{"id":4128,"date":"2020-04-06T02:44:43","date_gmt":"2020-04-06T02:44:43","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforlibscoreq\/?post_type=chapter&#038;p=4128"},"modified":"2021-02-06T00:03:02","modified_gmt":"2021-02-06T00:03:02","slug":"subtracting-fractions-with-common-denominators","status":"web-only","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/chapter\/subtracting-fractions-with-common-denominators\/","title":{"raw":"Subtracting Fractions With Common Denominators","rendered":"Subtracting Fractions With Common Denominators"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Use fraction circles to find the difference between two fractions with like denominators<\/li>\r\n \t<li>Subtract fractions with a like denominator without fraction circles<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2>Model Fraction Subtraction<\/h2>\r\nSubtracting two fractions with common denominators is much like adding fractions. Think of a pizza that was cut into [latex]12[\/latex] slices. Suppose five pieces are eaten for dinner. This means that, after dinner, there are seven pieces (or [latex]{\\Large\\frac{7}{12}}[\/latex] of the pizza) left in the box. If Leonardo eats [latex]2[\/latex] of these remaining pieces (or [latex]{\\Large\\frac{2}{12}}[\/latex] of the pizza), how much is left? There would be [latex]5[\/latex] pieces left (or [latex]{\\Large\\frac{5}{12}}[\/latex] of the pizza).\r\n<p style=\"text-align: center\">[latex]{\\Large\\frac{7}{12}}-{\\Large\\frac{2}{12}}={\\Large\\frac{5}{12}}[\/latex]<\/p>\r\nLet\u2019s use fraction circles to model the same example, [latex]{\\Large\\frac{7}{12}}-{\\Large\\frac{2}{12}}[\/latex].\r\n\r\nStart with seven [latex]{\\Large\\frac{1}{12}}[\/latex] pieces. Take away two [latex]{\\Large\\frac{1}{12}}[\/latex] pieces. How many twelfths are left?\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221006\/CNX_BMath_Figure_04_04_006_img.png\" alt=\"The bottom reads 7 twelfths minus 2 twelfths equals 5 twelfths. Above 7 twelfths, there is a circle divided into 12 equal pieces, with 7 pieces shaded in orange. Above 2 twelfths, the same circle is shown, but 2 of the 7 pieces are shaded in grey. Above 5 twelfths, the 2 grey pieces are no longer shaded, so there is a circle divided into 12 pieces with 5 of the pieces shaded in orange.\" \/>\r\nAgain, we have five twelfths, [latex]{\\Large\\frac{5}{12}}[\/latex].\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nUse fraction circles to find the difference: [latex]{\\Large\\frac{4}{5}}-{\\Large\\frac{1}{5}}[\/latex]\r\n\r\nSolution:\r\nStart with four [latex]{\\Large\\frac{1}{5}}[\/latex] pieces. Take away one [latex]{\\Large\\frac{1}{5}}[\/latex] piece. Count how many fifths are left. There are three [latex]{\\Large\\frac{1}{5}}[\/latex] pieces left.\r\n\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221008\/CNX_BMath_Figure_04_04_007_img.png\" alt=\"The bottom reads 4 fifths minus 1 fifth equals 3 fifths. Above 4 fifths, there is a circle divided into 5 equal pieces, with 4 pieces shaded in orange. Above 1 fifth, the same circle is shown, but 1 of the 4 shaded pieces is shaded in grey. Above 3 fifths, the 1 grey piece is no longer shaded, so there is a circle divided into 5 pieces with 3 of the pieces shaded in orange.\" \/>\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n[ohm_question height=\"270\"]146190[\/ohm_question]\r\n\r\n<\/div>\r\n<h2>Subtract Fractions with a Common Denominator<\/h2>\r\nWe subtract fractions with a common denominator in much the same way as we add fractions with a common denominator.\r\n<div class=\"textbox shaded\">\r\n<h3>Fraction Subtraction<\/h3>\r\nIf [latex]a,b,\\text{ and }c[\/latex] are numbers where [latex]c\\ne 0[\/latex], then\r\n<p style=\"text-align: center\">[latex]{\\Large\\frac{a}{c}}-{\\Large\\frac{b}{c}}={\\Large\\frac{a-b}{c}}[\/latex]<\/p>\r\nTo subtract fractions with a common denominators, we subtract the numerators and place the difference over the common denominator.\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nFind the difference: [latex]{\\Large\\frac{23}{24}}-{\\Large\\frac{14}{24}}[\/latex]\r\n[reveal-answer q=\"842015\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"842015\"]\r\n\r\nSolution:\r\n<table id=\"eip-id1168469826203\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>[latex]{\\Large\\frac{23}{24}}-{\\Large\\frac{14}{24}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Subtract the numerators and place the difference over the common denominator.<\/td>\r\n<td>[latex]{\\Large\\frac{23 - 14}{24}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify the numerator.<\/td>\r\n<td>[latex]{\\Large\\frac{9}{24}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify the fraction by removing common factors.<\/td>\r\n<td>[latex]{\\Large\\frac{3}{8}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\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 height=\"270\"]146191[\/ohm_question]\r\n\r\n<\/div>\r\nWatch the following video for more examples of subtracting fractions with like denominators.\r\n\r\nhttps:\/\/youtu.be\/7CeAQcpOJw0\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nFind the difference: [latex]{\\Large-\\frac{10}{7}-\\frac{4}{7}}[\/latex]\r\n[reveal-answer q=\"955589\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"955589\"]\r\n\r\nSolution:\r\nRemember, the fraction [latex]{\\Large-\\frac{10}{7}}[\/latex] can be written as [latex]{\\Large\\frac{-10}{7}}[\/latex]\r\n<table id=\"eip-id1168469856735\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>[latex]-\\frac{10}{7}-\\frac{4}{7}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Subtract the numerators.