{"id":4649,"date":"2023-06-19T13:28:42","date_gmt":"2023-06-19T13:28:42","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/?post_type=chapter&#038;p=4649"},"modified":"2024-10-18T20:52:43","modified_gmt":"2024-10-18T20:52:43","slug":"general-problem-solving-background-youll-need-2","status":"web-only","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/chapter\/general-problem-solving-background-youll-need-2\/","title":{"raw":"General Problem Solving: Background You'll Need 2","rendered":"General Problem Solving: Background You&#8217;ll Need 2"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li>Add and Subtract Fractions<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Adding Fractions<\/h2>\r\n<p>When you need to add or subtract fractions, you will need to first make sure that the fractions have the same denominator. The denominator tells you how many pieces the whole has been broken into, and the numerator tells you how many of those pieces you are using.<\/p>\r\n<section class=\"textbox proTip\">You need a common denominator, technically called the [pb_glossary id=\"12971\"]least common multiple[\/pb_glossary]<strong>. <\/strong>Remember that\u00a0if a number is a multiple of another, you can divide them and have no remainder.<\/section>\r\n<p>One way to find the least common multiple of two or more numbers is to first multiply each\u00a0by [latex]1[\/latex], [latex]2[\/latex], [latex]3[\/latex], [latex]4[\/latex], etc. \u00a0For example, find the least common multiple of [latex]2[\/latex] and [latex]5[\/latex].<\/p>\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td scope=\"col\">First, list all the multiples of [latex]2[\/latex]:<\/td>\r\n<td scope=\"col\">Then list all the multiples of [latex]5[\/latex]:<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]2\\cdot 1 = 2[\/latex]<\/td>\r\n<td>[latex]5\\cdot 1 = 5[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]2\\cdot 2 = 4[\/latex]<\/td>\r\n<td>[latex]5\\cdot 2 = 10[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]2\\cdot 3 = 6[\/latex]<\/td>\r\n<td>[latex]5\\cdot 3 = 15[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]2\\cdot 4 = 8[\/latex]<\/td>\r\n<td>[latex]5\\cdot 4 = 20[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]2\\cdot 5 = 10[\/latex]<\/td>\r\n<td>[latex]5\\cdot 5 = 25[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p>&nbsp;<\/p>\r\n<p>The smallest multiple they have in common will be the common denominator for the two!<\/p>\r\n<section class=\"textbox questionHelp\">\r\n<p><strong>How To: Adding Fractions with Unlike Denominators<\/strong><\/p>\r\n<ol>\r\n\t<li>Find a common denominator.<\/li>\r\n\t<li>Rewrite each fraction using the common denominator.<\/li>\r\n\t<li>Now that the fractions have a common denominator, you can add the numerators.<\/li>\r\n\t<li>Simplify by canceling out all common factors in the numerator and denominator.<\/li>\r\n<\/ol>\r\n<\/section>\r\n<section class=\"textbox example\">Add [latex] \\frac{2}{3}+\\frac{1}{5}[\/latex].\u00a0Simplify the answer.[reveal-answer q=\"296587\"]Show Answer[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"296587\"]Since the denominators are not alike, find a common denominator by multiplying the denominators.\r\n\r\n<p style=\"text-align: center;\">[latex]3\\cdot5=15[\/latex]<\/p>\r\n<p>Rewrite each fraction with a denominator of [latex]15[\/latex].<\/p>\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}\\frac{2}{3}\\cdot \\frac{5}{5}=\\frac{10}{15}\\\\\\\\\\frac{1}{5}\\cdot \\frac{3}{3}=\\frac{3}{15}\\end{array}[\/latex]<\/p>\r\n<p>Add the fractions by adding the numerators and keeping the denominator the same. Make sure the fraction cannot be simplified.<\/p>\r\n<p style=\"text-align: center;\">[latex] \\frac{10}{15}+\\frac{3}{15}=\\frac{13}{15}[\/latex]<\/p>\r\n<center>[latex] \\frac{2}{3}+\\frac{1}{5}=\\frac{13}{15}[\/latex]<\/center>\r\n<p>[\/hidden-answer]<\/p>\r\n<\/section>\r\n<section class=\"textbox proTip\">You can find a common denominator by finding the common multiples of the denominators. The least common multiple is the easiest to use.<\/section>\r\n<section class=\"textbox example\">Add\u00a0[latex] \\frac{3}{7}+\\frac{2}{21}[\/latex]. Simplify the answer.[reveal-answer q=\"553019\"]Show Answer[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"553019\"]\r\n\r\n<p>Since the denominators are not alike, find the least common denominator by finding the least common multiple (LCM) of [latex]7[\/latex] and [latex]21[\/latex].<\/p>\r\n<p>Multiples of [latex]7: 7, 14, 21[\/latex]<\/p>\r\n<p>Multiples of [latex]21: 21[\/latex]<\/p>\r\n<p>Rewrite each fraction with a denominator of [latex]21[\/latex].