nSolve for D.\n<p style=\"text-align: center;\">[latex]\\Large \\text{D} = 5 + 6 \\div 2 \\times 7 + {4}^{3} \\times (5+7)[\/latex]<\/p>\nhttps:\/\/media.bccampus.ca\/id\/0_imotk2cq?width=608&amp;height=402&amp;playerId=23449753\n\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Question 2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nSolve for R.\n<p style=\"text-align: center;\">[latex]\\Large \\text{M} = 17 + (6\\times 3) + {5}^{2} \\div 5 - 22[\/latex]<\/p>\nhttps:\/\/media.bccampus.ca\/id\/0_087vbnme?width=608&amp;height=402&amp;playerId=23449753\n\n<\/div>\n<\/div>","rendered":"<p>&nbsp;<\/p>\n<p>https:\/\/media.bccampus.ca\/id\/0_ufkbzxzk?width=608&#38;height=402&#38;playerId=23449753<\/p>\n<p>Click play on the following audio player to listen along as you read this section.<\/p>\n<p><iframe loading=\"lazy\" id=\"kaltura_player\" title=\"2.9 Order of Operations\" src=\"https:\/\/api.ca.kaltura.com\/p\/148\/sp\/14800\/embedIframeJs\/uiconf_id\/23449753\/partner_id\/148?iframeembed=true&#38;playerId=kaltura_player&#38;entry_id=0_clhe75vh&#38;flashvars[leadWithHTML5]=true&#38;flashvars[streamerType]=auto&#38;flashvars[localizationCode]=en&#38;flashvars[sideBarContainer.plugin]=true&#38;flashvars[sideBarContainer.position]=left&#38;flashvars[sideBarContainer.clickToClose]=true&#38;flashvars[chapters.plugin]=true&#38;flashvars[chapters.layout]=vertical&#38;flashvars[chapters.thumbnailRotator]=false&#38;flashvars[streamSelector.plugin]=true&#38;flashvars[EmbedPlayer.SpinnerTarget]=videoHolder&#38;flashvars[dualScreen.plugin]=true&#38;flashvars[Kaltura.addCrossoriginToIframe]=true&#38;wid=0_ux78snb4\" width=\"608\" height=\"402\" allowfullscreen=\"allowfullscreen\" sandbox=\"allow-downloads allow-forms allow-same-origin allow-scripts allow-top-navigation allow-pointer-lock allow-popups allow-modals allow-orientation-lock allow-popups-to-escape-sandbox allow-presentation allow-top-navigation-by-user-activation\" frameborder=\"0\"><\/iframe><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft wp-image-95\" src=\"https:\/\/pressbooks.bccampus.ca\/harpsample\/wp-content\/uploads\/sites\/1776\/2020\/06\/help-147419_1280-150x150.png\" alt=\"\" width=\"100\" height=\"100\" srcset=\"https:\/\/pressbooks.bccampus.ca\/mathfortrades2clone\/wp-content\/uploads\/sites\/1776\/2020\/06\/help-147419_1280-150x150.png 150w, https:\/\/pressbooks.bccampus.ca\/mathfortrades2clone\/wp-content\/uploads\/sites\/1776\/2020\/06\/help-147419_1280-300x300.png 300w, https:\/\/pressbooks.bccampus.ca\/mathfortrades2clone\/wp-content\/uploads\/sites\/1776\/2020\/06\/help-147419_1280-1024x1024.png 1024w, https:\/\/pressbooks.bccampus.ca\/mathfortrades2clone\/wp-content\/uploads\/sites\/1776\/2020\/06\/help-147419_1280-768x768.png 768w, https:\/\/pressbooks.bccampus.ca\/mathfortrades2clone\/wp-content\/uploads\/sites\/1776\/2020\/06\/help-147419_1280-65x65.png 65w, https:\/\/pressbooks.bccampus.ca\/mathfortrades2clone\/wp-content\/uploads\/sites\/1776\/2020\/06\/help-147419_1280-225x225.png 225w, https:\/\/pressbooks.bccampus.ca\/mathfortrades2clone\/wp-content\/uploads\/sites\/1776\/2020\/06\/help-147419_1280-350x350.png 350w, https:\/\/pressbooks.bccampus.ca\/mathfortrades2clone\/wp-content\/uploads\/sites\/1776\/2020\/06\/help-147419_1280.png 1280w\" sizes=\"auto, (max-width: 100px) 100vw, 100px\" \/><\/p>\n<p>What does it mean when we talk about &#8220;order of operations&#8221; in math? Well the order of operations are a set of rules that need to be followed when dealing with math equations. Why do we need rules you ask? If there were no rules then you might end up with two different answers to the same math question.