<\/td>\r\n<td>[latex]{\\Large\\frac{-10 - 4}{7}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]{\\Large\\frac{-14}{7}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rewrite with the negative sign in front of the fraction.<\/td>\r\n<td>[latex]{\\Large-\\frac{14}{7}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nNow lets do an example that involves both addition and subtraction.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nSimplify: [latex]{\\Large\\frac{3}{8}}+\\left(-{\\Large\\frac{5}{8}}\\right)-{\\Large\\frac{1}{8}}[\/latex]\r\n[reveal-answer q=\"637721\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"637721\"]\r\n\r\nSolution:\r\n<table id=\"eip-id1168468417178\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]\\Large\\frac{3}{8}+\\left(-\\frac{5}{8}\\right)-\\frac{1}{8}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Combine the numerators over the common denominator.<\/td>\r\n<td>[latex]{\\Large\\frac{3+\\left(-5\\right)-1}{8}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify the numerator, working left to right.<\/td>\r\n<td>[latex]{\\Large\\frac{-2 - 1}{8}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Subtract the terms in the numerator.<\/td>\r\n<td>[latex]{\\Large\\frac{-3}{8}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rewrite with the negative sign in front of the fraction.<\/td>\r\n<td>[latex]{\\Large-\\frac{3}{8}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\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 height=\"270\"]146250[\/ohm_question]\r\n\r\n<\/div>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Use fraction circles to find the difference between two fractions with like denominators<\/li>\n<li>Subtract fractions with a like denominator without fraction circles<\/li>\n<\/ul>\n<\/div>\n<h2>Model Fraction Subtraction<\/h2>\n<p>Subtracting two fractions with common denominators is much like adding fractions. Think of a pizza that was cut into [latex]12[\/latex] slices. Suppose five pieces are eaten for dinner. This means that, after dinner, there are seven pieces (or [latex]{\\Large\\frac{7}{12}}[\/latex] of the pizza) left in the box. If Leonardo eats [latex]2[\/latex] of these remaining pieces (or [latex]{\\Large\\frac{2}{12}}[\/latex] of the pizza), how much is left? There would be [latex]5[\/latex] pieces left (or [latex]{\\Large\\frac{5}{12}}[\/latex] of the pizza).<\/p>\n<p style=\"text-align: center\">[latex]{\\Large\\frac{7}{12}}-{\\Large\\frac{2}{12}}={\\Large\\frac{5}{12}}[\/latex]<\/p>\n<p>Let\u2019s use fraction circles to model the same example, [latex]{\\Large\\frac{7}{12}}-{\\Large\\frac{2}{12}}[\/latex].<\/p>\n<p>Start with seven [latex]{\\Large\\frac{1}{12}}[\/latex] pieces. Take away two [latex]{\\Large\\frac{1}{12}}[\/latex] pieces. How many twelfths are left?<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221006\/CNX_BMath_Figure_04_04_006_img.png\" alt=\"The bottom reads 7 twelfths minus 2 twelfths equals 5 twelfths. Above 7 twelfths, there is a circle divided into 12 equal pieces, with 7 pieces shaded in orange. Above 2 twelfths, the same circle is shown, but 2 of the 7 pieces are shaded in grey. Above 5 twelfths, the 2 grey pieces are no longer shaded, so there is a circle divided into 12 pieces with 5 of the pieces shaded in orange.\" \/><br \/>\nAgain, we have five twelfths, [latex]{\\Large\\frac{5}{12}}[\/latex].<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Use fraction circles to find the difference: [latex]{\\Large\\frac{4}{5}}-{\\Large\\frac{1}{5}}[\/latex]<\/p>\n<p>Solution:<br \/>\nStart with four [latex]{\\Large\\frac{1}{5}}[\/latex] pieces. Take away one [latex]{\\Large\\frac{1}{5}}[\/latex] piece. Count how many fifths are left. There are three [latex]{\\Large\\frac{1}{5}}[\/latex] pieces left.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221008\/CNX_BMath_Figure_04_04_007_img.png\" alt=\"The bottom reads 4 fifths minus 1 fifth equals 3 fifths. Above 4 fifths, there is a circle divided into 5 equal pieces, with 4 pieces shaded in orange. Above 1 fifth, the same circle is shown, but 1 of the 4 shaded pieces is shaded in grey. Above 3 fifths, the 1 grey piece is no longer shaded, so there is a circle divided into 5 pieces with 3 of the pieces shaded in orange.\" \/><\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146190\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146190&theme=oea&iframe_resize_id=ohm146190&show_question_numbers\" width=\"100%\" height=\"270\"><\/iframe><\/p>\n<\/div>\n<h2>Subtract Fractions with a Common Denominator<\/h2>\n<p>We subtract fractions with a common denominator in much the same way as we add fractions with a common denominator.<\/p>\n<div class=\"textbox shaded\">\n<h3>Fraction Subtraction<\/h3>\n<p>If [latex]a,b,\\text{ and }c[\/latex] are numbers where [latex]c\\ne 0[\/latex], then<\/p>\n<p style=\"text-align: center\">[latex]{\\Large\\frac{a}{c}}-{\\Large\\frac{b}{c}}={\\Large\\frac{a-b}{c}}[\/latex]<\/p>\n<p>To subtract fractions with a common denominators, we subtract the numerators and place the difference over the common denominator.