{"id":4663,"date":"2023-06-19T13:57:03","date_gmt":"2023-06-19T13:57:03","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/?post_type=chapter&#038;p=4663"},"modified":"2025-08-29T20:58:36","modified_gmt":"2025-08-29T20:58:36","slug":"general-problem-solving-background-youll-need-3","status":"web-only","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/chapter\/general-problem-solving-background-youll-need-3\/","title":{"raw":"General Problem Solving: Background You'll Need 3","rendered":"General Problem Solving: Background You&#8217;ll Need 3"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li>Multiply and Divide Fractions<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Multiply Fractions<\/h2>\r\n<p>There are many times when it is necessary to multiply fractions. A model may help you understand multiplication of fractions.<\/p>\r\n<p>When you multiply a fraction by a fraction, you are finding a \u201cfraction of a fraction.\u201d Suppose you have [latex]\\frac{3}{4}[\/latex]\u00a0of a candy bar and you want to find [latex]\\frac{1}{2}[\/latex]\u00a0of the [latex]\\frac{3}{4}[\/latex]:<\/p>\r\n<center>\r\n[caption id=\"\" align=\"aligncenter\" width=\"208\"]<img id=\"Picture 24\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1468\/2016\/03\/17170708\/image109.gif\" alt=\"3 out of four boxes are shaded. This is 3\/4.\" width=\"208\" height=\"65\" \/> Figure 1. 3\/4 of a candy bar[\/caption]\r\n<\/center>\r\n<p>&nbsp;<\/p>\r\n<p>By dividing each fourth in half, you can divide the candy bar into eighths.<\/p>\r\n<center>\r\n[caption id=\"\" align=\"aligncenter\" width=\"208\"]<img id=\"Picture 25\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1468\/2016\/03\/17170709\/image110.gif\" alt=\"Six of 8 boxes are shaded. This is 6\/8.\" width=\"208\" height=\"62\" \/> Figure 2. 6\/8 of a candy bar[\/caption]\r\n<\/center>\r\n<p>&nbsp;<\/p>\r\n<p>Then, choose half of those to get [latex]\\frac{3}{8}[\/latex].<\/p>\r\n<center>\r\n[caption id=\"\" align=\"aligncenter\" width=\"208\"]<img id=\"Picture 27\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1468\/2016\/03\/17170711\/image112.gif\" alt=\"Six of 8 boxes are shaded, and of those six, three of them are shaded purple. The 3 purple boxes represent 3\/8.\" width=\"208\" height=\"54\" \/> Figure 3. 3\/8 of a candy bar[\/caption]\r\n<\/center>\r\n<p>&nbsp;<\/p>\r\n<p>In the above case, to find the answer, you can multiply the numerators together and the denominators together.<\/p>\r\n<section class=\"textbox keyTakeaway\">\r\n<div>\r\n<h3>Multiplying Two Fractions<\/h3>\r\n<p>Multiplying two fractions is a fundamental arithmetic operation where each numerator is multiplied by the other fraction's numerator and each denominator by the other's denominator, resulting in a new fraction that represents the product of the two original fractions.<\/p>\r\n<p>&nbsp;<\/p>\r\n<center>[latex] \\frac{a}{b}\\cdot \\frac{c}{d}=\\frac{a\\cdot c}{b\\cdot d}=\\frac{\\text{product of the numerators}}{\\text{product of the denominators}}[\/latex]<\/center><\/div>\r\n<\/section>\r\n<section class=\"textbox keyTakeaway\">\r\n<div>\r\n<h3>Multiplying More Than Two Fractions<\/h3>\r\n<p>When multiplying more than two fractions, you continue the process of multiplying numerators together and denominators together.