<\/p>\n<p>Take a look at the following equation and calculate what you think the answer would be.<\/p>\n<p style=\"text-align: center;\">[latex]\\Large 5 + 4 \\times 3 = ?[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\Large \\begin{array}{lrl}\\text{Option A} & \\text{Start with:} & 5 + 4 = 9 \\\\ & \\text{Then:} & 9 \\times 3 = 27 \\end{array}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\Large \\begin{array}{lrl} \\text{Option B}& \\text{Start with:} & 4 \\times 3 = 12 \\\\ & \\text{Then:} & 12 + 5 = 17 \\end{array}[\/latex]<\/p>\n<p>The idea here is that you can\u2019t have two answers for the same question. That just won\u2019t work in math. One of the two answers must be correct and in both options the actual math (by that I mean if you plugged the numbers into a calculator) is correct. No mistakes were made. The issue is that the order of operations in one of the options is wrong.<\/p>\n<p style=\"text-align: left;\">And the correct answer is\u2026 Option B.<\/p>\n<p>The next question then becomes &#8220;what are the rules to follow when dealing with equations?&#8221;<\/p>\n<p>This is where the term &#8220;BEDMAS&#8221; comes into play.<\/p>\n<h1>Bedmas<\/h1>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft wp-image-96\" src=\"https:\/\/pressbooks.bccampus.ca\/harpsample\/wp-content\/uploads\/sites\/1776\/2022\/09\/business-1754904_1920.jpg\" alt=\"\" width=\"150\" height=\"47\" srcset=\"https:\/\/pressbooks.bccampus.ca\/mathfortrades2clone\/wp-content\/uploads\/sites\/1776\/2022\/09\/business-1754904_1920.jpg 1920w, https:\/\/pressbooks.bccampus.ca\/mathfortrades2clone\/wp-content\/uploads\/sites\/1776\/2022\/09\/business-1754904_1920-300x94.jpg 300w, https:\/\/pressbooks.bccampus.ca\/mathfortrades2clone\/wp-content\/uploads\/sites\/1776\/2022\/09\/business-1754904_1920-1024x320.jpg 1024w, https:\/\/pressbooks.bccampus.ca\/mathfortrades2clone\/wp-content\/uploads\/sites\/1776\/2022\/09\/business-1754904_1920-768x240.jpg 768w, https:\/\/pressbooks.bccampus.ca\/mathfortrades2clone\/wp-content\/uploads\/sites\/1776\/2022\/09\/business-1754904_1920-1536x480.jpg 1536w, https:\/\/pressbooks.bccampus.ca\/mathfortrades2clone\/wp-content\/uploads\/sites\/1776\/2022\/09\/business-1754904_1920-65x20.jpg 65w, https:\/\/pressbooks.bccampus.ca\/mathfortrades2clone\/wp-content\/uploads\/sites\/1776\/2022\/09\/business-1754904_1920-225x70.jpg 225w, https:\/\/pressbooks.bccampus.ca\/mathfortrades2clone\/wp-content\/uploads\/sites\/1776\/2022\/09\/business-1754904_1920-350x109.jpg 350w\" sizes=\"auto, (max-width: 150px) 100vw, 150px\" \/><\/p>\n<p>Bedmas is an acronym used to identify the order of operations when dealing with math. When you have equations that use different operations such as addition, subtraction, multiplication, and division, BEDMAS sets out the order to do those calculations.