{"id":1415,"date":"2021-11-01T18:56:02","date_gmt":"2021-11-01T18:56:02","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/uvu-introductoryalgebra\/?post_type=chapter&#038;p=1415"},"modified":"2024-06-02T23:45:41","modified_gmt":"2024-06-02T23:45:41","slug":"1-3-7-order-of-operations-with-fractions","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/uvu-introductoryalgebra\/chapter\/1-3-7-order-of-operations-with-fractions\/","title":{"raw":"1.3.7: Order of Operations with Fractions","rendered":"1.3.7: Order of Operations with Fractions"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\n<ul>\r\n \t<li>Use order of operations to simplify expressions involving fractions<\/li>\r\n<\/ul>\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Key words<\/h3>\r\n<ul>\r\n \t<li><strong>Fraction Bar<\/strong>: the bar in a fraction that acts like as grouping symbol<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2>Using the order of operations with fractions<\/h2>\r\nRecall that the order of operations outlines the order in which terms in an expression must be simplified.\r\n<div class=\"textbox shaded\">\r\n<h3>Order of Operations<\/h3>\r\nWhen simplifying mathematical expressions perform the operations in the following order:\r\n1. Grouping Symbols\r\n<ul id=\"fs-id1171104029952\">\r\n \t<li>Simplify all expressions inside the parentheses or other grouping symbols, working on the innermost parentheses first.<\/li>\r\n<\/ul>\r\n2. Exponents\r\n<ul id=\"fs-id1171104407077\">\r\n \t<li>Simplify all expressions with exponents.<\/li>\r\n<\/ul>\r\n3. Multiplication and Division from left to right\r\n<ul id=\"fs-id1171103140103\">\r\n \t<li>Perform all multiplication and division in order from left to right. These operations have equal priority.<\/li>\r\n<\/ul>\r\n4. Addition and Subtraction\r\n<ul id=\"fs-id1171104002792\">\r\n \t<li>Perform all addition and subtraction in order from left to right. These operations have equal priority.<\/li>\r\n<\/ul>\r\n<\/div>\r\nPerforming the order of operations for fractional expressions is no different than order of operations for integers.\r\n<div class=\"textbox examples\">\r\n<h3>Example<\/h3>\r\nSimplify: [latex]\\frac{3}{5} \\cdot \\frac{2}{3} \\div \\frac{1}{6}[\/latex]\r\n\r\nSolution:\r\n<table style=\"border-collapse: collapse; width: 59.2391%; height: 96px;\" border=\"0\">\r\n<tbody>\r\n<tr style=\"height: 12px;\">\r\n<td style=\"width: 540.359px; height: 12px;\">One term<\/td>\r\n<td style=\"width: 540.359px; height: 12px;\">[latex]\\frac{3}{5} \\cdot \\frac{2}{3} \\div \\frac{1}{6}[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 12px;\">\r\n<td style=\"width: 540.359px; height: 12px;\">Multiply or divide from left to right.<\/td>\r\n<td style=\"width: 540.359px; height: 12px;\">[latex]\\large\\frac{\\color{red}{\\cancel{3}} \\cdot 2}{5 \\cdot \\color{red}{\\cancel{3}}} \\div \\frac{1}{6}[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 12px;\">\r\n<td style=\"width: 540.359px; height: 12px;\">Simplify by cancelling.<\/td>\r\n<td style=\"width: 540.359px; height: 12px;\">[latex]\\frac{2}{5}\\div \\frac{1}{6}[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 12px;\">\r\n<td style=\"width: 540.359px; height: 12px;\">Turn the division into multiplication of the reciprocal.<\/td>\r\n<td style=\"width: 540.359px; height: 12px;\">[latex]\\frac{2}{5}\\cdot \\frac{6}{1}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 540.359px;\">Multiply.<\/td>\r\n<td style=\"width: 540.359px;\">[latex]\\frac{2\\cdot 6}{5\\cdot 1}[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 12px;\">\r\n<td style=\"width: 540.359px; height: 12px;\">Simplify.<\/td>\r\n<td style=\"width: 540.359px; height: 12px;\">[latex]\\frac{12}{5}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<div class=\"textbox tryit\">\r\n<h3>Try It<\/h3>\r\n[ohm_question]37987[\/ohm_question]\r\n\r\n[ohm_question]133412[\/ohm_question]\r\n\r\n<\/div>\r\nThe following video provides examples of how simplify fractional expression with order of operations.\r\n\r\n[embed]https:\/\/www.youtube.com\/watch?v=ro6yRADn3Mw[\/embed]\r\n<h2>Simplifying an Expression With a Fraction Bar<\/h2>\r\n<em><strong>Fraction bars<\/strong><\/em> act as grouping symbols. The expressions above and below the fraction bar should be treated as if they were in parentheses. For example, [latex]\\frac{4+8}{5 - 3}[\/latex] means [latex]\\left(4+8\\right)\\div\\left(5 - 3\\right)[\/latex]. The order of operations tells us to simplify the numerator and the denominator first\u2014as if there were parentheses\u2014before we divide.