<\/p>\r\n<p>&nbsp;<\/p>\r\n<center>[latex] \\frac{a}{b}\\cdot \\frac{c}{d}\\cdot \\frac{e}{f}=\\frac{a\\cdot c\\cdot e}{b\\cdot d\\cdot f}[\/latex]<\/center><\/div>\r\n<\/section>\r\n<section class=\"textbox recall\">\r\n<ul>\r\n\t<li><strong>product:\u00a0<\/strong>the result of \u00a0multiplication<\/li>\r\n\t<li><strong>factor:<\/strong> something being multiplied - for \u00a0[latex]3 \\cdot 2 = 6[\/latex] , both [latex]3[\/latex] and [latex]2[\/latex] are factors of [latex]6[\/latex]<\/li>\r\n\t<li><strong>numerator:<\/strong> the top part of a fraction - the numerator in the fraction\u00a0[latex]\\frac{2}{3}[\/latex] is [latex]2[\/latex]<\/li>\r\n\t<li><strong>denominator:<\/strong> the bottom part of a fraction - the denominator in the fraction\u00a0[latex]\\frac{2}{3}[\/latex] is [latex]3[\/latex]<\/li>\r\n<\/ul>\r\n<\/section>\r\n<section class=\"textbox example\">Multiply [latex] \\frac{2}{3}\\cdot \\frac{4}{5}[\/latex].[reveal-answer q=\"370291\"]Show Answer[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"370291\"]Multiply the numerators and multiply the denominators.\r\n\r\n<p style=\"text-align: center;\">[latex] \\frac{2\\cdot 4}{3\\cdot 5}[\/latex]<\/p>\r\n<p>Simplify, if possible. This fraction is already in lowest terms.<\/p>\r\n<p style=\"text-align: center;\">[latex] \\frac{8}{15}[\/latex]<\/p>\r\n<p>[\/hidden-answer]<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]8299[\/ohm2_question]<\/section>\r\n<h2>Divide Fractions<\/h2>\r\n<p>Dividing fractions is a key mathematical skill that extends our understanding of division beyond the realm of whole numbers. When we divide by a fraction, we are essentially asking how many of these fractional parts fit into the whole or another fraction. This process involves inverting the divisor (the fraction by which we are dividing) and then multiplying it by the dividend (the fraction to be divided).<\/p>\r\n<section class=\"textbox keyTakeaway\">\r\n<div>\r\n<h3>Dividing is Multiplying by the Reciprocal<\/h3>\r\n<p>For all division, you can turn the operation\u00a0into multiplication by using the reciprocal. Dividing is the same as multiplying by the reciprocal.<\/p>\r\n<\/div>\r\n<\/section>\r\n<section class=\"textbox recall\">\r\n<ul>\r\n\t<li><strong>reciprocal:<\/strong> two fractions are reciprocals if their product is [latex]1[\/latex] (Don't worry; we will show you examples of what this means.)<\/li>\r\n\t<li><strong>quotient:<\/strong> the result\u00a0of division<\/li>\r\n<\/ul>\r\n<\/section>\r\n<section class=\"textbox questionHelp\">\r\n<p><strong>How To: Dividing with Fractions<\/strong><\/p>\r\n<ol>\r\n\t<li>Find the reciprocal of the number that follows the division symbol.<\/li>\r\n\t<li>Multiply the first number (the one before the division symbol) by the reciprocal of the second number (the one after the division symbol).<\/li>\r\n<\/ol>\r\n<\/section>\r\n<section class=\"textbox proTip\">\r\n<p>Any easy way to remember how to divide fractions is the phrase \u201ckeep, change, flip.\u201d This means to <strong>KEEP<\/strong> the first number, <strong>CHANGE<\/strong> the division sign to multiplication, and then <strong>FLIP<\/strong> (use the reciprocal) of the second number.<\/p>\r\n<\/section>\r\n<section class=\"textbox keyTakeaway\">\r\n<div>\r\n<h3>Division by Zero<\/h3>\r\n<p>Caution! Division by zero is undefined and so is the reciprocal of any fraction that has a zero in the numerator. For any real number [latex]a[\/latex], [latex]\\frac{a}{0}[\/latex] is undefined.<\/p>\r\n<p>&nbsp;<\/p>\r\n<p>Additionally, the reciprocal of [latex]\\frac{0}{a}[\/latex] will always be [latex]0[\/latex].<\/p>\r\n<\/div>\r\n<\/section>\r\n<section class=\"textbox example\">Find [latex] \\frac{2}{3}\\div 4[\/latex].[reveal-answer q=\"5475\"]Show Answer[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"5475\"]Write your answer in lowest terms. Dividing by [latex]4[\/latex] or [latex] \\frac{4}{1}[\/latex] is the same as multiplying by the reciprocal of [latex]4[\/latex], which is [latex] \\frac{1}{4}[\/latex].