<\/p>\n<p>The example above shows us that having these guidelines will make sure that we don\u2019t get the wrong answer when working through math problems.<\/p>\n<p><span class=\"big\">BEDMAS<\/span><\/p>\n<ul>\n<li><span class=\"big\">Brackets<\/span><\/li>\n<li><span class=\"big\">Exponents<\/span><\/li>\n<li><span class=\"big\">Division<\/span><\/li>\n<li><span class=\"big\">Multiplication<\/span><\/li>\n<li><span class=\"big\">Addition<\/span><\/li>\n<li><span class=\"big\">Subtraction<\/span><\/li>\n<\/ul>\n<p>Bedmas tells us the order of operations when performing calculations within an equation. For example we multiply before we add which in turn is done before we subtract.<\/p>\n<p>We should all be familiar with division, multiplication, addition and subtraction at this point but what about dealing with brackets and exponents? What are they and how do they work?<\/p>\n<p>Brackets are the first order of business in Bedmas and look like the following:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-97 size-full\" src=\"https:\/\/pressbooks.bccampus.ca\/harpsample\/wp-content\/uploads\/sites\/1776\/2022\/09\/picture-3-e1611611514718.png\" alt=\"A left square bracket and a right square bracket.\" width=\"128\" height=\"67\" srcset=\"https:\/\/pressbooks.bccampus.ca\/mathfortrades2clone\/wp-content\/uploads\/sites\/1776\/2022\/09\/picture-3-e1611611514718.png 128w, https:\/\/pressbooks.bccampus.ca\/mathfortrades2clone\/wp-content\/uploads\/sites\/1776\/2022\/09\/picture-3-e1611611514718-65x34.png 65w\" sizes=\"auto, (max-width: 128px) 100vw, 128px\" \/><\/p>\n<p>Sometimes brackets can also be referred to as &#8220;parenthesis&#8221; and you may see the acronym PEDMAS used instead of BEDMAS. It means the same thing, and the symbol for parenthesis looks like the following:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/harpsample\/wp-content\/uploads\/sites\/1776\/2022\/09\/picture-4-e1611611558394.png\" width=\"127\" height=\"72\" alt=\"image\" \/><\/p>\n<p>You can look at brackets as a mechanism that is used to group numbers or symbols together. The calculations within the brackets (or parenthesis) are then the first to be done.<\/p>\n<p>For example:<\/p>\n<p style=\"text-align: center;\">[latex]\\Large \\text{Z} = 4 \\times 2 \\times (5 \\times 9)[\/latex]<\/p>\n<p>This situation would indicate the first calculation we perform is 5 \u00d7 9. Then we would work through the rest of the equation.<\/p>\n<p>Exponents are the second order of operation in Bedmas. Have you ever looked at a math problem and seen the following?<\/p>\n<p style=\"text-align: center;\">[latex]\\Large \\text{D} = 4 + 8 \\times 5 - 3 + {9}^{3}[\/latex]<\/p>\n<p>Well the 9<sup>3<\/sup> is what we are talking about when dealing with exponents. Specifically we are dealing with the 3 portion.<\/p>\n<p>Exponents tell you how many times you multiply a number by itself within an equation. In this case the 3 indicates that we multiply the 9 three times.<\/p>\n<p style=\"text-align: center;\">[latex]\\Large {9}^{3} = 9 \\times 9 \\times 9[\/latex]<\/p>\n<p>We can look at another example to see how exponents work.<\/p>\n<p style=\"text-align: center;\">[latex]\\Large {5}^{6} = 5 \\times 5 \\times 5 \\times 5 \\times 5 \\times 5[\/latex]<\/p>\n<p>After brackets and exponents we move onto dividing, multiplying, adding and subtracting.