{"id":3688,"date":"2020-01-29T03:16:22","date_gmt":"2020-01-29T03:16:22","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforlibscoreq\/?post_type=chapter&#038;p=3688"},"modified":"2021-02-05T23:51:10","modified_gmt":"2021-02-05T23:51:10","slug":"simplifying-expressions-using-the-properties-of-identities-inverses-and-zero","status":"web-only","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/chapter\/simplifying-expressions-using-the-properties-of-identities-inverses-and-zero\/","title":{"raw":"Simplifying Expressions Using the Properties of Identities, Inverses, and Zero","rendered":"Simplifying Expressions Using the Properties of Identities, Inverses, and Zero"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Simplify algebraic expressions using identity, inverse and zero properties<\/li>\r\n \t<li>Identify which property(ies) to use to simplify an algebraic expression<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2>Simplify Expressions using the Properties of Identities, Inverses, and Zero<\/h2>\r\nWe will now practice using the properties of identities, inverses, and zero to simplify expressions.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nSimplify: [latex]3x+15 - 3x[\/latex]\r\n\r\nSolution:\r\n<table id=\"eip-id1168469344078\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>[latex]3x+15 - 3x[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Notice the additive inverses, [latex]3x[\/latex] and [latex]-3x[\/latex] .<\/td>\r\n<td>[latex]0+15[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add.<\/td>\r\n<td>[latex]15[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146488[\/ohm_question]\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nSimplify: [latex]4\\left(0.25q\\right)[\/latex]\r\n[reveal-answer q=\"169628\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"169628\"]\r\n\r\nSolution:\r\n<table id=\"eip-id1168469838348\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]4\\left(0.25q\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Regroup, using the associative property.<\/td>\r\n<td>[latex]\\left[4\\left(0.25\\right)\\right]q[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]1.00q[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify; 1 is the multiplicative identity.<\/td>\r\n<td>[latex]q[\/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]146489[\/ohm_question]\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nSimplify: [latex]{\\Large\\frac{0}{n+5}}[\/latex] , where [latex]n\\ne -5[\/latex]\r\n[reveal-answer q=\"35911\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"35911\"]\r\n\r\nSolution:\r\n<table id=\"eip-id1168468294495\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]{\\Large\\frac{0}{n+5}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Zero divided by any real number except itself is zero.<\/td>\r\n<td>[latex]0[\/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]146490[\/ohm_question]\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nSimplify: [latex]{\\Large\\frac{10 - 3p}{0}}[\/latex].\r\n[reveal-answer q=\"419108\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"419108\"]\r\n\r\nSolution:\r\n<table id=\"eip-id1168468312547\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]{\\Large\\frac{10 - 3p}{0}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Division by zero is undefined.<\/td>\r\n<td>undefined<\/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]146491[\/ohm_question]\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nSimplify: [latex]{\\Large\\frac{3}{4}}\\cdot {\\Large\\frac{4}{3}}\\left(6x+12\\right)[\/latex].\r\n[reveal-answer q=\"39067\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"39067\"]\r\n\r\nSolution:\r\nWe cannot combine the terms in parentheses, so we multiply the two fractions first.\r\n<table id=\"eip-id1168469858071\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]{\\Large\\frac{3}{4}}\\cdot {\\Large\\frac{4}{3}}\\left(6x+12\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply; the product of reciprocals is 1.<\/td>\r\n<td>[latex]1\\left(6x+12\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify by recognizing the multiplicative identity.<\/td>\r\n<td>[latex]6x+12[\/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]146493[\/ohm_question]\r\n\r\n<\/div>\r\nAll the properties of real numbers we have used in this chapter are summarized in the table below.