\r\n<div class=\"textbox shaded\">\r\n<h3>Simplify an expression with a fraction bar<\/h3>\r\n<ol id=\"eip-id1168467312752\" class=\"stepwise\">\r\n \t<li>Simplify the numerator.<\/li>\r\n \t<li>Simplify the denominator.<\/li>\r\n \t<li>Simplify the fraction.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nSimplify: [latex]\\frac{4+8}{5 - 3}[\/latex]\r\n[reveal-answer q=\"735944\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"735944\"]\r\n\r\nSolution:\r\n<table id=\"eip-id1168468328592\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]\\frac{4+8}{5 - 3}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify the expression in the numerator.<\/td>\r\n<td>[latex]\\frac{12}{5 - 3}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify the expression in the denominator.<\/td>\r\n<td>[latex]\\frac{12}{2}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify the fraction.<\/td>\r\n<td>[latex]6[\/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\"]146163[\/ohm_question]\r\n\r\n<\/div>\r\nthe following video provides another example of how to simplify various expressions that contain a fraction bar.\r\n\r\nhttps:\/\/youtu.be\/eF_jiZvb79w\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nSimplify: [latex]\\frac{4 - 2\\left(3\\right)}{{2}^{2}+2}[\/latex]\r\n[reveal-answer q=\"176453\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"176453\"]\r\n\r\nSolution:\r\n<table id=\"eip-id1168466112842\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]\\frac{4 - \\color{red}{2\\left(3\\right)}}{\\color{red}{{2}^{2}}+2}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Use the order of operations. Multiply in the numerator and use the exponent in the denominator.<\/td>\r\n<td>[latex]\\frac{4 - 6}{4+2}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify the numerator and the denominator.<\/td>\r\n<td>[latex]\\frac{-2}{6}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify the fraction.<\/td>\r\n<td>[latex]-\\frac{1}{3}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<h3><\/h3>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n[ohm_question height=\"270\"]146164[\/ohm_question]\r\n\r\n<\/div>\r\n<h3><\/h3>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nSimplify: [latex]\\frac{{\\left(8 - 4\\right)}^{2}}{{8}^{2}-{4}^{2}}[\/latex]\r\n[reveal-answer q=\"724012\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"724012\"]\r\n\r\nSolution:\r\n<table id=\"eip-id1168468576501\" class=\"unnumbered unstyled\" style=\"width: 99.83633387888707%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 53.84615384615385%;\"><\/td>\r\n<td style=\"width: 45.99018003273322%;\">[latex]\\frac{{\\left(8 - 4\\right)}^{2}}{{8}^{2}-{4}^{2}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 53.84615384615385%;\">Use the order of operations (parentheses first, then exponents).<\/td>\r\n<td style=\"width: 45.99018003273322%;\">[latex]\\frac{{\\left(4\\right)}^{2}}{64 - 16}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 53.84615384615385%;\">Simplify the numerator and denominator.<\/td>\r\n<td style=\"width: 45.99018003273322%;\">[latex]\\frac{16}{48}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 53.84615384615385%;\">Simplify the fraction.<\/td>\r\n<td style=\"width: 45.99018003273322%;\">[latex]\\frac{1}{3}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<h3><\/h3>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n[ohm_question height=\"270\"]146165[\/ohm_question]\r\n\r\n<\/div>\r\n<h3><\/h3>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nSimplify: [latex]\\frac{4\\left(-3\\right)+6\\left(-2\\right)}{-3\\left(2\\right)-2}[\/latex]\r\n[reveal-answer q=\"414011\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"414011\"]\r\n\r\nSolution:\r\n<table id=\"eip-id1168468477542\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]\\frac{4\\left(-3\\right)+6\\left(-2\\right)}{-3\\left(2\\right)-2}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]\\frac{-12+\\left(-12\\right)}{-6 - 2}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]\\frac{-24}{-8}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide.<\/td>\r\n<td>[latex]3[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<h3><\/h3>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n[ohm_question height=\"270\"]146167[\/ohm_question]\r\n\r\n<\/div>\r\nWatch this video to see another example of how to simplify an expression with a fraction bar that contains several different operations.\r\n\r\nhttps:\/\/youtu.be\/fK7-w77cgVQ\r\n\r\nWhen there are two or more fractions, we work each fraction separately, then add or subtract them once they are simplified to lowest terms.\r\n<div class=\"textbox examples\">\r\n<h3>Example<\/h3>\r\nSimplify: \u00a0[latex]\\frac{-3^2+4\\cdot (-6)}{(-5)^2-(6-2)} - \\left [\\frac{6-2^2}{-4}\\right ]^{2}[\/latex]\r\n\r\nSolution\r\n\r\nLet's work each fraction separately, then subtract them.\r\n\r\n1. \u00a0\u00a0[latex]\\frac{-3^2+4\\cdot (-6)}{(-5)^2-(6-2)}[\/latex] \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Exponent and parentheses\r\n\r\n[latex]=\\frac{-9+(-24)}{25-(4)}[\/latex] \u00a0 \u00a0 \u00a0 \u00a0Addition and subtraction\r\n\r\n[latex]=\\frac{-33}{21}[\/latex] \u00a0 \u00a0 \u00a0 \u00a0Simplify\r\n\r\n[latex]=\\frac{-11}{7}[\/latex]\r\n\r\n&nbsp;\r\n\r\n2. \u00a0 [latex]\\left [\\frac{6-2^2}{-4}\\right ]^{2}[\/latex] \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Exponent\r\n\r\n[latex]=\\left [\\frac{6-4}{-4}\\right ]^{2}[\/latex] \u00a0 \u00a0 \u00a0 \u00a0 Subtract\r\n\r\n[latex]=\\left [\\frac{2}{-4}\\right ]^{2}[\/latex] \u00a0 \u00a0 \u00a0 \u00a0 Simplify\r\n\r\n[latex]=\\left [\\frac{1}{-2}\\right ]^{2}[\/latex] \u00a0 \u00a0 \u00a0 \u00a0Square the numerator and denominator\r\n\r\n[latex]=\\frac{1}{4}[\/latex]\r\n\r\n&nbsp;\r\n\r\nFinally, we subtract:\r\n\r\n[latex]\\frac{-3^2+4\\cdot (-6)}{(-5)^2-(6-2)} - \\left [\\frac{6-2^2}{-4}\\right ]^{2}[\/latex]\r\n\r\n[latex]=\\frac{-11}{7}-\\frac{1}{4}[\/latex] \u00a0 \u00a0 \u00a0 LCD = 28. \u00a0Build equivalent fraction with LCD\r\n\r\n[latex]=\\frac{-11\\cdot 4}{7\\cdot 4}-\\frac{1\\cdot 7}{4\\cdot 7}[\/latex] \u00a0 \u00a0 \u00a0 \u00a0 Multiply numerators and denominators\r\n\r\n[latex]=\\frac{-44}{28}-\\frac{7}{28}[\/latex] \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Subtract numerators and keep common denominator\r\n\r\n[latex]=\\frac{-44-7}{28}[\/latex] \u00a0 \u00a0 \u00a0 \u00a0 Subtract\r\n\r\n[latex]=\\frac{-51}{28}[\/latex]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox tryit\">\r\n<h3>Try It<\/h3>\r\nSimplify: \u00a0[latex]\\frac{4\\cdot 3 - 7}{5\\cdot 2 - 4}-\\frac{3-5^2}{(7-3)^2 - 5}[\/latex]\r\n\r\n[reveal-answer q=\"656307\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"656307\"][latex]\\frac{17}{6}[\/latex][\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<ul>\n<li>Use order of operations to simplify expressions involving fractions<\/li>\n<\/ul>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Key words<\/h3>\n<ul>\n<li><strong>Fraction Bar<\/strong>: the bar in a fraction that acts like as grouping symbol<\/li>\n<\/ul>\n<\/div>\n<h2>Using the order of operations with fractions<\/h2>\n<p>Recall that the order of operations outlines the order in which terms in an expression must be simplified.<\/p>\n<div class=\"textbox shaded\">\n<h3>Order of Operations<\/h3>\n<p>When simplifying mathematical expressions perform the operations in the following order:<br \/>\n1. Grouping Symbols<\/p>\n<ul id=\"fs-id1171104029952\">\n<li>Simplify all expressions inside the parentheses or other grouping symbols, working on the innermost parentheses first.<\/li>\n<\/ul>\n<p>2. Exponents<\/p>\n<ul id=\"fs-id1171104407077\">\n<li>Simplify all expressions with exponents.<\/li>\n<\/ul>\n<p>3. Multiplication and Division from left to right<\/p>\n<ul id=\"fs-id1171103140103\">\n<li>Perform all multiplication and division in order from left to right. These operations have equal priority.<\/li>\n<\/ul>\n<p>4. Addition and Subtraction<\/p>\n<ul id=\"fs-id1171104002792\">\n<li>Perform all addition and subtraction in order from left to right. These operations have equal priority.<\/li>\n<\/ul>\n<\/div>\n<p>Performing the order of operations for fractional expressions is no different than order of operations for integers.<\/p>\n<div class=\"textbox examples\">\n<h3>Example<\/h3>\n<p>Simplify: [latex]\\frac{3}{5} \\cdot \\frac{2}{3} \\div \\frac{1}{6}[\/latex]<\/p>\n<p>Solution:<\/p>\n<table style=\"border-collapse: collapse; width: 59.2391%; height: 96px;\">\n<tbody>\n<tr style=\"height: 12px;\">\n<td style=\"width: 540.359px; height: 12px;\">One term<\/td>\n<td style=\"width: 540.359px; height: 12px;\">[latex]\\frac{3}{5} \\cdot \\frac{2}{3} \\div \\frac{1}{6}[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 12px;\">\n<td style=\"width: 540.359px; height: 12px;\">Multiply or divide from left to right.