{"id":477,"date":"2016-11-14T18:50:02","date_gmt":"2016-11-14T18:50:02","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/?post_type=chapter&#038;p=477"},"modified":"2019-05-30T16:28:02","modified_gmt":"2019-05-30T16:28:02","slug":"percents","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/chapter\/percents\/","title":{"raw":"Percents","rendered":"Percents"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Given the part and the whole, write a percent<\/li>\r\n \t<li>Calculate both relative\u00a0and absolute change of a quantity<\/li>\r\n \t<li>Calculate tax on a purchase<\/li>\r\n<\/ul>\r\n<\/div>\r\nIn the 2004 vice-presidential debates, Democratic contender John Edwards claimed that\u00a0US forces have suffered \"90% of the coalition casualties\" in Iraq. Incumbent Vice President Dick Cheney disputed this, saying that in fact Iraqi security forces and coalition allies \"have taken almost 50 percent\" of the casualties.[footnote]<a href=\"http:\/\/www.factcheck.org\/cheney_edwards_mangle_facts.html\" target=\"_blank\" rel=\"noopener\">http:\/\/www.factcheck.org\/cheney_edwards_mangle_facts.html<\/a>[\/footnote]\r\n\r\nWho was\u00a0correct? How can we make sense of these numbers?\r\n\r\n<strong>Percent <\/strong>literally means \u201cper 100,\u201d or \u201cparts per hundred.\u201d When we write 40%, this is equivalent to the fraction [latex]\\displaystyle\\frac{40}{100}[\/latex] or the decimal 0.40. Notice that 80 out of 200 and 10 out of 25 are also 40%, since [latex]\\displaystyle\\frac{80}{200}=\\frac{10}{25}=\\frac{40}{100}[\/latex].\r\n\r\n[caption id=\"attachment_494\" align=\"aligncenter\" width=\"500\"]<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/14203900\/percent-40844_1280.png\"><img class=\"wp-image-494\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/14203900\/percent-40844_1280.png\" alt=\"Rounded rectangle divided into ten vertical sections. The left four are shaded yellow, while the right 6 are empty.\" width=\"500\" height=\"282\" \/><\/a> A visual depiction of 40%[\/caption]\r\n\r\n<div class=\"textbox\">\r\n<h3>Percent<\/h3>\r\nIf we have a <em>part<\/em> that is some <em>percent<\/em> of a <em>whole<\/em>, then\u00a0[latex]\\displaystyle\\text{percent}=\\frac{\\text{part}}{\\text{whole}}[\/latex], or equivalently, [latex]\\text{part}\\cdot\\text{whole}=\\text{percent}[\/latex].\r\n\r\nTo do the calculations, we write the percent as a decimal.\r\n\r\nFor a refresher on basic percentage rules, using the examples on this page, view the following video.\r\n\r\nhttps:\/\/youtu.be\/Z229RysttR8\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Examples<\/h3>\r\nIn a survey, 243 out of 400 people state that they like dogs. What percent is this?\r\n[reveal-answer q=\"987171\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"987171\"]\r\n\r\n[latex]\\displaystyle\\frac{243}{400}=0.6075=\\frac{60.75}{100}[\/latex] This is 60.75%.\r\n\r\nNotice that the percent can be found from the equivalent decimal by moving the decimal point two places to the right.\r\n\r\n[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nWrite each as a percent:\r\n<ol>\r\n \t<li>[latex]\\displaystyle\\frac{1}{4}[\/latex]<\/li>\r\n \t<li>0.02<\/li>\r\n \t<li>2.35<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"660805\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"660805\"]\r\n<ol>\r\n \t<li>[latex]\\displaystyle\\frac{1}{4}=0.25[\/latex] = 25%<\/li>\r\n \t<li>0.02 = 2%<\/li>\r\n \t<li>2.35 = 235%<\/li>\r\n<\/ol>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\nThroughout this text, you will be given opportunities to answer questions and know immediately whether you answered correctly. To answer the question below, do the calculation on a separate piece of paper and enter your answer in the box. Click on the submit button , and if you are correct, a green box will appear around your answer. \u00a0If you are incorrect, a red box will appear. \u00a0You can click on \"Try Another Version of This Question\" as many times as you like. Practice all you want!\r\n\r\n<iframe id=\"mom1\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=17441&amp;theme=oea&amp;iframe_resize_id=mom1\" width=\"100%\" height=\"350\"><\/iframe>\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nIn the news, you hear \u201ctuition is expected to increase by 7% next year.\u201d If tuition this year was $1200 per quarter, what will it be next year?\r\n[reveal-answer q=\"475615\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"475615\"]The tuition next year will be the current tuition plus an additional 7%, so it will be 107% of this year\u2019s tuition:\u00a0$1200(1.07) = $1284.\r\n\r\nAlternatively, we could have first calculated 7% of $1200: $1200(0.07) = $84.\r\n\r\nNotice this is not the expected tuition for next year (we could only wish). Instead, this is the expected increase, so to calculate the expected tuition, we\u2019ll need to add this change to the previous year\u2019s tuition:\u00a0$1200 + $84 = $1284.