\r\n<table id=\"fs-id1166497502402\" style=\"width: 85%\" summary=\"The table is labeled above as \"><caption>Properties of Real Numbers<\/caption>\r\n<thead>\r\n<tr valign=\"top\">\r\n<th>Property<\/th>\r\n<th>Of Addition<\/th>\r\n<th>Of Multiplication<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td><strong>Commutative Property<\/strong><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>If <em>a<\/em> and <em>b<\/em> are real numbers then\u2026<\/td>\r\n<td>[latex]a+b=b+a[\/latex]<\/td>\r\n<td>[latex]a\\cdot b=b\\cdot a[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td><strong>Associative Property<\/strong><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>If <em>a<\/em>, <em>b<\/em>, and <em>c<\/em> are real numbers then\u2026<\/td>\r\n<td>[latex]\\left(a+b\\right)+c=a+\\left(b+c\\right)[\/latex]<\/td>\r\n<td>[latex]\\left(a\\cdot b\\right)\\cdot c=a\\cdot \\left(b\\cdot c\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td><strong>Identity Property<\/strong><\/td>\r\n<td>[latex]0[\/latex] is the additive identity<\/td>\r\n<td>[latex]1[\/latex] is the multiplicative identity<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>For any real number <em>a<\/em>,<\/td>\r\n<td>[latex]\\begin{array}{l}a+0=a\\\\ 0+a=a\\end{array}[\/latex]<\/td>\r\n<td>[latex]\\begin{array}{l}a\\cdot 1=a\\\\ 1\\cdot a=a\\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td><strong>Inverse Property<\/strong><\/td>\r\n<td>[latex]-\\mathit{\\text{a}}[\/latex] is the additive inverse of [latex]a[\/latex]<\/td>\r\n<td>[latex]a,a\\ne 0[\/latex]\r\n\r\n[latex]\\frac{1}{a}[\/latex] is the multiplicative inverse of [latex]a[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>For any real number <em>a<\/em>,<\/td>\r\n<td>[latex]a+\\text{(}\\text{-}\\mathit{\\text{a}}\\text{)}=0[\/latex]<\/td>\r\n<td>[latex]a\\cdot 1a=1[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td colspan=\"3\"><strong>Distributive Property<\/strong>\r\n\r\nIf [latex]a,b,c[\/latex] are real numbers, then [latex]a\\left(b+c\\right)=ab+ac[\/latex]<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td><strong>Properties of Zero<\/strong><\/td>\r\n<td><\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>For any real number <em>a<\/em>,<\/td>\r\n<td>[latex]\\begin{array}{l}a\\cdot 0=0\\\\ 0\\cdot a=0\\end{array}[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>For any real number [latex]a,a\\ne 0[\/latex]<\/td>\r\n<td>[latex]{\\Large\\frac{0}{a}}=0[\/latex]\r\n\r\n[latex]{\\Large\\frac{a}{0}}[\/latex] is undefined<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n&nbsp;","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Simplify algebraic expressions using identity, inverse and zero properties<\/li>\n<li>Identify which property(ies) to use to simplify an algebraic expression<\/li>\n<\/ul>\n<\/div>\n<h2>Simplify Expressions using the Properties of Identities, Inverses, and Zero<\/h2>\n<p>We will now practice using the properties of identities, inverses, and zero to simplify expressions.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Simplify: [latex]3x+15 - 3x[\/latex]<\/p>\n<p>Solution:<\/p>\n<table id=\"eip-id1168469344078\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\n<tbody>\n<tr>\n<td>[latex]3x+15 - 3x[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Notice the additive inverses, [latex]3x[\/latex] and [latex]-3x[\/latex] .<\/td>\n<td>[latex]0+15[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td>[latex]15[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146488\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146488&theme=oea&iframe_resize_id=ohm146488&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Simplify: [latex]4\\left(0.25q\\right)[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q169628\">Show Solution<\/span><\/p>\n<div id=\"q169628\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168469838348\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]4\\left(0.25q\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Regroup, using the associative property.<\/td>\n<td>[latex]\\left[4\\left(0.25\\right)\\right]q[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]1.00q[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify; 1 is the multiplicative identity.<\/td>\n<td>[latex]q[\/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=\"ohm146489\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146489&theme=oea&iframe_resize_id=ohm146489&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Simplify: [latex]{\\Large\\frac{0}{n+5}}[\/latex] , where [latex]n\\ne -5[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q35911\">Show Solution<\/span><\/p>\n<div id=\"q35911\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168468294495\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]{\\Large\\frac{0}{n+5}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Zero divided by any real number except itself is zero.