{"id":3503,"date":"2019-12-29T22:33:52","date_gmt":"2019-12-29T22:33:52","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforlibscoreq\/?post_type=chapter&#038;p=3503"},"modified":"2021-02-05T23:47:52","modified_gmt":"2021-02-05T23:47:52","slug":"simplifying-complex-fractions","status":"web-only","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/chapter\/simplifying-complex-fractions\/","title":{"raw":"Simplifying Complex Fractions","rendered":"Simplifying Complex Fractions"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Translate phrases into algebraic expressions that involve division<\/li>\r\n \t<li>Identify a complex fraction<\/li>\r\n \t<li>Simplify complex fractions<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h3>Translate Phrases to Expressions with Fractions<\/h3>\r\nThe words <em>quotient<\/em> and <em>ratio<\/em> are often used to describe fractions. In Subtract Whole Numbers, we defined quotient as the result of division. The quotient of [latex]a\\text{ and }b[\/latex] is the result you get from dividing [latex]a\\text{ by }b[\/latex], or [latex]\\Large\\frac{a}{b}[\/latex]. Let\u2019s practice translating some phrases into algebraic expressions using these terms.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nTranslate the phrase into an algebraic expression: \"the quotient of [latex]3x[\/latex] and [latex]8[\/latex].\"\r\n\r\nSolution:\r\nThe keyword is <em>quotient<\/em>; it tells us that the operation is division. Look for the words <em>of<\/em> and <em>and<\/em> to find the numbers to divide.\r\n<p style=\"text-align: center;\">[latex]\\text{The quotient }\\text{of }3x\\text{ and }8\\text{.}[\/latex]<\/p>\r\n<p style=\"text-align: left;\">This tells us that we need to divide [latex]3x[\/latex] by [latex]8[\/latex].<\/p>\r\n<p style=\"text-align: center;\">[latex]\\Large\\frac{3x}{8}[\/latex]<\/p>\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question height=\"270\"]146101[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nTranslate the phrase into an algebraic expression: the quotient of the difference of [latex]m[\/latex] and [latex]n[\/latex], and [latex]p[\/latex].\r\n[reveal-answer q=\"123871\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"123871\"]\r\n\r\nSolution:\r\nWe are looking for the <em>quotient<\/em> of the <em>difference<\/em> of [latex]m[\/latex] and [latex]n[\/latex], and [latex]p[\/latex]. This means we want to divide the difference of <em> [latex]m[\/latex] <\/em> and [latex]n[\/latex] by [latex]p[\/latex]\r\n<p style=\"text-align: center;\">[latex]\\Large\\frac{m-n}{p}[\/latex]<\/p>\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\"]146103[\/ohm_question]\r\n\r\n<\/div>\r\nIn the following video we show more examples of translating English expressions into algebraic expressions.\r\n\r\nhttps:\/\/youtu.be\/WxJxY4aJ9Vk\r\n<h3>Simplify Complex Fractions<\/h3>\r\nOur work with fractions so far has included proper fractions, improper fractions, and mixed numbers. Another kind of fraction is called complex fraction, which is a fraction in which the numerator or the denominator contains a fraction.\r\nSome examples of complex fractions are:\r\n<p style=\"text-align: center;\">[latex]\\LARGE\\frac{\\frac{6}{7}}{ 3}, \\frac{\\frac{3}{4}}{\\frac{5}{8}}, \\frac{\\frac{x}{2}}{\\frac{5}{6}}[\/latex]\r\nTo simplify a complex fraction, remember that the fraction bar means division. So the complex fraction [latex]\\LARGE\\frac{\\frac{3}{4}}{\\frac{5}{8}}[\/latex] can be written as [latex]\\Large\\frac{3}{4}\\normalsize\\div\\Large\\frac{5}{8}[\/latex].<\/p>\r\n\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nSimplify: [latex]\\LARGE\\frac{\\frac{3}{4}}{\\frac{5}{8}}[\/latex]\r\n[reveal-answer q=\"853762\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"853762\"]\r\n\r\nSolution:\r\n<table id=\"eip-id1168468527734\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]\\LARGE\\frac{\\frac{3}{4}}{\\frac{5}{8}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rewrite as division.<\/td>\r\n<td>[latex]\\Large\\frac{3}{4}\\normalsize\\div\\Large\\frac{5}{8}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply the first fraction by the reciprocal of the second.<\/td>\r\n<td>[latex]\\Large\\frac{3}{4}\\cdot \\frac{8}{5}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]\\Large\\frac{3\\cdot 8}{4\\cdot 5}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Look for common factors.<\/td>\r\n<td>[latex]\\Large\\frac{3\\cdot\\color{red}{4}\\cdot 2}{\\color{red}{4} \\cdot 5}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Remove common factors and simplify.<\/td>\r\n<td>[latex]\\Large\\frac{6}{5}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try it<\/h3>\r\n[ohm_question height=\"270\"]146109[\/ohm_question]\r\n\r\n<\/div>\r\nThe following video shows another example of how to simplify a complex fraction.\r\n\r\nhttps:\/\/youtu.be\/CLmWfkeKBg0\r\n<div class=\"textbox shaded\">\r\n<h3>Simplify a complex fraction.<\/h3>\r\n<ol id=\"eip-id1168468756479\" class=\"stepwise\">\r\n \t<li>Rewrite the complex fraction as a division problem.<\/li>\r\n \t<li>Follow the rules for dividing fractions.<\/li>\r\n \t<li>Simplify if possible.