[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n<iframe id=\"mom2\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=17447&amp;theme=oea&amp;iframe_resize_id=mom2\" width=\"100%\" height=\"350\"><\/iframe>\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nThe value of a car dropped from $7400 to $6800 over the last year. What percent decrease is this?\r\n[reveal-answer q=\"573833\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"573833\"]\r\n\r\nTo compute the percent change, we first need to find the dollar value change: $6800 \u2013\u00a0$7400 = \u2013$600. Often we will take the absolute value of this amount, which is called the <strong>absolute change<\/strong>: |\u2013600| = 600.\r\n\r\nSince we are computing the decrease relative to the starting value, we compute this percent out of $7400:\r\n\r\n[latex]\\displaystyle\\frac{600}{7400}=0.081=[\/latex] 8.1% decrease. This is called a <strong>relative change<\/strong>.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox\">\r\n<h3>Absolute and Relative Change<\/h3>\r\nGiven two quantities,\r\n\r\nAbsolute change =[latex]\\displaystyle|\\text{ending quantity}-\\text{starting quantity}|[\/latex]\r\n\r\nRelative change: [latex]\\displaystyle\\frac{\\text{absolute change}}{\\text{starting quantity}}[\/latex]\r\n<ul>\r\n \t<li>Absolute change has the same units as the original quantity.<\/li>\r\n \t<li>Relative change gives a percent change.<\/li>\r\n<\/ul>\r\nThe starting quantity is called the <strong>base<\/strong> of the percent change.\r\n\r\nFor a deeper dive on absolute and relative change, using the examples on this page, view the following video.\r\n\r\nhttps:\/\/youtu.be\/QjVeurkg8CQ\r\n\r\n<\/div>\r\nThe base of a percent is very important. For example, while Nixon was president, it was argued that marijuana was a \u201cgateway\u201d drug, claiming that 80% of marijuana smokers went on to use harder drugs like cocaine. The problem is, this isn\u2019t true. The true claim is that 80% of harder drug users first smoked marijuana. The difference is one of base: 80% of marijuana smokers using hard drugs, vs. 80% of hard drug users having smoked marijuana. These numbers are not equivalent. As it turns out, only one in 2,400 marijuana users actually go on to use harder drugs.[footnote]<a href=\"http:\/\/tvtropes.org\/pmwiki\/pmwiki.php\/Main\/LiesDamnedLiesAndStatistics\" target=\"_blank\" rel=\"noopener\">http:\/\/tvtropes.org\/pmwiki\/pmwiki.php\/Main\/LiesDamnedLiesAndStatistics<\/a>[\/footnote]\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nThere are about 75 QFC supermarkets in the United States. Albertsons has about 215 stores. Compare the size of the two companies.\r\n[reveal-answer q=\"933757\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"933757\"]\r\n\r\nWhen we make comparisons, we must ask first whether an absolute or relative comparison. The absolute difference is 215 \u2013 75 = 140. From this, we could say \u201cAlbertsons has 140 more stores than QFC.\u201d However, if you wrote this in an article or paper, that number does not mean much. The relative difference may be more meaningful. There are two different relative changes we could calculate, depending on which store we use as the base:\r\n\r\nUsing QFC as the base, [latex]\\displaystyle\\frac{140}{75}=1.867[\/latex].\r\n\r\nThis tells us Albertsons is 186.7% larger than QFC.\r\n\r\nUsing Albertsons as the base,[latex]\\displaystyle\\frac{140}{215}=0.651[\/latex].\r\n\r\nThis tells us QFC is 65.1% smaller than Albertsons.\r\n\r\nNotice both of these are showing percent <em>differences<\/em>. We could also calculate the size of Albertsons relative to QFC:[latex]\\displaystyle\\frac{215}{75}=2.867[\/latex], which tells us Albertsons is 2.867 times the size of QFC. Likewise, we could calculate the size of QFC relative to Albertsons:[latex]\\displaystyle\\frac{75}{215}=0.349[\/latex], which tells us that QFC is 34.9% of the size of Albertsons.\r\n\r\n[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nSuppose a stock drops in value by 60% one week, then increases in value the next week by 75%. Is the value higher or lower than where it started?\r\n[reveal-answer q=\"568319\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"568319\"]\r\n\r\nTo answer this question, suppose the value started at $100. After one week, the value dropped by 60%:\u00a0$100 \u2013 $100(0.60) = $100 \u2013 $60 = $40.\r\n\r\nIn the next week, notice that base of the percent has changed to the new value, $40. Computing the 75% increase:\u00a0$40 + $40(0.75) = $40 + $30 = $70.\r\n\r\nIn the end, the stock is still $30 lower, or [latex]\\displaystyle\\frac{\\$30}{100}[\/latex] = 30% lower, valued than it started.\r\n\r\n[\/hidden-answer]\r\n\r\nA video walk-through of this example can be seen here.\r\n\r\nhttps:\/\/youtu.be\/4HNxwYMTNl8\r\n\r\n<\/div>\r\nConsideration of the base of percentages is explored in this video, using the examples on this page.