<\/p>\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}\\frac{3}{7}\\cdot \\frac{3}{3}=\\frac{9}{21}\\\\\\\\\\frac{2}{21}\\end{array}[\/latex]<\/p>\r\n<p>Add the fractions by adding the numerators and keeping the denominator the same. Make sure the fraction cannot be simplified.<\/p>\r\n<p style=\"text-align: center;\">[latex] \\frac{9}{21}+\\frac{2}{21}=\\frac{11}{21}[\/latex]<\/p>\r\n<center>[latex] \\frac{3}{7}+\\frac{2}{21}=\\frac{11}{21}[\/latex]<\/center>\r\n<p>[\/hidden-answer]<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]8297[\/ohm2_question]<\/section>\r\n<h2>Subtracting Fractions<\/h2>\r\n<p>Subtracting fractions follows a similar process to adding fractions. When you subtract fractions, you must think about whether they have a common denominator, just like with adding fractions.<\/p>\r\n<section class=\"textbox questionHelp\">\r\n<p><strong>How To: Subtracting Fractions with Unlike Denominators<\/strong><\/p>\r\n<ol>\r\n\t<li>Find a common denominator.<\/li>\r\n\t<li>Rewrite each fraction using the common denominator.<\/li>\r\n\t<li>Now that the fractions have a common denominator, you can subtract the numerators.<\/li>\r\n\t<li>Simplify by canceling out all common factors in the numerator and denominator.<\/li>\r\n<\/ol>\r\n<\/section>\r\n<p>Below are some examples of subtracting fractions whose denominators are not alike.<\/p>\r\n<section class=\"textbox example\">Subtract\u00a0[latex]\\frac{1}{5}-\\frac{1}{6}[\/latex]. Simplify the answer.[reveal-answer q=\"504725\"]Show Answer[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"504725\"]The fractions have unlike denominators, so you need to find a common denominator. Recall that a common denominator can be found by multiplying the two denominators together.\r\n\r\n<p style=\"text-align: center;\">[latex]5\\cdot6=30[\/latex]<\/p>\r\n<p>Rewrite each fraction as an equivalent fraction with a denominator of [latex]30[\/latex].<\/p>\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}\\frac{1}{5}\\cdot \\frac{6}{6}=\\frac{6}{30}\\\\\\\\\\frac{1}{6}\\cdot \\frac{5}{5}=\\frac{5}{30}\\end{array}[\/latex]<\/p>\r\n<p>Subtract the numerators. Simplify the answer if needed.<\/p>\r\n<p style=\"text-align: center;\">[latex] \\frac{6}{30}-\\frac{5}{30}=\\frac{1}{30}[\/latex]<\/p>\r\n<center>[latex] \\frac{1}{5}-\\frac{1}{6}=\\frac{1}{30}[\/latex]<\/center>\r\n<p>[\/hidden-answer]<\/p>\r\n<\/section>\r\n<p>The example below shows how to use\u00a0multiples to find the least common multiple, which will be the least common denominator.<\/p>\r\n<section class=\"textbox example\">Subtract [latex]\\frac{5}{6}-\\frac{1}{4}[\/latex]. Simplify the answer.[reveal-answer q=\"845475\"]Show Answer[\/reveal-answer]<br \/>\r\n[hidden-answer a=\"845475\"]\r\n\r\n<p>Find the least common multiple of the denominators\u2014this is the least common denominator.<\/p>\r\n<p>Multiples of [latex]6: 6, 12, 18, 24[\/latex]<\/p>\r\n<p>Multiples of [latex]4: 4, 8, 12, 16, 20[\/latex]<\/p>\r\n<p>[latex]12[\/latex] is the least common multiple of [latex]6[\/latex] and [latex]4[\/latex].<\/p>\r\n<p>Rewrite each fraction with a denominator of [latex]12[\/latex].<\/p>\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}\\frac{5}{6}\\cdot \\frac{2}{2}=\\frac{10}{12}\\\\\\\\\\frac{1}{4}\\cdot \\frac{3}{3}=\\frac{3}{12}\\end{array}[\/latex]<\/p>\r\n<p>Subtract the fractions. Simplify the answer if needed.<\/p>\r\n<p style=\"text-align: center;\">[latex]\\frac{10}{12}-\\frac{3}{12}=\\frac{7}{12}[\/latex]<\/p>\r\n<center>[latex] \\frac{5}{6}-\\frac{1}{4}=\\frac{7}{12}[\/latex]<\/center>\r\n<p>[\/hidden-answer]<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]8298[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Add and Subtract Fractions<\/li>\n<\/ul>\n<\/section>\n<h2>Adding Fractions<\/h2>\n<p>When you need to add or subtract fractions, you will need to first make sure that the fractions have the same denominator. The denominator tells you how many pieces the whole has been broken into, and the numerator tells you how many of those pieces you are using.<\/p>\n<section class=\"textbox proTip\">You need a common denominator, technically called the <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_4649_12971\">least common multiple<\/a><strong>. <\/strong>Remember that\u00a0if a number is a multiple of another, you can divide them and have no remainder.<\/section>\n<p>One way to find the least common multiple of two or more numbers is to first multiply each\u00a0by [latex]1[\/latex], [latex]2[\/latex], [latex]3[\/latex], [latex]4[\/latex], etc. \u00a0For example, find the least common multiple of [latex]2[\/latex] and [latex]5[\/latex].