<\/p>\n<p>Let\u2019s we go through a couple of examples to see if you get the idea.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p style=\"text-align: center;\">[latex]\\Large\\text{A}=1+2\\times 6\\div 3[\/latex]<\/p>\n<p>Although we won\u2019t include this in the steps to answer the question, the first thing you might want to do is write down Bedmas so you can refer to it visually.<\/p>\n<ul>\n<li><strong>B<\/strong>rackets<\/li>\n<li><strong>E<\/strong>xponents<\/li>\n<li><strong>D<\/strong>ivision<\/li>\n<li><strong>M<\/strong>ultiplication<\/li>\n<li><strong>A<\/strong>ddition<\/li>\n<li><strong>S<\/strong>ubtraction<\/li>\n<\/ul>\n<p><strong>Step 1: <\/strong>There are no brackets in this equation and no exponents either. The first calculation we come to is division.<\/p>\n<p style=\"text-align: center;\">[latex]\\Large \\begin{array}{c}\\text{A}=1+2\\times \\mathbf{6 \\div 3} \\\\ 6 \\div 3 = 2 \\\\ \\text{So now we have:} \\\\ \\text{A}=1+2 \\times 2 \\end{array}[\/latex]<\/p>\n<p><strong>Step 2: <\/strong>Move on to the next step in Bedmas which is multiplication.<\/p>\n<p style=\"text-align: center;\">[latex]\\Large\\begin{array}{c} \\text{A} = 1+ \\mathbf{2\\times 2} \\\\ 2 \\times 2 = 4 \\\\ \\text{So now we have:} \\\\ \\text{A} = 1 + 4 \\end{array}[\/latex]<\/p>\n<p><strong>Step 3: <\/strong>We only have one more operation to go so we are nearing the end. Just add the one and four and we have our answer.<\/p>\n<p style=\"text-align: center;\">[latex]\\Large \\begin{array}{c} \\text{A} = 1 + 4 \\\\ \\text{A} = 5 \\end{array}[\/latex]<\/p>\n<\/div>\n<\/div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft\" style=\"font-size: 18.6667px; orphans: 1;\" src=\"https:\/\/pressbooks.bccampus.ca\/harpsample\/wp-content\/uploads\/sites\/1776\/2022\/09\/math-work-4711302_1920-e1619713950146.jpg\" width=\"150\" height=\"150\" alt=\"image\" \/><\/p>\n<p>You can now see that if you didn\u2019t follow the rules for order of operations, things could get a little fuzzy. There might be a few different answers you could come up with. Could you imagine writing a multiple-choice math exam where every answer seems to be right depending on how you did the math?<\/p>\n<p>This is the importance of BEDMAS!<\/p>\n<p>We\u2019re probably at the point now where a few more examples are in order.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Solve for Y.<\/p>\n<p style=\"text-align: center;\">[latex]\\Large \\text{Y} = (24+36) \\times 2 + {4}^{2}[\/latex]<\/p>\n<p><strong>Step 1:<\/strong> Refer to BEDMAS. Work through the brackets first.<\/p>\n<p style=\"text-align: center;\">[latex]\\Large \\begin{array}{c} \\text{Y}=\\mathbf{(24+36)} \\times 2 + {4}^{2} \\\\ 24 + 36 = 60 \\\\ \\text{Y} = 60 \\times 2 +{4}^{2} \\end{array}[\/latex]<\/p>\n<p><strong>Step 2: <\/strong>Deal with the exponents next.<\/p>\n<p style=\"text-align: center;\">[latex]\\Large \\begin{array}{c} \\text{Y} = 60 \\times 2 + \\mathbf{{4}^{2}} \\\\ {4}^{2} = 4 \\times 4 = 16 \\\\ \\text{Y} = 60 \\times 2 + 16 \\end{array}[\/latex]<\/p>\n<p><strong>Step 3: <\/strong>Work through the multiplying.