<\/td>\n<td style=\"width: 540.359px; height: 12px;\">[latex]\\large\\frac{\\color{red}{\\cancel{3}} \\cdot 2}{5 \\cdot \\color{red}{\\cancel{3}}} \\div \\frac{1}{6}[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 12px;\">\n<td style=\"width: 540.359px; height: 12px;\">Simplify by cancelling.<\/td>\n<td style=\"width: 540.359px; height: 12px;\">[latex]\\frac{2}{5}\\div \\frac{1}{6}[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 12px;\">\n<td style=\"width: 540.359px; height: 12px;\">Turn the division into multiplication of the reciprocal.<\/td>\n<td style=\"width: 540.359px; height: 12px;\">[latex]\\frac{2}{5}\\cdot \\frac{6}{1}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 540.359px;\">Multiply.<\/td>\n<td style=\"width: 540.359px;\">[latex]\\frac{2\\cdot 6}{5\\cdot 1}[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 12px;\">\n<td style=\"width: 540.359px; height: 12px;\">Simplify.<\/td>\n<td style=\"width: 540.359px; height: 12px;\">[latex]\\frac{12}{5}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div class=\"textbox tryit\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm37987\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=37987&theme=oea&iframe_resize_id=ohm37987&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm133412\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=133412&theme=oea&iframe_resize_id=ohm133412&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>The following video provides examples of how simplify fractional expression with order of operations.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Order of Operations Involving Fractions\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/ro6yRADn3Mw?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h2>Simplifying an Expression With a Fraction Bar<\/h2>\n<p><em><strong>Fraction bars<\/strong><\/em> act as grouping symbols. The expressions above and below the fraction bar should be treated as if they were in parentheses. For example, [latex]\\frac{4+8}{5 - 3}[\/latex] means [latex]\\left(4+8\\right)\\div\\left(5 - 3\\right)[\/latex]. The order of operations tells us to simplify the numerator and the denominator first\u2014as if there were parentheses\u2014before we divide.<\/p>\n<div class=\"textbox shaded\">\n<h3>Simplify an expression with a fraction bar<\/h3>\n<ol id=\"eip-id1168467312752\" class=\"stepwise\">\n<li>Simplify the numerator.<\/li>\n<li>Simplify the denominator.<\/li>\n<li>Simplify the fraction.<\/li>\n<\/ol>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Simplify: [latex]\\frac{4+8}{5 - 3}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q735944\">Show Solution<\/span><\/p>\n<div id=\"q735944\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168468328592\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]\\frac{4+8}{5 - 3}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify the expression in the numerator.<\/td>\n<td>[latex]\\frac{12}{5 - 3}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify the expression in the denominator.<\/td>\n<td>[latex]\\frac{12}{2}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify the fraction.<\/td>\n<td>[latex]6[\/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=\"ohm146163\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146163&theme=oea&iframe_resize_id=ohm146163&show_question_numbers\" width=\"100%\" height=\"270\"><\/iframe><\/p>\n<\/div>\n<p>the following video provides another example of how to simplify various expressions that contain a fraction bar.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Simplify Basic Expressions in Fraction Form\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/eF_jiZvb79w?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Simplify: [latex]\\frac{4 - 2\\left(3\\right)}{{2}^{2}+2}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q176453\">Show Solution<\/span><\/p>\n<div id=\"q176453\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168466112842\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]\\frac{4 - \\color{red}{2\\left(3\\right)}}{\\color{red}{{2}^{2}}+2}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Use the order of operations. Multiply in the numerator and use the exponent in the denominator.