\r\n\r\n<p style=\"text-align: center;\">[latex] \\frac{2}{3}\\div 4=\\frac{2}{3}\\cdot \\frac{1}{4}[\/latex]<\/p>\r\n<p>Multiply numerators and multiply denominators.<\/p>\r\n<p style=\"text-align: center;\">[latex] \\frac{2\\cdot 1}{3\\cdot 4}=\\frac{2}{12}[\/latex]<\/p>\r\n<p>Simplify to lowest terms by dividing numerator and denominator by the common factor [latex]4[\/latex].<\/p>\r\n<p style=\"text-align: center;\">[latex] \\frac{1}{6}[\/latex]<\/p>\r\n<center>[latex]\\frac{2}{3}\\div4=\\frac{1}{6}[\/latex]<\/center>\r\n<p>[\/hidden-answer]<\/p>\r\n<\/section>\r\n<section class=\"textbox example\">Divide [latex] \\frac{2}{3}\\div \\frac{1}{6}[\/latex].[reveal-answer q=\"756257\"]Show Answer[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"756257\"]Multiply by the reciprocal. <strong>KEEP<\/strong> [latex] \\frac{2}{3}[\/latex], <strong>CHANGE<\/strong>\u00a0 [latex] \\div [\/latex] to \u00a0[latex]\\cdot[\/latex] , and <strong>FLIP\u00a0<\/strong> [latex]\\frac{1}{6}[\/latex]:\r\n\r\n<p style=\"text-align: center;\">[latex] \\frac{2}{3}\\cdot \\frac{6}{1}[\/latex]<\/p>\r\n<p>Multiply numerators and multiply denominators.<\/p>\r\n<p style=\"text-align: center;\">[latex]\\frac{2\\cdot6}{3\\cdot1}=\\frac{12}{3}[\/latex]<\/p>\r\n<p>&nbsp;<\/p>\r\n<p>Simplify.<\/p>\r\n<p style=\"text-align: center;\">[latex] \\frac{12}{3}=4[\/latex]<\/p>\r\n<center>[latex] \\frac{2}{3}\\div \\frac{1}{6}=4[\/latex]<\/center>\r\n<p>[\/hidden-answer]<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]8300[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Multiply and Divide Fractions<\/li>\n<\/ul>\n<\/section>\n<h2>Multiply Fractions<\/h2>\n<p>There are many times when it is necessary to multiply fractions. A model may help you understand multiplication of fractions.<\/p>\n<p>When you multiply a fraction by a fraction, you are finding a \u201cfraction of a fraction.\u201d Suppose you have [latex]\\frac{3}{4}[\/latex]\u00a0of a candy bar and you want to find [latex]\\frac{1}{2}[\/latex]\u00a0of the [latex]\\frac{3}{4}[\/latex]:<\/p>\n<div style=\"text-align: center;\">\n<figure style=\"width: 208px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1468\/2016\/03\/17170708\/image109.gif\" alt=\"3 out of four boxes are shaded. This is 3\/4.\" width=\"208\" height=\"65\" \/><figcaption class=\"wp-caption-text\">Figure 1. 3\/4 of a candy bar<\/figcaption><\/figure>\n<\/div>\n<p>&nbsp;<\/p>\n<p>By dividing each fourth in half, you can divide the candy bar into eighths.<\/p>\n<div style=\"text-align: center;\">\n<figure style=\"width: 208px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1468\/2016\/03\/17170709\/image110.gif\" alt=\"Six of 8 boxes are shaded. This is 6\/8.\" width=\"208\" height=\"62\" \/><figcaption class=\"wp-caption-text\">Figure 2. 6\/8 of a candy bar<\/figcaption><\/figure>\n<\/div>\n<p>&nbsp;<\/p>\n<p>Then, choose half of those to get [latex]\\frac{3}{8}[\/latex].<\/p>\n<div style=\"text-align: center;\">\n<figure style=\"width: 208px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1468\/2016\/03\/17170711\/image112.gif\" alt=\"Six of 8 boxes are shaded, and of those six, three of them are shaded purple. The 3 purple boxes represent 3\/8.\" width=\"208\" height=\"54\" \/><figcaption class=\"wp-caption-text\">Figure 3. 3\/8 of a candy bar<\/figcaption><\/figure>\n<\/div>\n<p>&nbsp;<\/p>\n<p>In the above case, to find the answer, you can multiply the numerators together and the denominators together.<\/p>\n<section class=\"textbox keyTakeaway\">\n<div>\n<h3>Multiplying Two Fractions<\/h3>\n<p>Multiplying two fractions is a fundamental arithmetic operation where each numerator is multiplied by the other fraction&#8217;s numerator and each denominator by the other&#8217;s denominator, resulting in a new fraction that represents the product of the two original fractions.