<\/p>\n<p style=\"text-align: center;\">[latex]\\Large \\begin{array}{c} \\text{Y}= \\mathbf{60 \\times 2} + 16 \\\\ 60 \\times 2 = 120 \\\\ \\text{Y} = 120 + 16 \\end{array}[\/latex]<\/p>\n<p><strong>Step 4: <\/strong>The last step in this question is to do the addition.<\/p>\n<p style=\"text-align: center;\">[latex]\\Large \\begin{array}{c} \\text{Y} = 120 + 16 \\\\ \\text{Y} = 136 \\\\ \\text{Final Answer: Y} = 36 \\end{array}[\/latex]<\/p>\n<\/div>\n<\/div>\n<p>Once you go through a few questions and learn to work things out using Bedmas, working through any math equation or formula becomes routine. After a while, you will just naturally know the steps to take.<\/p>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Solve for M.<\/p>\n<p style=\"text-align: center;\">[latex]\\Large \\text{M} = {17}^{2} \\times 24 + 13 + 7 \\times (45 \\div 5)[\/latex]<\/p>\n<p><strong>Step 1: <\/strong>Work through the brackets first.<\/p>\n<p style=\"text-align: center;\">[latex]\\Large \\begin{array}{c} \\text{M} = {17}^{2} \\times 24 + 13 + 7 \\times \\mathbf{(45 \\div 5) }\\\\ 45 \\div 5 = 9 \\\\ \\text{M} = {17}^{2} \\times 24 + 13 + 7 \\times 9 \\end{array}[\/latex]<\/p>\n<p><strong>Step 2: <\/strong>Deal with the exponents next.<\/p>\n<p style=\"text-align: center;\">[latex]\\Large \\begin{array}{c} \\text{M} = \\mathbf{{17}^{2}} \\times 24 + 13 + 7 \\times (45 \\div 5) \\\\ {17}^{2} = 17 \\times 17 = 289 \\\\ \\text{M} = 289 \\times 24 + 13 + 7 \\times 9 \\end{array}[\/latex]<\/p>\n<p><strong>Step 3: <\/strong>Work through the multiplying.<\/p>\n<p style=\"text-align: center;\">[latex]\\Large \\begin{array}{c} \\text{M} = \\mathbf{289 \\times 24} + 13 + \\mathbf{7 \\times 9} \\\\ 289 \\times 24 = 6936 \\\\ 7 \\times 9 = 63 \\\\ \\text{M} = 6939 + 13 + 63 \\end{array}[\/latex]<\/p>\n<p><strong>Step 4: <\/strong>Complete the addition.<\/p>\n<p style=\"text-align: center;\">[latex]\\Large \\begin{array}{c} \\text{M} = 6939 + 13 + 63 \\\\ \\text{M} = 7012 \\\\ \\text{Final Answer: M} = 7012 \\end{array}[\/latex]<\/p>\n<\/div>\n<\/div>\n<h1>Practice Questions<\/h1>\n<p>Try a couple practice questions for yourself and check the video answers to see how you did.<\/p>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Question 1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Solve for D.<\/p>\n<p style=\"text-align: center;\">[latex]\\Large \\text{D} = 5 + 6 \\div 2 \\times 7 + {4}^{3} \\times (5+7)[\/latex]<\/p>\n<p><iframe loading=\"lazy\" id=\"kaltura_player\" title=\"Order of Operations #1\" src=\"https:\/\/api.ca.kaltura.com\/p\/148\/sp\/14800\/embedIframeJs\/uiconf_id\/23449753\/partner_id\/148?iframeembed=true&#38;playerId=kaltura_player&#38;entry_id=0_imotk2cq&#38;flashvars[leadWithHTML5]=true&#38;flashvars[streamerType]=auto&#38;flashvars[localizationCode]=en&#38;flashvars[sideBarContainer.plugin]=true&#38;flashvars[sideBarContainer.position]=left&#38;flashvars[sideBarContainer.clickToClose]=true&#38;flashvars[chapters.plugin]=true&#38;flashvars[chapters.layout]=vertical&#38;flashvars[chapters.thumbnailRotator]=false&#38;flashvars[streamSelector.plugin]=true&#38;flashvars[EmbedPlayer.SpinnerTarget]=videoHolder&#38;flashvars[dualScreen.plugin]=true&#38;flashvars[Kaltura.addCrossoriginToIframe]=true&#38;wid=0_fuzupmrg\" width=\"608\" height=\"402\" allowfullscreen=\"allowfullscreen\" sandbox=\"allow-downloads allow-forms allow-same-origin allow-scripts allow-top-navigation allow-pointer-lock allow-popups allow-modals allow-orientation-lock allow-popups-to-escape-sandbox allow-presentation allow-top-navigation-by-user-activation\" frameborder=\"0\"><\/iframe><\/p>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Question 2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Solve for R.