\r\n\r\nhttps:\/\/youtu.be\/nygw69JqwoQ\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n<iframe id=\"mom3\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=17443&amp;theme=oea&amp;iframe_resize_id=mom3\" width=\"100%\" height=\"350\"><\/iframe>\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nA <em>Seattle Times<\/em> article on high school graduation rates reported \u201cThe number of schools graduating 60 percent or fewer students in four years\u2014sometimes referred to as 'dropout factories'\u2014decreased by 17 during that time period. The number of kids attending schools with such low graduation rates was cut in half.\u201d\r\n<ol>\r\n \t<li>Is the \u201cdecreased by 17\u201d number a useful comparison?<\/li>\r\n \t<li>Considering the last sentence, can we conclude that the number of \u201cdropout factories\u201d was originally 34?<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"713382\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"713382\"]\r\n<ol>\r\n \t<li>This number is hard to evaluate, since we have no basis for judging whether this is a larger or small change. If the number of \u201cdropout factories\u201d dropped from 20 to 3, that\u2019d be a very significant change, but if the number dropped from 217 to 200, that\u2019d be less of an improvement.<\/li>\r\n \t<li>The last sentence provides relative change, which helps put the first sentence in perspective. We can estimate that the number of \u201cdropout factories\u201d was probably previously around 34. However, it\u2019s possible that students simply moved schools rather than the school improving, so that estimate might not be fully accurate.<\/li>\r\n<\/ol>\r\n[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nLet's return to the example at the top of this page. In the 2004 vice-presidential debates, Democratic candidate John Edwards claimed that\u00a0US forces have suffered \"90% of the coalition casualties\" in Iraq. Cheney disputed this, saying that in fact Iraqi security forces and coalition allies \"have taken almost 50 percent\" of the casualties. Who is correct?\r\n[reveal-answer q=\"908531\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"908531\"]Without more information, it is hard for us to judge who is correct, but we can easily conclude that these two percents are talking about different things, so one does not necessarily contradict the other. Edward\u2019s claim was a percent with coalition forces as the base of the percent, while Cheney\u2019s claim was a percent with both coalition and Iraqi security forces as the base of the percent. It turns out both statistics are in fact fairly accurate.[\/hidden-answer]\r\n\r\nA detailed explanation of these examples can be viewed here.\r\n\r\nhttps:\/\/youtu.be\/Svlu2Lurmsc\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox shaded\">\r\n<h3>Think About It<\/h3>\r\nIn the 2012 presidential elections, one candidate argued that \u201cthe president\u2019s plan will cut $716 billion from Medicare, leading to fewer services for seniors,\u201d while the other candidate rebuts that \u201cour plan does not cut current spending and actually expands benefits for seniors, while implementing cost saving measures.\u201d Are these claims in conflict, in agreement, or not comparable because they\u2019re talking about different things?\r\n<p class=\"p1\"><span class=\"s1\">[practice-area rows=\"8\"][\/practice-area]<\/span><\/p>\r\n\r\n<\/div>\r\n<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/14201133\/industrial-safety-1492046.png\"><img class=\"alignleft wp-image-492\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/14201133\/industrial-safety-1492046.png\" alt=\"Yellow triangle sign of black exclamation mark\" width=\"95\" height=\"85\" \/><\/a>We\u2019ll wrap up our review of percents with a couple cautions. First, when talking about a change of quantities that are already measured in percents, we have to be careful in how we describe the change.\r\n\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nA politician\u2019s support increases from 40% of voters to 50% of voters. Describe the change.\r\n[reveal-answer q=\"27288\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"27288\"]\r\n\r\nWe could describe this using an absolute change: [latex]|50\\%-40\\%|=10\\%[\/latex]. Notice that since the original quantities were percents, this change also has the units of percent. In this case, it is best to describe this as an increase of 10 <strong>percentage points<\/strong>.\r\n\r\nIn contrast, we could compute the percent change:[latex]\\displaystyle\\frac{10\\%}{40\\%}=0.25=25\\%[\/latex] increase. This is the relative change, and we\u2019d say the politician\u2019s support has increased by 25%.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nLastly, a caution against averaging percents.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nA basketball player scores on 40% of 2-point field goal attempts, and on 30% of 3-point of field goal attempts. Find the player\u2019s overall field goal percentage.