<\/p>\n<p>&nbsp;<\/p>\n<div style=\"text-align: center;\">[latex]\\frac{a}{b}\\cdot \\frac{c}{d}=\\frac{a\\cdot c}{b\\cdot d}=\\frac{\\text{product of the numerators}}{\\text{product of the denominators}}[\/latex]<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox keyTakeaway\">\n<div>\n<h3>Multiplying More Than Two Fractions<\/h3>\n<p>When multiplying more than two fractions, you continue the process of multiplying numerators together and denominators together.<\/p>\n<p>&nbsp;<\/p>\n<div style=\"text-align: center;\">[latex]\\frac{a}{b}\\cdot \\frac{c}{d}\\cdot \\frac{e}{f}=\\frac{a\\cdot c\\cdot e}{b\\cdot d\\cdot f}[\/latex]<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox recall\">\n<ul>\n<li><strong>product:\u00a0<\/strong>the result of \u00a0multiplication<\/li>\n<li><strong>factor:<\/strong> something being multiplied &#8211; for \u00a0[latex]3 \\cdot 2 = 6[\/latex] , both [latex]3[\/latex] and [latex]2[\/latex] are factors of [latex]6[\/latex]<\/li>\n<li><strong>numerator:<\/strong> the top part of a fraction &#8211; the numerator in the fraction\u00a0[latex]\\frac{2}{3}[\/latex] is [latex]2[\/latex]<\/li>\n<li><strong>denominator:<\/strong> the bottom part of a fraction &#8211; the denominator in the fraction\u00a0[latex]\\frac{2}{3}[\/latex] is [latex]3[\/latex]<\/li>\n<\/ul>\n<\/section>\n<section class=\"textbox example\">Multiply [latex]\\frac{2}{3}\\cdot \\frac{4}{5}[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q370291\">Show Answer<\/button><\/p>\n<div id=\"q370291\" class=\"hidden-answer\" style=\"display: none\">Multiply the numerators and multiply the denominators.<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{2\\cdot 4}{3\\cdot 5}[\/latex]<\/p>\n<p>Simplify, if possible. This fraction is already in lowest terms.<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{8}{15}[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm8299\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=8299&theme=lumen&iframe_resize_id=ohm8299&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<h2>Divide Fractions<\/h2>\n<p>Dividing fractions is a key mathematical skill that extends our understanding of division beyond the realm of whole numbers. When we divide by a fraction, we are essentially asking how many of these fractional parts fit into the whole or another fraction. This process involves inverting the divisor (the fraction by which we are dividing) and then multiplying it by the dividend (the fraction to be divided).<\/p>\n<section class=\"textbox keyTakeaway\">\n<div>\n<h3>Dividing is Multiplying by the Reciprocal<\/h3>\n<p>For all division, you can turn the operation\u00a0into multiplication by using the reciprocal. Dividing is the same as multiplying by the reciprocal.<\/p>\n<\/div>\n<\/section>\n<section class=\"textbox recall\">\n<ul>\n<li><strong>reciprocal:<\/strong> two fractions are reciprocals if their product is [latex]1[\/latex] (Don&#8217;t worry; we will show you examples of what this means.)<\/li>\n<li><strong>quotient:<\/strong> the result\u00a0of division<\/li>\n<\/ul>\n<\/section>\n<section class=\"textbox questionHelp\">\n<p><strong>How To: Dividing with Fractions<\/strong><\/p>\n<ol>\n<li>Find the reciprocal of the number that follows the division symbol.<\/li>\n<li>Multiply the first number (the one before the division symbol) by the reciprocal of the second number (the one after the division symbol).<\/li>\n<\/ol>\n<\/section>\n<section class=\"textbox proTip\">\n<p>Any easy way to remember how to divide fractions is the phrase \u201ckeep, change, flip.