<\/td>\n<td>[latex]\\frac{4 - 6}{4+2}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify the numerator and the denominator.<\/td>\n<td>[latex]\\frac{-2}{6}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify the fraction.<\/td>\n<td>[latex]-\\frac{1}{3}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<h3><\/h3>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146164\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146164&theme=oea&iframe_resize_id=ohm146164&show_question_numbers\" width=\"100%\" height=\"270\"><\/iframe><\/p>\n<\/div>\n<h3><\/h3>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Simplify: [latex]\\frac{{\\left(8 - 4\\right)}^{2}}{{8}^{2}-{4}^{2}}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q724012\">Show Solution<\/span><\/p>\n<div id=\"q724012\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168468576501\" class=\"unnumbered unstyled\" style=\"width: 99.83633387888707%;\" summary=\".\">\n<tbody>\n<tr>\n<td style=\"width: 53.84615384615385%;\"><\/td>\n<td style=\"width: 45.99018003273322%;\">[latex]\\frac{{\\left(8 - 4\\right)}^{2}}{{8}^{2}-{4}^{2}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 53.84615384615385%;\">Use the order of operations (parentheses first, then exponents).<\/td>\n<td style=\"width: 45.99018003273322%;\">[latex]\\frac{{\\left(4\\right)}^{2}}{64 - 16}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 53.84615384615385%;\">Simplify the numerator and denominator.<\/td>\n<td style=\"width: 45.99018003273322%;\">[latex]\\frac{16}{48}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 53.84615384615385%;\">Simplify the fraction.<\/td>\n<td style=\"width: 45.99018003273322%;\">[latex]\\frac{1}{3}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<h3><\/h3>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146165\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146165&theme=oea&iframe_resize_id=ohm146165&show_question_numbers\" width=\"100%\" height=\"270\"><\/iframe><\/p>\n<\/div>\n<h3><\/h3>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Simplify: [latex]\\frac{4\\left(-3\\right)+6\\left(-2\\right)}{-3\\left(2\\right)-2}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q414011\">Show Solution<\/span><\/p>\n<div id=\"q414011\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168468477542\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]\\frac{4\\left(-3\\right)+6\\left(-2\\right)}{-3\\left(2\\right)-2}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]\\frac{-12+\\left(-12\\right)}{-6 - 2}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]\\frac{-24}{-8}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Divide.<\/td>\n<td>[latex]3[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<h3><\/h3>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146167\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146167&theme=oea&iframe_resize_id=ohm146167&show_question_numbers\" width=\"100%\" height=\"270\"><\/iframe><\/p>\n<\/div>\n<p>Watch this video to see another example of how to simplify an expression with a fraction bar that contains several different operations.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-3\" title=\"Ex 1: Simplify an Expression in Fraction form (Order of Operations)\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/fK7-w77cgVQ?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>When there are two or more fractions, we work each fraction separately, then add or subtract them once they are simplified to lowest terms.<\/p>\n<div class=\"textbox examples\">\n<h3>Example<\/h3>\n<p>Simplify: \u00a0[latex]\\frac{-3^2+4\\cdot (-6)}{(-5)^2-(6-2)} - \\left [\\frac{6-2^2}{-4}\\right ]^{2}[\/latex]<\/p>\n<p>Solution<\/p>\n<p>Let&#8217;s work each fraction separately, then subtract them.