\r\n\r\n[reveal-answer q=\"831091\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"831091\"]It is very tempting to average these values, and claim the overall average is 35%, but this is likely not correct, since most players make many more 2-point attempts than 3-point attempts. We don\u2019t actually have enough information to answer the question. Suppose the player attempted 200 2-point field goals and 100 3-point field goals. Then that player\u00a0made 200(0.40) = 80 2-point shots and 100(0.30) = 30 3-point shots. Overall, they player made 110 shots out of 300, for a [latex]\\displaystyle\\frac{110}{300}=0.367=36.7\\%[\/latex] overall field goal percentage.[\/hidden-answer]\r\n\r\n<\/div>\r\nFor more information about these cautionary tales using percentages, view the following.\r\n\r\nhttps:\/\/youtu.be\/vtgEkQUB5F8","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Given the part and the whole, write a percent<\/li>\n<li>Calculate both relative\u00a0and absolute change of a quantity<\/li>\n<li>Calculate tax on a purchase<\/li>\n<\/ul>\n<\/div>\n<p>In the 2004 vice-presidential debates, Democratic contender John Edwards claimed that\u00a0US forces have suffered &#8220;90% of the coalition casualties&#8221; in Iraq. Incumbent Vice President Dick Cheney disputed this, saying that in fact Iraqi security forces and coalition allies &#8220;have taken almost 50 percent&#8221; of the casualties.<a class=\"footnote\" title=\"http:\/\/www.factcheck.org\/cheney_edwards_mangle_facts.html\" id=\"return-footnote-477-1\" href=\"#footnote-477-1\" aria-label=\"Footnote 1\"><sup class=\"footnote\">[1]<\/sup><\/a><\/p>\n<p>Who was\u00a0correct? How can we make sense of these numbers?<\/p>\n<p><strong>Percent <\/strong>literally means \u201cper 100,\u201d or \u201cparts per hundred.\u201d When we write 40%, this is equivalent to the fraction [latex]\\displaystyle\\frac{40}{100}[\/latex] or the decimal 0.40. Notice that 80 out of 200 and 10 out of 25 are also 40%, since [latex]\\displaystyle\\frac{80}{200}=\\frac{10}{25}=\\frac{40}{100}[\/latex].<\/p>\n<div id=\"attachment_494\" style=\"width: 510px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/14203900\/percent-40844_1280.png\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-494\" class=\"wp-image-494\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/14203900\/percent-40844_1280.png\" alt=\"Rounded rectangle divided into ten vertical sections. The left four are shaded yellow, while the right 6 are empty.\" width=\"500\" height=\"282\" \/><\/a><\/p>\n<p id=\"caption-attachment-494\" class=\"wp-caption-text\">A visual depiction of 40%<\/p>\n<\/div>\n<div class=\"textbox\">\n<h3>Percent<\/h3>\n<p>If we have a <em>part<\/em> that is some <em>percent<\/em> of a <em>whole<\/em>, then\u00a0[latex]\\displaystyle\\text{percent}=\\frac{\\text{part}}{\\text{whole}}[\/latex], or equivalently, [latex]\\text{part}\\cdot\\text{whole}=\\text{percent}[\/latex].<\/p>\n<p>To do the calculations, we write the percent as a decimal.<\/p>\n<p>For a refresher on basic percentage rules, using the examples on this page, view the following video.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Review of basic percents\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/Z229RysttR8?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Examples<\/h3>\n<p>In a survey, 243 out of 400 people state that they like dogs. What percent is this?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q987171\">Show Solution<\/span><\/p>\n<div id=\"q987171\" class=\"hidden-answer\" style=\"display: none\">\n<p>[latex]\\displaystyle\\frac{243}{400}=0.6075=\\frac{60.75}{100}[\/latex] This is 60.75%.<\/p>\n<p>Notice that the percent can be found from the equivalent decimal by moving the decimal point two places to the right.<\/p>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Write each as a percent:<\/p>\n<ol>\n<li>[latex]\\displaystyle\\frac{1}{4}[\/latex]<\/li>\n<li>0.02<\/li>\n<li>2.35<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q660805\">Show Solution<\/span><\/p>\n<div id=\"q660805\" class=\"hidden-answer\" style=\"display: none\">\n<ol>\n<li>[latex]\\displaystyle\\frac{1}{4}=0.25[\/latex] = 25%<\/li>\n<li>0.02 = 2%<\/li>\n<li>2.35 = 235%<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p>Throughout this text, you will be given opportunities to answer questions and know immediately whether you answered correctly. To answer the question below, do the calculation on a separate piece of paper and enter your answer in the box. Click on the submit button , and if you are correct, a green box will appear around your answer. \u00a0If you are incorrect, a red box will appear. \u00a0You can click on &#8220;Try Another Version of This Question&#8221; as many times as you like. Practice all you want!<\/p>\n<p><iframe loading=\"lazy\" id=\"mom1\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=17441&amp;theme=oea&amp;iframe_resize_id=mom1\" width=\"100%\" height=\"350\"><\/iframe><\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>In the news, you hear \u201ctuition is expected to increase by 7% next year.