{"id":17203,"date":"2020-02-27T19:43:39","date_gmt":"2020-02-27T19:43:39","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/?post_type=chapter&#038;p=17203"},"modified":"2024-04-30T16:36:53","modified_gmt":"2024-04-30T16:36:53","slug":"translating-phrases-to-expressions-with-fractions","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/chapter\/translating-phrases-to-expressions-with-fractions\/","title":{"raw":"Translating Phrases to Expressions with Fractions","rendered":"Translating Phrases to Expressions with Fractions"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Translate word phrases to expressions with fractions<\/li>\r\n<\/ul>\r\n<\/div>\r\nHave you noticed that the examples in this section used the comparison words <em>ratio of, to, per, in, for, on<\/em>, and <em>from<\/em>? When you translate phrases that include these words, you should think either ratio or rate. If the units measure the same quantity (length, time, etc.), you have a ratio. If the units are different, you have a rate. In both cases, you write a fraction.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nTranslate the word phrase into an algebraic expression:\r\n\u24d0 [latex]427[\/latex] miles per [latex]h[\/latex] hours\r\n\u24d1 [latex]x[\/latex] students to [latex]3[\/latex] teachers\r\n\u24d2 [latex]y[\/latex] dollars for [latex]18[\/latex] hours\r\n\r\nSolution\r\n<table id=\"eip-id1168467446163\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>\u24d0<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]\\text{427 miles per }h\\text{ hours}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write as a rate.<\/td>\r\n<td>[latex]\\dfrac{\\text{427 miles }}{h\\text{ hours}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168468694066\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>\u24d1<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]x\\text{ students to 3 teachers}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write as a rate.<\/td>\r\n<td>[latex]\\dfrac{x\\text{ students}}{\\text{3 teachers}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168469794516\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>\u24d2<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]y\\text{ dollars for 18 hours}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write as a rate.<\/td>\r\n<td>[latex]\\dfrac{y\\text{ dollars}}{\\text{18 hours}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n&nbsp;\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>TRY IT<\/h3>\r\nTranslate the word phrase into an algebraic expression.\r\n\r\na. [latex]689[\/latex] miles per [latex]h[\/latex] hours\r\n\r\nb. [latex]y[\/latex] parents to [latex]22[\/latex] students\r\n\r\nc. [latex]d[\/latex] dollars for [latex]9[\/latex] minutes\r\n\r\n[reveal-answer q=\"338899\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"338899\"]\r\n\r\na. [latex]\\dfrac{689\\text{ mi}}{h\\text{ hrs}}[\/latex]\r\nb.\u00a0[latex]\\dfrac{y\\text{ parents}}{22\\text{ students}}[\/latex]\r\nc.[latex]\\dfrac{$d}{9\\text{ min}}[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\nTranslate the word phrase into an algebraic expression.\r\na. [latex]m[\/latex] miles per [latex]9[\/latex] hours\r\n\r\nb. [latex]x[\/latex] students to [latex]8[\/latex] buses\r\n\r\nc. [latex]y[\/latex] dollars for [latex]40[\/latex] hours\r\n\r\n[reveal-answer q=\"224455\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"224455\"]\r\n\r\na.\u00a0[latex]\\dfrac{m\\text{ mi}}{9\\text{ hrs}}[\/latex]\r\n\r\nb.[latex]\\dfrac{x\\text{ students}}{8\\text{ buses}}[\/latex]\r\n\r\nc.\u00a0[latex]\\dfrac{$y}{40\\text{ hrs}}[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n[ohm_question]195432[\/ohm_question]\r\n\r\n<\/div>\r\n<h2>Applications of Ratios<\/h2>\r\nOne real-world application of ratios that affects many people involves measuring cholesterol in blood. The ratio of total cholesterol to HDL cholesterol is one way doctors assess a person's overall health. A ratio of less than [latex]5[\/latex] to [latex]1[\/latex] is considered good.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nHector's total cholesterol is [latex]249[\/latex] mg\/dl and his HDL cholesterol is [latex]39[\/latex] mg\/dl. \u24d0 Find the ratio of his total cholesterol to his HDL cholesterol. \u24d1 Assuming that a ratio less than [latex]5[\/latex] to [latex]1[\/latex] is considered good, what would you suggest to Hector?\r\n\r\nSolution\r\n\u24d0 First, write the words that express the ratio. We want to know the ratio of Hector's total cholesterol to his HDL cholesterol.