<\/p>\n<p>1. \u00a0\u00a0[latex]\\frac{-3^2+4\\cdot (-6)}{(-5)^2-(6-2)}[\/latex] \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Exponent and parentheses<\/p>\n<p>[latex]=\\frac{-9+(-24)}{25-(4)}[\/latex] \u00a0 \u00a0 \u00a0 \u00a0Addition and subtraction<\/p>\n<p>[latex]=\\frac{-33}{21}[\/latex] \u00a0 \u00a0 \u00a0 \u00a0Simplify<\/p>\n<p>[latex]=\\frac{-11}{7}[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p>2. \u00a0 [latex]\\left [\\frac{6-2^2}{-4}\\right ]^{2}[\/latex] \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Exponent<\/p>\n<p>[latex]=\\left [\\frac{6-4}{-4}\\right ]^{2}[\/latex] \u00a0 \u00a0 \u00a0 \u00a0 Subtract<\/p>\n<p>[latex]=\\left [\\frac{2}{-4}\\right ]^{2}[\/latex] \u00a0 \u00a0 \u00a0 \u00a0 Simplify<\/p>\n<p>[latex]=\\left [\\frac{1}{-2}\\right ]^{2}[\/latex] \u00a0 \u00a0 \u00a0 \u00a0Square the numerator and denominator<\/p>\n<p>[latex]=\\frac{1}{4}[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p>Finally, we subtract:<\/p>\n<p>[latex]\\frac{-3^2+4\\cdot (-6)}{(-5)^2-(6-2)} - \\left [\\frac{6-2^2}{-4}\\right ]^{2}[\/latex]<\/p>\n<p>[latex]=\\frac{-11}{7}-\\frac{1}{4}[\/latex] \u00a0 \u00a0 \u00a0 LCD = 28. \u00a0Build equivalent fraction with LCD<\/p>\n<p>[latex]=\\frac{-11\\cdot 4}{7\\cdot 4}-\\frac{1\\cdot 7}{4\\cdot 7}[\/latex] \u00a0 \u00a0 \u00a0 \u00a0 Multiply numerators and denominators<\/p>\n<p>[latex]=\\frac{-44}{28}-\\frac{7}{28}[\/latex] \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Subtract numerators and keep common denominator<\/p>\n<p>[latex]=\\frac{-44-7}{28}[\/latex] \u00a0 \u00a0 \u00a0 \u00a0 Subtract<\/p>\n<p>[latex]=\\frac{-51}{28}[\/latex]<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox tryit\">\n<h3>Try It<\/h3>\n<p>Simplify: \u00a0[latex]\\frac{4\\cdot 3 - 7}{5\\cdot 2 - 4}-\\frac{3-5^2}{(7-3)^2 - 5}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q656307\">Show Answer<\/span><\/p>\n<div id=\"q656307\" class=\"hidden-answer\" style=\"display: none\">[latex]\\frac{17}{6}[\/latex]<\/div>\n<\/div>\n<\/div>\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-1415\">\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: 146162, 146163, 146164, 146165, 146167. <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>Example ; Try It with two fractions. <strong>Authored by<\/strong>: Hazel McKenna. <strong>Provided by<\/strong>: Utah Valley University. <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>Simplify Basic Expressions in Fraction Form. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/eF_jiZvb79w\">https:\/\/youtu.be\/eF_jiZvb79w<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Ex 1: Simplify an Expression in Fraction form (Order of Operations). <strong>Authored by<\/strong>: James Sousa (mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/fK7-w77cgVQ\">https:\/\/youtu.be\/fK7-w77cgVQ<\/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":422605,"menu_order":15,"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\":\"Simplify Basic Expressions in Fraction Form\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/eF_jiZvb79w\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Ex 1: Simplify an Expression in Fraction form (Order of Operations)\",\"author\":\"James Sousa 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University\",\"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-1415","chapter","type-chapter","status-publish","hentry"],"part":587,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/uvu-introductoryalgebra\/wp-json\/pressbooks\/v2\/chapters\/1415","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/uvu-introductoryalgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/uvu-introductoryalgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/uvu-introductoryalgebra\/wp-json\/wp\/v2\/users\/422605"}],"version-history":[{"count":15,"href":"https:\/\/courses.lumenlearning.com\/uvu-introductoryalgebra\/wp-json\/pressbooks\/v2\/chapters\/1415\/revisions"}],"predecessor-version":[{"id":2999,"href":"https:\/\/courses.lumenlearning.com\/uvu-introductoryalgebra\/wp-json\/pressbooks\/v2\/chapters\/1415\/revisions\/2999"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/uvu-introductoryalgebra\/wp-json\/pressbooks\/v2\/parts\/587"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/uvu-introductoryalgebra\/wp-json\/pressbooks\/v2\/chapters\/1415\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/uvu-introductoryalgebra\/wp-json\/wp\/v2\/media?parent=1415"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/uvu-introductoryalgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=1415"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/uvu-introductoryalgebra\/wp-json\/wp\/v2\/contributor?post=1415"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/uvu-introductoryalgebra\/wp-json\/wp\/v2\/license?post=1415"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}