<\/p>\n<table>\n<tbody>\n<tr>\n<td scope=\"col\">First, list all the multiples of [latex]2[\/latex]:<\/td>\n<td scope=\"col\">Then list all the multiples of [latex]5[\/latex]:<\/td>\n<\/tr>\n<tr>\n<td>[latex]2\\cdot 1 = 2[\/latex]<\/td>\n<td>[latex]5\\cdot 1 = 5[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]2\\cdot 2 = 4[\/latex]<\/td>\n<td>[latex]5\\cdot 2 = 10[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]2\\cdot 3 = 6[\/latex]<\/td>\n<td>[latex]5\\cdot 3 = 15[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]2\\cdot 4 = 8[\/latex]<\/td>\n<td>[latex]5\\cdot 4 = 20[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]2\\cdot 5 = 10[\/latex]<\/td>\n<td>[latex]5\\cdot 5 = 25[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p>The smallest multiple they have in common will be the common denominator for the two!<\/p>\n<section class=\"textbox questionHelp\">\n<p><strong>How To: Adding Fractions with Unlike Denominators<\/strong><\/p>\n<ol>\n<li>Find a common denominator.<\/li>\n<li>Rewrite each fraction using the common denominator.<\/li>\n<li>Now that the fractions have a common denominator, you can add the numerators.<\/li>\n<li>Simplify by canceling out all common factors in the numerator and denominator.<\/li>\n<\/ol>\n<\/section>\n<section class=\"textbox example\">Add [latex]\\frac{2}{3}+\\frac{1}{5}[\/latex].\u00a0Simplify the answer.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q296587\">Show Answer<\/button><\/p>\n<div id=\"q296587\" class=\"hidden-answer\" style=\"display: none\">Since the denominators are not alike, find a common denominator by multiplying the denominators.<\/p>\n<p style=\"text-align: center;\">[latex]3\\cdot5=15[\/latex]<\/p>\n<p>Rewrite each fraction with a denominator of [latex]15[\/latex].<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}\\frac{2}{3}\\cdot \\frac{5}{5}=\\frac{10}{15}\\\\\\\\\\frac{1}{5}\\cdot \\frac{3}{3}=\\frac{3}{15}\\end{array}[\/latex]<\/p>\n<p>Add the fractions by adding the numerators and keeping the denominator the same. Make sure the fraction cannot be simplified.<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{10}{15}+\\frac{3}{15}=\\frac{13}{15}[\/latex]<\/p>\n<div style=\"text-align: center;\">[latex]\\frac{2}{3}+\\frac{1}{5}=\\frac{13}{15}[\/latex]<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox proTip\">You can find a common denominator by finding the common multiples of the denominators. The least common multiple is the easiest to use.<\/section>\n<section class=\"textbox example\">Add\u00a0[latex]\\frac{3}{7}+\\frac{2}{21}[\/latex]. Simplify the answer.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q553019\">Show Answer<\/button><\/p>\n<div id=\"q553019\" class=\"hidden-answer\" style=\"display: none\">\n<p>Since the denominators are not alike, find the least common denominator by finding the least common multiple (LCM) of [latex]7[\/latex] and [latex]21[\/latex].<\/p>\n<p>Multiples of [latex]7: 7, 14, 21[\/latex]<\/p>\n<p>Multiples of [latex]21: 21[\/latex]<\/p>\n<p>Rewrite each fraction with a denominator of [latex]21[\/latex].<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}\\frac{3}{7}\\cdot \\frac{3}{3}=\\frac{9}{21}\\\\\\\\\\frac{2}{21}\\end{array}[\/latex]<\/p>\n<p>Add the fractions by adding the numerators and keeping the denominator the same. Make sure the fraction cannot be simplified.<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{9}{21}+\\frac{2}{21}=\\frac{11}{21}[\/latex]<\/p>\n<div style=\"text-align: center;\">[latex]\\frac{3}{7}+\\frac{2}{21}=\\frac{11}{21}[\/latex]<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm8297\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=8297&theme=lumen&iframe_resize_id=ohm8297&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<h2>Subtracting Fractions<\/h2>\n<p>Subtracting fractions follows a similar process to adding fractions. When you subtract fractions, you must think about whether they have a common denominator, just like with adding fractions.<\/p>\n<section class=\"textbox questionHelp\">\n<p><strong>How To: Subtracting Fractions with Unlike Denominators<\/strong><\/p>\n<ol>\n<li>Find a common denominator.<\/li>\n<li>Rewrite each fraction using the common denominator.<\/li>\n<li>Now that the fractions have a common denominator, you can subtract the numerators.<\/li>\n<li>Simplify by canceling out all common factors in the numerator and denominator.