\u201d If tuition this year was $1200 per quarter, what will it be next year?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q475615\">Show Solution<\/span><\/p>\n<div id=\"q475615\" class=\"hidden-answer\" style=\"display: none\">The tuition next year will be the current tuition plus an additional 7%, so it will be 107% of this year\u2019s tuition:\u00a0$1200(1.07) = $1284.<\/p>\n<p>Alternatively, we could have first calculated 7% of $1200: $1200(0.07) = $84.<\/p>\n<p>Notice this is not the expected tuition for next year (we could only wish). Instead, this is the expected increase, so to calculate the expected tuition, we\u2019ll need to add this change to the previous year\u2019s tuition:\u00a0$1200 + $84 = $1284.<\/p><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"mom2\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=17447&amp;theme=oea&amp;iframe_resize_id=mom2\" width=\"100%\" height=\"350\"><\/iframe><\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>The value of a car dropped from $7400 to $6800 over the last year. What percent decrease is this?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q573833\">Show Solution<\/span><\/p>\n<div id=\"q573833\" class=\"hidden-answer\" style=\"display: none\">\n<p>To compute the percent change, we first need to find the dollar value change: $6800 \u2013\u00a0$7400 = \u2013$600. Often we will take the absolute value of this amount, which is called the <strong>absolute change<\/strong>: |\u2013600| = 600.<\/p>\n<p>Since we are computing the decrease relative to the starting value, we compute this percent out of $7400:<\/p>\n<p>[latex]\\displaystyle\\frac{600}{7400}=0.081=[\/latex] 8.1% decrease. This is called a <strong>relative change<\/strong>.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox\">\n<h3>Absolute and Relative Change<\/h3>\n<p>Given two quantities,<\/p>\n<p>Absolute change =[latex]\\displaystyle|\\text{ending quantity}-\\text{starting quantity}|[\/latex]<\/p>\n<p>Relative change: [latex]\\displaystyle\\frac{\\text{absolute change}}{\\text{starting quantity}}[\/latex]<\/p>\n<ul>\n<li>Absolute change has the same units as the original quantity.<\/li>\n<li>Relative change gives a percent change.<\/li>\n<\/ul>\n<p>The starting quantity is called the <strong>base<\/strong> of the percent change.<\/p>\n<p>For a deeper dive on absolute and relative change, using the examples on this page, view the following video.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Absolute and Relative Differences\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/QjVeurkg8CQ?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<\/div>\n<p>The base of a percent is very important. For example, while Nixon was president, it was argued that marijuana was a \u201cgateway\u201d drug, claiming that 80% of marijuana smokers went on to use harder drugs like cocaine. The problem is, this isn\u2019t true. The true claim is that 80% of harder drug users first smoked marijuana. The difference is one of base: 80% of marijuana smokers using hard drugs, vs. 80% of hard drug users having smoked marijuana. These numbers are not equivalent. As it turns out, only one in 2,400 marijuana users actually go on to use harder drugs.<a class=\"footnote\" title=\"http:\/\/tvtropes.org\/pmwiki\/pmwiki.php\/Main\/LiesDamnedLiesAndStatistics\" id=\"return-footnote-477-2\" href=\"#footnote-477-2\" aria-label=\"Footnote 2\"><sup class=\"footnote\">[2]<\/sup><\/a><\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>There are about 75 QFC supermarkets in the United States. Albertsons has about 215 stores. Compare the size of the two companies.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q933757\">Show Solution<\/span><\/p>\n<div id=\"q933757\" class=\"hidden-answer\" style=\"display: none\">\n<p>When we make comparisons, we must ask first whether an absolute or relative comparison. The absolute difference is 215 \u2013 75 = 140. From this, we could say \u201cAlbertsons has 140 more stores than QFC.\u201d However, if you wrote this in an article or paper, that number does not mean much. The relative difference may be more meaningful. There are two different relative changes we could calculate, depending on which store we use as the base:<\/p>\n<p>Using QFC as the base, [latex]\\displaystyle\\frac{140}{75}=1.867[\/latex].<\/p>\n<p>This tells us Albertsons is 186.7% larger than QFC.<\/p>\n<p>Using Albertsons as the base,[latex]\\displaystyle\\frac{140}{215}=0.651[\/latex].<\/p>\n<p>This tells us QFC is 65.1% smaller than Albertsons.<\/p>\n<p>Notice both of these are showing percent <em>differences<\/em>. We could also calculate the size of Albertsons relative to QFC:[latex]\\displaystyle\\frac{215}{75}=2.867[\/latex], which tells us Albertsons is 2.867 times the size of QFC. Likewise, we could calculate the size of QFC relative to Albertsons:[latex]\\displaystyle\\frac{75}{215}=0.349[\/latex], which tells us that QFC is 34.9% of the size of Albertsons.