\u201d This means to <strong>KEEP<\/strong> the first number, <strong>CHANGE<\/strong> the division sign to multiplication, and then <strong>FLIP<\/strong> (use the reciprocal) of the second number.<\/p>\n<\/section>\n<section class=\"textbox keyTakeaway\">\n<div>\n<h3>Division by Zero<\/h3>\n<p>Caution! Division by zero is undefined and so is the reciprocal of any fraction that has a zero in the numerator. For any real number [latex]a[\/latex], [latex]\\frac{a}{0}[\/latex] is undefined.<\/p>\n<p>&nbsp;<\/p>\n<p>Additionally, the reciprocal of [latex]\\frac{0}{a}[\/latex] will always be [latex]0[\/latex].<\/p>\n<\/div>\n<\/section>\n<section class=\"textbox example\">Find [latex]\\frac{2}{3}\\div 4[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q5475\">Show Answer<\/button><\/p>\n<div id=\"q5475\" class=\"hidden-answer\" style=\"display: none\">Write your answer in lowest terms. Dividing by [latex]4[\/latex] or [latex]\\frac{4}{1}[\/latex] is the same as multiplying by the reciprocal of [latex]4[\/latex], which is [latex]\\frac{1}{4}[\/latex].<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{2}{3}\\div 4=\\frac{2}{3}\\cdot \\frac{1}{4}[\/latex]<\/p>\n<p>Multiply numerators and multiply denominators.<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{2\\cdot 1}{3\\cdot 4}=\\frac{2}{12}[\/latex]<\/p>\n<p>Simplify to lowest terms by dividing numerator and denominator by the common factor [latex]4[\/latex].<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{1}{6}[\/latex]<\/p>\n<div style=\"text-align: center;\">[latex]\\frac{2}{3}\\div4=\\frac{1}{6}[\/latex]<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox example\">Divide [latex]\\frac{2}{3}\\div \\frac{1}{6}[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q756257\">Show Answer<\/button><\/p>\n<div id=\"q756257\" class=\"hidden-answer\" style=\"display: none\">Multiply by the reciprocal. <strong>KEEP<\/strong> [latex]\\frac{2}{3}[\/latex], <strong>CHANGE<\/strong>\u00a0 [latex]\\div[\/latex] to \u00a0[latex]\\cdot[\/latex] , and <strong>FLIP\u00a0<\/strong> [latex]\\frac{1}{6}[\/latex]:<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{2}{3}\\cdot \\frac{6}{1}[\/latex]<\/p>\n<p>Multiply numerators and multiply denominators.<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{2\\cdot6}{3\\cdot1}=\\frac{12}{3}[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p>Simplify.<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{12}{3}=4[\/latex]<\/p>\n<div style=\"text-align: center;\">[latex]\\frac{2}{3}\\div \\frac{1}{6}=4[\/latex]<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm8300\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=8300&theme=lumen&iframe_resize_id=ohm8300&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":16,"menu_order":4,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":23,"module-header":"background_you_need","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/4663"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/users\/16"}],"version-history":[{"count":32,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/4663\/revisions"}],"predecessor-version":[{"id":15533,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/4663\/revisions\/15533"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/parts\/23"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/4663\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/media?parent=4663"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapter-type?post=4663"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/contributor?post=4663"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/license?post=4663"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}