<\/li>\n<\/ol>\n<\/section>\n<p>Below are some examples of subtracting fractions whose denominators are not alike.<\/p>\n<section class=\"textbox example\">Subtract\u00a0[latex]\\frac{1}{5}-\\frac{1}{6}[\/latex]. Simplify the answer.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q504725\">Show Answer<\/button><\/p>\n<div id=\"q504725\" class=\"hidden-answer\" style=\"display: none\">The fractions have unlike denominators, so you need to find a common denominator. Recall that a common denominator can be found by multiplying the two denominators together.<\/p>\n<p style=\"text-align: center;\">[latex]5\\cdot6=30[\/latex]<\/p>\n<p>Rewrite each fraction as an equivalent fraction with a denominator of [latex]30[\/latex].<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}\\frac{1}{5}\\cdot \\frac{6}{6}=\\frac{6}{30}\\\\\\\\\\frac{1}{6}\\cdot \\frac{5}{5}=\\frac{5}{30}\\end{array}[\/latex]<\/p>\n<p>Subtract the numerators. Simplify the answer if needed.<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{6}{30}-\\frac{5}{30}=\\frac{1}{30}[\/latex]<\/p>\n<div style=\"text-align: center;\">[latex]\\frac{1}{5}-\\frac{1}{6}=\\frac{1}{30}[\/latex]<\/div>\n<\/div>\n<\/div>\n<\/section>\n<p>The example below shows how to use\u00a0multiples to find the least common multiple, which will be the least common denominator.<\/p>\n<section class=\"textbox example\">Subtract [latex]\\frac{5}{6}-\\frac{1}{4}[\/latex]. Simplify the answer.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q845475\">Show Answer<\/button><\/p>\n<div id=\"q845475\" class=\"hidden-answer\" style=\"display: none\">\n<p>Find the least common multiple of the denominators\u2014this is the least common denominator.<\/p>\n<p>Multiples of [latex]6: 6, 12, 18, 24[\/latex]<\/p>\n<p>Multiples of [latex]4: 4, 8, 12, 16, 20[\/latex]<\/p>\n<p>[latex]12[\/latex] is the least common multiple of [latex]6[\/latex] and [latex]4[\/latex].<\/p>\n<p>Rewrite each fraction with a denominator of [latex]12[\/latex].<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}\\frac{5}{6}\\cdot \\frac{2}{2}=\\frac{10}{12}\\\\\\\\\\frac{1}{4}\\cdot \\frac{3}{3}=\\frac{3}{12}\\end{array}[\/latex]<\/p>\n<p>Subtract the fractions. Simplify the answer if needed.<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{10}{12}-\\frac{3}{12}=\\frac{7}{12}[\/latex]<\/p>\n<div style=\"text-align: center;\">[latex]\\frac{5}{6}-\\frac{1}{4}=\\frac{7}{12}[\/latex]<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm8298\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=8298&theme=lumen&iframe_resize_id=ohm8298&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<div class=\"glossary\"><span class=\"screen-reader-text\" id=\"definition\">definition<\/span><template id=\"term_4649_12971\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_4649_12971\"><div tabindex=\"-1\"><p>The least common multiple (LCM) of two or more integers is the smallest positive integer that is divisible by each of those integers without leaving a remainder. <\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><\/div>","protected":false},"author":16,"menu_order":3,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"Revision and Adaptation\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Unit 2: Fractions and Mixed Numbers, from Developmental Math: An Open Program\",\"author\":\"\",\"organization\":\"Monterey Institute of Technology and Education\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","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":[{"type":"original","description":"Revision and Adaptation","author":"","organization":"Lumen Learning","url":"","project":"","license":"cc-by","license_terms":""},{"type":"cc","description":"Unit 2: Fractions and Mixed Numbers, from Developmental Math: An Open Program","author":"","organization":"Monterey Institute of Technology and Education","url":"","project":"","license":"cc-by","license_terms":""}],"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\/4649"}],"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":26,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/4649\/revisions"}],"predecessor-version":[{"id":14965,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/4649\/revisions\/14965"}],"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\/4649\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/media?parent=4649"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapter-type?post=4649"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/contributor?post=4649"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/license?post=4649"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}