<\/p>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Suppose a stock drops in value by 60% one week, then increases in value the next week by 75%. Is the value higher or lower than where it started?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q568319\">Show Solution<\/span><\/p>\n<div id=\"q568319\" class=\"hidden-answer\" style=\"display: none\">\n<p>To answer this question, suppose the value started at $100. After one week, the value dropped by 60%:\u00a0$100 \u2013 $100(0.60) = $100 \u2013 $60 = $40.<\/p>\n<p>In the next week, notice that base of the percent has changed to the new value, $40. Computing the 75% increase:\u00a0$40 + $40(0.75) = $40 + $30 = $70.<\/p>\n<p>In the end, the stock is still $30 lower, or [latex]\\displaystyle\\frac{\\$30}{100}[\/latex] = 30% lower, valued than it started.<\/p>\n<\/div>\n<\/div>\n<p>A video walk-through of this example can be seen here.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-3\" title=\"Combining percents\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/4HNxwYMTNl8?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<\/div>\n<p>Consideration of the base of percentages is explored in this video, using the examples on this page.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-4\" title=\"Importance of base in percents\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/nygw69JqwoQ?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"mom3\" class=\"resizable\" src=\"https:\/\/www.myopenmath.com\/multiembedq.php?id=17443&amp;theme=oea&amp;iframe_resize_id=mom3\" width=\"100%\" height=\"350\"><\/iframe><\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>A <em>Seattle Times<\/em> article on high school graduation rates reported \u201cThe number of schools graduating 60 percent or fewer students in four years\u2014sometimes referred to as &#8216;dropout factories&#8217;\u2014decreased by 17 during that time period. The number of kids attending schools with such low graduation rates was cut in half.\u201d<\/p>\n<ol>\n<li>Is the \u201cdecreased by 17\u201d number a useful comparison?<\/li>\n<li>Considering the last sentence, can we conclude that the number of \u201cdropout factories\u201d was originally 34?<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q713382\">Show Solution<\/span><\/p>\n<div id=\"q713382\" class=\"hidden-answer\" style=\"display: none\">\n<ol>\n<li>This number is hard to evaluate, since we have no basis for judging whether this is a larger or small change. If the number of \u201cdropout factories\u201d dropped from 20 to 3, that\u2019d be a very significant change, but if the number dropped from 217 to 200, that\u2019d be less of an improvement.<\/li>\n<li>The last sentence provides relative change, which helps put the first sentence in perspective. We can estimate that the number of \u201cdropout factories\u201d was probably previously around 34. However, it\u2019s possible that students simply moved schools rather than the school improving, so that estimate might not be fully accurate.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Let&#8217;s return to the example at the top of this page. In the 2004 vice-presidential debates, Democratic candidate John Edwards claimed that\u00a0US forces have suffered &#8220;90% of the coalition casualties&#8221; in Iraq. Cheney disputed this, saying that in fact Iraqi security forces and coalition allies &#8220;have taken almost 50 percent&#8221; of the casualties. Who is correct?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q908531\">Show Solution<\/span><\/p>\n<div id=\"q908531\" class=\"hidden-answer\" style=\"display: none\">Without more information, it is hard for us to judge who is correct, but we can easily conclude that these two percents are talking about different things, so one does not necessarily contradict the other. Edward\u2019s claim was a percent with coalition forces as the base of the percent, while Cheney\u2019s claim was a percent with both coalition and Iraqi security forces as the base of the percent. It turns out both statistics are in fact fairly accurate.<\/div>\n<\/div>\n<p>A detailed explanation of these examples can be viewed here.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-5\" title=\"Evaluating claims involving percents\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/Svlu2Lurmsc?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox shaded\">\n<h3>Think About It<\/h3>\n<p>In the 2012 presidential elections, one candidate argued that \u201cthe president\u2019s plan will cut $716 billion from Medicare, leading to fewer services for seniors,\u201d while the other candidate rebuts that \u201cour plan does not cut current spending and actually expands benefits for seniors, while implementing cost saving measures.\u201d Are these claims in conflict, in agreement, or not comparable because they\u2019re talking about different things?