<\/td>\n<td>[latex]0[\/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=\"ohm146490\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146490&theme=oea&iframe_resize_id=ohm146490&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Simplify: [latex]{\\Large\\frac{10 - 3p}{0}}[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q419108\">Show Solution<\/span><\/p>\n<div id=\"q419108\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168468312547\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]{\\Large\\frac{10 - 3p}{0}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Division by zero is undefined.<\/td>\n<td>undefined<\/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=\"ohm146491\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146491&theme=oea&iframe_resize_id=ohm146491&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Simplify: [latex]{\\Large\\frac{3}{4}}\\cdot {\\Large\\frac{4}{3}}\\left(6x+12\\right)[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q39067\">Show Solution<\/span><\/p>\n<div id=\"q39067\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<br \/>\nWe cannot combine the terms in parentheses, so we multiply the two fractions first.<\/p>\n<table id=\"eip-id1168469858071\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]{\\Large\\frac{3}{4}}\\cdot {\\Large\\frac{4}{3}}\\left(6x+12\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply; the product of reciprocals is 1.<\/td>\n<td>[latex]1\\left(6x+12\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify by recognizing the multiplicative identity.<\/td>\n<td>[latex]6x+12[\/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=\"ohm146493\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146493&theme=oea&iframe_resize_id=ohm146493&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>All the properties of real numbers we have used in this chapter are summarized in the table below.<\/p>\n<table id=\"fs-id1166497502402\" style=\"width: 85%\" summary=\"The table is labeled above as\">\n<caption>Properties of Real Numbers<\/caption>\n<thead>\n<tr valign=\"top\">\n<th>Property<\/th>\n<th>Of Addition<\/th>\n<th>Of Multiplication<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td><strong>Commutative Property<\/strong><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>If <em>a<\/em> and <em>b<\/em> are real numbers then\u2026<\/td>\n<td>[latex]a+b=b+a[\/latex]<\/td>\n<td>[latex]a\\cdot b=b\\cdot a[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td><strong>Associative Property<\/strong><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>If <em>a<\/em>, <em>b<\/em>, and <em>c<\/em> are real numbers then\u2026<\/td>\n<td>[latex]\\left(a+b\\right)+c=a+\\left(b+c\\right)[\/latex]<\/td>\n<td>[latex]\\left(a\\cdot b\\right)\\cdot c=a\\cdot \\left(b\\cdot c\\right)[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td><strong>Identity Property<\/strong><\/td>\n<td>[latex]0[\/latex] is the additive identity<\/td>\n<td>[latex]1[\/latex] is the multiplicative identity<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>For any real number <em>a<\/em>,<\/td>\n<td>[latex]\\begin{array}{l}a+0=a\\\\ 0+a=a\\end{array}[\/latex]<\/td>\n<td>[latex]\\begin{array}{l}a\\cdot 1=a\\\\ 1\\cdot a=a\\end{array}[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td><strong>Inverse Property<\/strong><\/td>\n<td>[latex]-\\mathit{\\text{a}}[\/latex] is the additive inverse of [latex]a[\/latex]<\/td>\n<td>[latex]a,a\\ne 0[\/latex]<\/p>\n<p>[latex]\\frac{1}{a}[\/latex] is the multiplicative inverse of [latex]a[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>For any real number <em>a<\/em>,<\/td>\n<td>[latex]a+\\text{(}\\text{-}\\mathit{\\text{a}}\\text{)}=0[\/latex]<\/td>\n<td>[latex]a\\cdot 1a=1[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td colspan=\"3\"><strong>Distributive Property<\/strong><\/p>\n<p>If [latex]a,b,c[\/latex] are real numbers, then [latex]a\\left(b+c\\right)=ab+ac[\/latex]<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td><strong>Properties of Zero<\/strong><\/td>\n<td><\/td>\n<td><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>For any real number <em>a<\/em>,<\/td>\n<td>[latex]\\begin{array}{l}a\\cdot 0=0\\\\ 0\\cdot a=0\\end{array}[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>For any real number [latex]a,a\\ne 0[\/latex]<\/td>\n<td>[latex]{\\Large\\frac{0}{a}}=0[\/latex]<\/p>\n<p>[latex]{\\Large\\frac{a}{0}}[\/latex] is undefined<\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/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-3688\">\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 146493, 146491, 146490, 146487. <strong>Authored 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, 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":11,"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\":\"original\",\"description\":\"Question ID 146493, 146491, 146490, 146487\",\"author\":\"Lumen 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