<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Find the difference: [latex]{\\Large\\frac{23}{24}}-{\\Large\\frac{14}{24}}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q842015\">Show Solution<\/span><\/p>\n<div id=\"q842015\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168469826203\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\n<tbody>\n<tr>\n<td>[latex]{\\Large\\frac{23}{24}}-{\\Large\\frac{14}{24}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Subtract the numerators and place the difference over the common denominator.<\/td>\n<td>[latex]{\\Large\\frac{23 - 14}{24}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify the numerator.<\/td>\n<td>[latex]{\\Large\\frac{9}{24}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify the fraction by removing common factors.<\/td>\n<td>[latex]{\\Large\\frac{3}{8}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146191\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146191&theme=oea&iframe_resize_id=ohm146191&show_question_numbers\" width=\"100%\" height=\"270\"><\/iframe><\/p>\n<\/div>\n<p>Watch the following video for more examples of subtracting fractions with like denominators.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Ex:  Subtract Fractions with Like Denominators\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/7CeAQcpOJw0?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Find the difference: [latex]{\\Large-\\frac{10}{7}-\\frac{4}{7}}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q955589\">Show Solution<\/span><\/p>\n<div id=\"q955589\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<br \/>\nRemember, the fraction [latex]{\\Large-\\frac{10}{7}}[\/latex] can be written as [latex]{\\Large\\frac{-10}{7}}[\/latex]<\/p>\n<table id=\"eip-id1168469856735\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\n<tbody>\n<tr>\n<td>[latex]-\\frac{10}{7}-\\frac{4}{7}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Subtract the numerators.<\/td>\n<td>[latex]{\\Large\\frac{-10 - 4}{7}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]{\\Large\\frac{-14}{7}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Rewrite with the negative sign in front of the fraction.<\/td>\n<td>[latex]{\\Large-\\frac{14}{7}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>Now lets do an example that involves both addition and subtraction.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Simplify: [latex]{\\Large\\frac{3}{8}}+\\left(-{\\Large\\frac{5}{8}}\\right)-{\\Large\\frac{1}{8}}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q637721\">Show Solution<\/span><\/p>\n<div id=\"q637721\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168468417178\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]\\Large\\frac{3}{8}+\\left(-\\frac{5}{8}\\right)-\\frac{1}{8}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Combine the numerators over the common denominator.<\/td>\n<td>[latex]{\\Large\\frac{3+\\left(-5\\right)-1}{8}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify the numerator, working left to right.<\/td>\n<td>[latex]{\\Large\\frac{-2 - 1}{8}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Subtract the terms in the numerator.<\/td>\n<td>[latex]{\\Large\\frac{-3}{8}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Rewrite with the negative sign in front of the fraction.<\/td>\n<td>[latex]{\\Large-\\frac{3}{8}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146250\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146250&theme=oea&iframe_resize_id=ohm146250&show_question_numbers\" width=\"100%\" height=\"270\"><\/iframe><\/p>\n<\/div>\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-4128\">\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>Question ID: 146190, 146191, 146192, 146250. <strong>Authored by<\/strong>: Alyson Day. <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><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>Ex: Subtract Fractions with Like Denominators. <strong>Authored by<\/strong>: James Sousa (mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/7CeAQcpOJw0\">https:\/\/youtu.be\/7CeAQcpOJw0<\/a>. <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, Specific attribution<\/div><ul class=\"citation-list\"><li>Prealgebra. <strong>Provided by<\/strong>: OpenStax. <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>: Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":25777,"menu_order":5,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757\"},{\"type\":\"cc\",\"description\":\"Ex: Subtract Fractions with Like Denominators\",\"author\":\"James Sousa (mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/7CeAQcpOJw0\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Question ID: 146190, 146191, 146192, 146250\",\"author\":\"Alyson Day\",\"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":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-4128","chapter","type-chapter","status-web-only","hentry"],"part":329,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4128","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/users\/25777"}],"version-history":[{"count":4,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4128\/revisions"}],"predecessor-version":[{"id":5264,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4128\/revisions\/5264"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/parts\/329"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/4128\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/media?parent=4128"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=4128"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/contributor?post=4128"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/license?post=4128"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}