<\/p>\n<p class=\"p1\"><span class=\"s1\"><textarea aria-label=\"Your Answer\" rows=\"8\"><\/textarea><\/span><\/p>\n<\/div>\n<p><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/14201133\/industrial-safety-1492046.png\"><img loading=\"lazy\" decoding=\"async\" class=\"alignleft wp-image-492\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/1141\/2016\/11\/14201133\/industrial-safety-1492046.png\" alt=\"Yellow triangle sign of black exclamation mark\" width=\"95\" height=\"85\" \/><\/a>We\u2019ll wrap up our review of percents with a couple cautions. First, when talking about a change of quantities that are already measured in percents, we have to be careful in how we describe the change.<\/p>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>A politician\u2019s support increases from 40% of voters to 50% of voters. Describe the change.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q27288\">Show Solution<\/span><\/p>\n<div id=\"q27288\" class=\"hidden-answer\" style=\"display: none\">\n<p>We could describe this using an absolute change: [latex]|50\\%-40\\%|=10\\%[\/latex]. Notice that since the original quantities were percents, this change also has the units of percent. In this case, it is best to describe this as an increase of 10 <strong>percentage points<\/strong>.<\/p>\n<p>In contrast, we could compute the percent change:[latex]\\displaystyle\\frac{10\\%}{40\\%}=0.25=25\\%[\/latex] increase. This is the relative change, and we\u2019d say the politician\u2019s support has increased by 25%.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>Lastly, a caution against averaging percents.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>A basketball player scores on 40% of 2-point field goal attempts, and on 30% of 3-point of field goal attempts. Find the player\u2019s overall field goal percentage.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q831091\">Show Solution<\/span><\/p>\n<div id=\"q831091\" class=\"hidden-answer\" style=\"display: none\">It is very tempting to average these values, and claim the overall average is 35%, but this is likely not correct, since most players make many more 2-point attempts than 3-point attempts. We don\u2019t actually have enough information to answer the question. Suppose the player attempted 200 2-point field goals and 100 3-point field goals. Then that player\u00a0made 200(0.40) = 80 2-point shots and 100(0.30) = 30 3-point shots. Overall, they player made 110 shots out of 300, for a [latex]\\displaystyle\\frac{110}{300}=0.367=36.7\\%[\/latex] overall field goal percentage.<\/div>\n<\/div>\n<\/div>\n<p>For more information about these cautionary tales using percentages, view the following.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-6\" title=\"Percentage points and averaging percents\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/vtgEkQUB5F8?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-477\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Revision and Adaptation. <strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Problem Solving. <strong>Authored by<\/strong>: David Lippman. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/www.opentextbookstore.com\/mathinsociety\/\">http:\/\/www.opentextbookstore.com\/mathinsociety\/<\/a>. <strong>Project<\/strong>: Math in Society. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/\">CC BY-SA: Attribution-ShareAlike<\/a><\/em><\/li><li>Caution sign. <strong>Authored by<\/strong>: JDDesign. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/pixabay.com\/en\/industrial-safety-signal-symbol-1492046\/\">https:\/\/pixabay.com\/en\/industrial-safety-signal-symbol-1492046\/<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/about\/cc0\">CC0: No Rights Reserved<\/a><\/em><\/li><li>40% shaded rectangle. <strong>Authored by<\/strong>: Clker-Free-Vector-Images. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/pixabay.com\/en\/percent-40-bar-progress-meter-40844\/\">https:\/\/pixabay.com\/en\/percent-40-bar-progress-meter-40844\/<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/about\/cc0\">CC0: No Rights Reserved<\/a><\/em><\/li><li>Review of basic percents. <strong>Authored by<\/strong>: OCLPhase2&#039;s channel. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/Z229RysttR8\">https:\/\/youtu.be\/Z229RysttR8<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Absolute and Relative Differences. <strong>Authored by<\/strong>: OCLPhase2&#039;s channel. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/QjVeurkg8CQ\">https:\/\/youtu.be\/QjVeurkg8CQ<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Importance of base in percents. <strong>Authored by<\/strong>: OCLPhase2&#039;s channel. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/nygw69JqwoQ\">https:\/\/youtu.be\/nygw69JqwoQ<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Combining percents. <strong>Authored by<\/strong>: OCLPhase2&#039;s channel. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/4HNxwYMTNl8\">https:\/\/youtu.be\/4HNxwYMTNl8<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Evaluating claims involving percents. <strong>Authored by<\/strong>: OCLPhase2&#039;s channel. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/Svlu2Lurmsc\">https:\/\/youtu.be\/Svlu2Lurmsc<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Percentage points and averaging percents. <strong>Authored by<\/strong>: OCLPhase2&#039;s channel. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/vtgEkQUB5F8\">https:\/\/youtu.be\/vtgEkQUB5F8<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Question ID 17441, 17447, 17443. <strong>Authored by<\/strong>: Lippman, David. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: IMathAS Community License CC-BY + GPL<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section><hr class=\"before-footnotes clear\" \/><div class=\"footnotes\"><ol><li id=\"footnote-477-1\"><a href=\"http:\/\/www.factcheck.org\/cheney_edwards_mangle_facts.html\" target=\"_blank\" rel=\"noopener\">http:\/\/www.factcheck.org\/cheney_edwards_mangle_facts.html<\/a> <a href=\"#return-footnote-477-1\" class=\"return-footnote\" aria-label=\"Return to footnote 1\">&crarr;<\/a><\/li><li id=\"footnote-477-2\"><a href=\"http:\/\/tvtropes.org\/pmwiki\/pmwiki.php\/Main\/LiesDamnedLiesAndStatistics\" target=\"_blank\" rel=\"noopener\">http:\/\/tvtropes.org\/pmwiki\/pmwiki.php\/Main\/LiesDamnedLiesAndStatistics<\/a> <a href=\"#return-footnote-477-2\" class=\"return-footnote\" aria-label=\"Return to footnote 2\">&crarr;<\/a><\/li><\/ol><\/div>","protected":false},"author":19,"menu_order":3,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Problem Solving\",\"author\":\"David Lippman\",\"organization\":\"\",\"url\":\"http:\/\/www.opentextbookstore.com\/mathinsociety\/\",\"project\":\"Math in Society\",\"license\":\"cc-by-sa\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Caution sign\",\"author\":\"JDDesign\",\"organization\":\"\",\"url\":\"https:\/\/pixabay.com\/en\/industrial-safety-signal-symbol-1492046\/\",\"project\":\"\",\"license\":\"cc0\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"40% shaded rectangle\",\"author\":\"Clker-Free-Vector-Images\",\"organization\":\"\",\"url\":\"https:\/\/pixabay.com\/en\/percent-40-bar-progress-meter-40844\/\",\"project\":\"\",\"license\":\"cc0\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Review of basic percents\",\"author\":\"OCLPhase2\\'s channel\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/Z229RysttR8\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Absolute and Relative Differences\",\"author\":\"OCLPhase2\\'s channel\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/QjVeurkg8CQ\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Importance of base in percents\",\"author\":\"OCLPhase2\\'s channel\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/nygw69JqwoQ\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Combining percents\",\"author\":\"OCLPhase2\\'s channel\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/4HNxwYMTNl8\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Evaluating claims involving percents\",\"author\":\"OCLPhase2\\'s channel\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/Svlu2Lurmsc\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Percentage points and averaging percents\",\"author\":\"OCLPhase2\\'s channel\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/vtgEkQUB5F8\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Question ID 17441, 17447, 17443\",\"author\":\"Lippman, David\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"IMathAS Community License CC-BY + GPL\"},{\"type\":\"original\",\"description\":\"Revision and Adaptation\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"17b09601-9d36-4cc6-9fdf-954c6c740864","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-477","chapter","type-chapter","status-publish","hentry"],"part":35,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/pressbooks\/v2\/chapters\/477","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/wp\/v2\/users\/19"}],"version-history":[{"count":29,"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/pressbooks\/v2\/chapters\/477\/revisions"}],"predecessor-version":[{"id":2946,"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/pressbooks\/v2\/chapters\/477\/revisions\/2946"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/pressbooks\/v2\/parts\/35"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/pressbooks\/v2\/chapters\/477\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/wp\/v2\/media?parent=477"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/pressbooks\/v2\/chapter-type?post=477"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/wp\/v2\/contributor?post=477"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/waymakermath4libarts\/wp-json\/wp\/v2\/license?post=477"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}