\r\n<table id=\"eip-id1168468767905\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>Write as a fraction.<\/td>\r\n<td>[latex]\\dfrac{\\text{total cholesterol}}{\\text{HDL cholesterol}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute the values.<\/td>\r\n<td>[latex]\\dfrac{249}{39}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]\\dfrac{83}{13}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\u24d1 Is Hector's cholesterol ratio ok? If we divide [latex]83[\/latex] by [latex]13[\/latex] we obtain approximately [latex]6.4[\/latex], so [latex]\\dfrac{83}{13}\\normalsize\\approx\\dfrac{6.4}{1}[\/latex]. Hector's cholesterol ratio is high! Hector should either lower his total cholesterol or raise his HDL cholesterol.\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>TRY IT<\/h3>\r\n1. Find the patient's ratio of total cholesterol to HDL cholesterol using the given information.\r\nTotal cholesterol is [latex]185[\/latex] mg\/dL and HDL cholesterol is [latex]40[\/latex] mg\/dL.\r\n\r\n[reveal-answer q=\"113322\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"113322\"]\r\n\r\n[latex]\\dfrac{37}{8}[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\n2. Find the patient\u2019s ratio of total cholesterol to HDL cholesterol using the given information.\r\nTotal cholesterol is [latex]204[\/latex] mg\/dL and HDL cholesterol is [latex]38[\/latex] mg\/dL.\r\n\r\n[reveal-answer q=\"789987\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"789987\"]\r\n\r\n[latex]\\dfrac{102}{19}[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<h3>Ratios of Two Measurements in Different Units<\/h3>\r\nTo find the ratio of two measurements, we must make sure the quantities have been measured with the same unit. If the measurements are not in the same units, we must first convert them to the same units.\r\n\r\nWe know that to simplify a fraction, we divide out common factors. Similarly in a ratio of measurements, we divide out the common unit.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nThe Americans with Disabilities Act (ADA) Guidelines for wheel chair ramps require a maximum vertical rise of [latex]1[\/latex] inch for every [latex]1[\/latex] foot of horizontal run. What is the ratio of the rise to the run?\r\n\r\nSolution\r\nIn a ratio, the measurements must be in the same units. We can change feet to inches, or inches to feet. It is usually easier to convert to the smaller unit, since this avoids introducing more fractions into the problem.\r\nWrite the words that express the ratio.\r\n<table id=\"eip-id1168467133951\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>Ratio of the rise to the run<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write the ratio as a fraction.<\/td>\r\n<td>[latex]\\dfrac{\\text{rise}}{\\text{run}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Substitute in the given values.<\/td>\r\n<td>[latex]\\dfrac{\\text{1 inch}}{\\text{1 foot}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Convert [latex]1[\/latex] foot to inches.<\/td>\r\n<td>[latex]\\dfrac{\\text{1 inch}}{\\text{12 inches}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify, dividing out common factors and units.<\/td>\r\n<td>[latex]\\dfrac{1}{12}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nSo the ratio of rise to run is [latex]1[\/latex] to [latex]12[\/latex]. This means that the ramp should rise [latex]1[\/latex] inch for every [latex]12[\/latex] inches of horizontal run to comply with the guidelines.\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>TRY IT<\/h3>\r\n1. Find the ratio of the first length to the second length: [latex]32[\/latex] inches to [latex]1[\/latex] foot.\r\n\r\n[reveal-answer q=\"246864\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"246864\"]\r\n\r\n[latex]\\dfrac{8}{3}[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\n2. Find the ratio of the first length to the second length: [latex]1[\/latex] foot to [latex]54[\/latex] inches.\r\n\r\n[reveal-answer q=\"176350\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"176350\"]\r\n\r\n[latex]\\dfrac{2}{9}[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Translate word phrases to expressions with fractions<\/li>\n<\/ul>\n<\/div>\n<p>Have you noticed that the examples in this section used the comparison words <em>ratio of, to, per, in, for, on<\/em>, and <em>from<\/em>? When you translate phrases that include these words, you should think either ratio or rate. If the units measure the same quantity (length, time, etc.), you have a ratio. If the units are different, you have a rate. In both cases, you write a fraction.