<\/p>\n<p style=\"text-align: center;\">[latex]\\Large \\text{M} = 17 + (6\\times 3) + {5}^{2} \\div 5 - 22[\/latex]<\/p>\n<p><iframe loading=\"lazy\" id=\"kaltura_player\" title=\"Order of Operations #2\" src=\"https:\/\/api.ca.kaltura.com\/p\/148\/sp\/14800\/embedIframeJs\/uiconf_id\/23449753\/partner_id\/148?iframeembed=true&#38;playerId=kaltura_player&#38;entry_id=0_087vbnme&#38;flashvars[leadWithHTML5]=true&#38;flashvars[streamerType]=auto&#38;flashvars[localizationCode]=en&#38;flashvars[sideBarContainer.plugin]=true&#38;flashvars[sideBarContainer.position]=left&#38;flashvars[sideBarContainer.clickToClose]=true&#38;flashvars[chapters.plugin]=true&#38;flashvars[chapters.layout]=vertical&#38;flashvars[chapters.thumbnailRotator]=false&#38;flashvars[streamSelector.plugin]=true&#38;flashvars[EmbedPlayer.SpinnerTarget]=videoHolder&#38;flashvars[dualScreen.plugin]=true&#38;flashvars[Kaltura.addCrossoriginToIframe]=true&#38;wid=0_kgzciubt\" width=\"608\" height=\"402\" allowfullscreen=\"allowfullscreen\" sandbox=\"allow-downloads allow-forms allow-same-origin allow-scripts allow-top-navigation allow-pointer-lock allow-popups allow-modals allow-orientation-lock allow-popups-to-escape-sandbox allow-presentation allow-top-navigation-by-user-activation\" frameborder=\"0\"><\/iframe><\/p>\n<\/div>\n<\/div>\n","protected":false},"author":940,"menu_order":2,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-100","chapter","type-chapter","status-publish","hentry"],"part":92,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/mathfortrades2clone\/wp-json\/pressbooks\/v2\/chapters\/100","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/mathfortrades2clone\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/mathfortrades2clone\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/mathfortrades2clone\/wp-json\/wp\/v2\/users\/940"}],"version-history":[{"count":1,"href":"https:\/\/pressbooks.bccampus.ca\/mathfortrades2clone\/wp-json\/pressbooks\/v2\/chapters\/100\/revisions"}],"predecessor-version":[{"id":101,"href":"https:\/\/pressbooks.bccampus.ca\/mathfortrades2clone\/wp-json\/pressbooks\/v2\/chapters\/100\/revisions\/101"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/mathfortrades2clone\/wp-json\/pressbooks\/v2\/parts\/92"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/mathfortrades2clone\/wp-json\/pressbooks\/v2\/chapters\/100\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/mathfortrades2clone\/wp-json\/wp\/v2\/media?parent=100"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/mathfortrades2clone\/wp-json\/pressbooks\/v2\/chapter-type?post=100"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/mathfortrades2clone\/wp-json\/wp\/v2\/contributor?post=100"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/mathfortrades2clone\/wp-json\/wp\/v2\/license?post=100"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}