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Translate the word phrase into an algebraic expression:<br \/>\n\u24d0 [latex]427[\/latex] miles per [latex]h[\/latex] hours<br \/>\n\u24d1 [latex]x[\/latex] students to [latex]3[\/latex] teachers<br \/>\n\u24d2 [latex]y[\/latex] dollars for [latex]18[\/latex] hours<\/p>\n<p>Solution<\/p>\n<table id=\"eip-id1168467446163\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>\u24d0<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]\\text{427 miles per }h\\text{ hours}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write as a rate.<\/td>\n<td>[latex]\\dfrac{\\text{427 miles }}{h\\text{ hours}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168468694066\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>\u24d1<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]x\\text{ students to 3 teachers}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write as a rate.<\/td>\n<td>[latex]\\dfrac{x\\text{ students}}{\\text{3 teachers}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168469794516\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>\u24d2<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]y\\text{ dollars for 18 hours}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write as a rate.<\/td>\n<td>[latex]\\dfrac{y\\text{ dollars}}{\\text{18 hours}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>TRY IT<\/h3>\n<p>Translate the word phrase into an algebraic expression.<\/p>\n<p>a. [latex]689[\/latex] miles per [latex]h[\/latex] hours<\/p>\n<p>b. [latex]y[\/latex] parents to [latex]22[\/latex] students<\/p>\n<p>c. [latex]d[\/latex] dollars for [latex]9[\/latex] minutes<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q338899\">Show Solution<\/span><\/p>\n<div id=\"q338899\" class=\"hidden-answer\" style=\"display: none\">\n<p>a. [latex]\\dfrac{689\\text{ mi}}{h\\text{ hrs}}[\/latex]<br \/>\nb.\u00a0[latex]\\dfrac{y\\text{ parents}}{22\\text{ students}}[\/latex]<br \/>\nc.[latex]\\dfrac{$d}{9\\text{ min}}[\/latex]<\/p>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>Translate the word phrase into an algebraic expression.<br \/>\na. [latex]m[\/latex] miles per [latex]9[\/latex] hours<\/p>\n<p>b. [latex]x[\/latex] students to [latex]8[\/latex] buses<\/p>\n<p>c. [latex]y[\/latex] dollars for [latex]40[\/latex] hours<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q224455\">Show Solution<\/span><\/p>\n<div id=\"q224455\" class=\"hidden-answer\" style=\"display: none\">\n<p>a.\u00a0[latex]\\dfrac{m\\text{ mi}}{9\\text{ hrs}}[\/latex]<\/p>\n<p>b.[latex]\\dfrac{x\\text{ students}}{8\\text{ buses}}[\/latex]<\/p>\n<p>c.\u00a0[latex]\\dfrac{$y}{40\\text{ hrs}}[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm195432\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=195432&theme=oea&iframe_resize_id=ohm195432&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<h2>Applications of Ratios<\/h2>\n<p>One real-world application of ratios that affects many people involves measuring cholesterol in blood. The ratio of total cholesterol to HDL cholesterol is one way doctors assess a person&#8217;s overall health. A ratio of less than [latex]5[\/latex] to [latex]1[\/latex] is considered good.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Hector&#8217;s total cholesterol is [latex]249[\/latex] mg\/dl and his HDL cholesterol is [latex]39[\/latex] mg\/dl. \u24d0 Find the ratio of his total cholesterol to his HDL cholesterol. \u24d1 Assuming that a ratio less than [latex]5[\/latex] to [latex]1[\/latex] is considered good, what would you suggest to Hector?<\/p>\n<p>Solution<br \/>\n\u24d0 First, write the words that express the ratio. We want to know the ratio of Hector&#8217;s total cholesterol to his HDL cholesterol.<\/p>\n<table id=\"eip-id1168468767905\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>Write as a fraction.<\/td>\n<td>[latex]\\dfrac{\\text{total cholesterol}}{\\text{HDL cholesterol}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Substitute the values.<\/td>\n<td>[latex]\\dfrac{249}{39}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]\\dfrac{83}{13}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\u24d1 Is Hector&#8217;s cholesterol ratio ok? If we divide [latex]83[\/latex] by [latex]13[\/latex] we obtain approximately [latex]6.4[\/latex], so [latex]\\dfrac{83}{13}\\normalsize\\approx\\dfrac{6.4}{1}[\/latex]. Hector&#8217;s cholesterol ratio is high! Hector should either lower his total cholesterol or raise his HDL cholesterol.<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>TRY IT<\/h3>\n<p>1. Find the patient&#8217;s ratio of total cholesterol to HDL cholesterol using the given information.<br \/>\nTotal cholesterol is [latex]185[\/latex] mg\/dL and HDL cholesterol is [latex]40[\/latex] mg\/dL.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q113322\">Show Solution<\/span><\/p>\n<div id=\"q113322\" class=\"hidden-answer\" style=\"display: none\">\n<p>[latex]\\dfrac{37}{8}[\/latex]<\/p>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>2. Find the patient\u2019s ratio of total cholesterol to HDL cholesterol using the given information.<br \/>\nTotal cholesterol is [latex]204[\/latex] mg\/dL and HDL cholesterol is [latex]38[\/latex] mg\/dL.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q789987\">Show Solution<\/span><\/p>\n<div id=\"q789987\" class=\"hidden-answer\" style=\"display: none\">\n<p>[latex]\\dfrac{102}{19}[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<h3>Ratios of Two Measurements in Different Units<\/h3>\n<p>To find the ratio of two measurements, we must make sure the quantities have been measured with the same unit. If the measurements are not in the same units, we must first convert them to the same units.<\/p>\n<p>We know that to simplify a fraction, we divide out common factors. Similarly in a ratio of measurements, we divide out the common unit.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>The Americans with Disabilities Act (ADA) Guidelines for wheel chair ramps require a maximum vertical rise of [latex]1[\/latex] inch for every [latex]1[\/latex] foot of horizontal run. What is the ratio of the rise to the run?<\/p>\n<p>Solution<br \/>\nIn a ratio, the measurements must be in the same units. We can change feet to inches, or inches to feet. It is usually easier to convert to the smaller unit, since this avoids introducing more fractions into the problem.<br \/>\nWrite the words that express the ratio.<\/p>\n<table id=\"eip-id1168467133951\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>Ratio of the rise to the run<\/td>\n<\/tr>\n<tr>\n<td>Write the ratio as a fraction.<\/td>\n<td>[latex]\\dfrac{\\text{rise}}{\\text{run}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Substitute in the given values.<\/td>\n<td>[latex]\\dfrac{\\text{1 inch}}{\\text{1 foot}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Convert [latex]1[\/latex] foot to inches.<\/td>\n<td>[latex]\\dfrac{\\text{1 inch}}{\\text{12 inches}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify, dividing out common factors and units.<\/td>\n<td>[latex]\\dfrac{1}{12}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>So the ratio of rise to run is [latex]1[\/latex] to [latex]12[\/latex]. This means that the ramp should rise [latex]1[\/latex] inch for every [latex]12[\/latex] inches of horizontal run to comply with the guidelines.<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>TRY IT<\/h3>\n<p>1. Find the ratio of the first length to the second length: [latex]32[\/latex] inches to [latex]1[\/latex] foot.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q246864\">Show Solution<\/span><\/p>\n<div id=\"q246864\" class=\"hidden-answer\" style=\"display: none\">\n<p>[latex]\\dfrac{8}{3}[\/latex]<\/p>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>2. Find the ratio of the first length to the second length: [latex]1[\/latex] foot to [latex]54[\/latex] inches.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q176350\">Show Solution<\/span><\/p>\n<div id=\"q176350\" class=\"hidden-answer\" style=\"display: none\">\n<p>[latex]\\dfrac{2}{9}[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"author":253111,"menu_order":11,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"0cacc03eb3a74b46b005616aee47dbd5, 7d58ede6a2294af6b1195b21114dc343","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-17203","chapter","type-chapter","status-publish","hentry"],"part":13985,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/17203","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/wp\/v2\/users\/253111"}],"version-history":[{"count":10,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/17203\/revisions"}],"predecessor-version":[{"id":19831,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/17203\/revisions\/19831"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/parts\/13985"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/17203\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/wp\/v2\/media?parent=17203"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapter-type?post=17203"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/wp\/v2\/contributor?post=17203"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/wp\/v2\/license?post=17203"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}