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nSimplify: [latex]\\LARGE\\frac{-\\frac{6}{7}}{ 3}[\/latex]\r\n[reveal-answer q=\"652451\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"652451\"]\r\n\r\nSolution:\r\n<table id=\"eip-id1168466330347\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>[latex]\\LARGE\\frac{-\\frac{6}{7}}{ 3}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rewrite as division.<\/td>\r\n<td>[latex]\\Large-\\frac{6}{7}\\normalsize\\div 3[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply the first fraction by the reciprocal of the second.<\/td>\r\n<td>[latex]\\Large-\\frac{6}{7}\\cdot \\frac{1}{3}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply; the product will be negative.<\/td>\r\n<td>[latex]\\Large-\\frac{6\\cdot 1}{7\\cdot 3}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Look for common factors.<\/td>\r\n<td>[latex]\\Large-\\frac{\\color{red}{3} \\cdot 2\\cdot 1}{7\\cdot \\color{red}{3} }[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Remove common factors and simplify.<\/td>\r\n<td>[latex]\\Large-\\frac{2}{7}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try it<\/h3>\r\n[ohm_question height=\"270\"]146110[\/ohm_question]\r\n\r\n[ohm_question height=\"270\"]146111[\/ohm_question]\r\n\r\n<\/div>\r\nhttps:\/\/youtu.be\/T1PIfrU3NTw\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nSimplify: [latex]\\LARGE\\frac{\\frac{x}{2}}{\\frac{xy}{6}}[\/latex]\r\n[reveal-answer q=\"663304\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"663304\"]\r\n\r\nSolution:\r\n<table id=\"eip-id1168468401740\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]\\LARGE\\frac{\\frac{x}{2}}{\\frac{xy}{6}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rewrite as division.<\/td>\r\n<td>[latex]\\Large\\frac{x}{2}\\div \\frac{xy}{6}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply the first fraction by the reciprocal of the second.<\/td>\r\n<td>[latex]\\Large\\frac{x}{2}\\cdot \\frac{6}{xy}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]\\Large\\frac{x\\cdot 6}{2\\cdot xy}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Look for common factors.<\/td>\r\n<td>[latex]\\Large\\frac{\\color{red}{x}\\cdot 3\\cdot \\color{red}{2}}{\\color{red}{2}\\cdot \\color{red}{x}\\cdot y}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Remove common factors and simplify.<\/td>\r\n<td>[latex]\\Large\\frac{3}{y}[\/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\"]146112[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nSimplify: [latex]\\LARGE\\frac{2\\frac{3}{4}}{\\frac{1}{8}}[\/latex]\r\n[reveal-answer q=\"216274\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"216274\"]\r\n\r\nSolution:\r\n<table id=\"eip-id1168467162804\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]\\LARGE\\frac{2\\frac{3}{4}}{\\frac{1}{8}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rewrite as division.<\/td>\r\n<td>[latex]2\\Large\\frac{3}{4}\\normalsize\\div\\Large\\frac{1}{8}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Change the mixed number to an improper fraction.<\/td>\r\n<td>[latex]\\Large\\frac{11}{4}\\normalsize\\div\\Large\\frac{1}{8}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply the first fraction by the reciprocal of the second.<\/td>\r\n<td>[latex]\\Large\\frac{11}{4}\\cdot \\frac{8}{1}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]\\Large\\frac{11\\cdot 8}{4\\cdot 1}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Look for common factors.<\/td>\r\n<td>[latex]\\Large\\frac{11\\cdot \\color{red}{4} \\cdot 2}{\\color{red}{4} \\cdot 1}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Remove common factors and simplify.<\/td>\r\n<td>[latex]22[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try it<\/h3>\r\n[ohm_question height=\"270\"]146161[\/ohm_question]\r\n\r\n<\/div>\r\nhttps:\/\/youtu.be\/H5K4ESHLBks","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Translate phrases into algebraic expressions that involve division<\/li>\n<li>Identify a complex fraction<\/li>\n<li>Simplify complex fractions<\/li>\n<\/ul>\n<\/div>\n<h3>Translate Phrases to Expressions with Fractions<\/h3>\n<p>The words <em>quotient<\/em> and <em>ratio<\/em> are often used to describe fractions. In Subtract Whole Numbers, we defined quotient as the result of division. The quotient of [latex]a\\text{ and }b[\/latex] is the result you get from dividing [latex]a\\text{ by }b[\/latex], or [latex]\\Large\\frac{a}{b}[\/latex]. Let\u2019s practice translating some phrases into algebraic expressions using these terms.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Translate the phrase into an algebraic expression: &#8220;the quotient of [latex]3x[\/latex] and [latex]8[\/latex].&#8221;<\/p>\n<p>Solution:<br \/>\nThe keyword is <em>quotient<\/em>; it tells us that the operation is division. Look for the words <em>of<\/em> and <em>and<\/em> to find the numbers to divide.<\/p>\n<p style=\"text-align: center;\">[latex]\\text{The quotient }\\text{of }3x\\text{ and }8\\text{.}[\/latex]<\/p>\n<p style=\"text-align: left;\">This tells us that we need to divide [latex]3x[\/latex] by [latex]8[\/latex].<\/p>\n<p style=\"text-align: center;\">[latex]\\Large\\frac{3x}{8}[\/latex]<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146101\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146101&theme=oea&iframe_resize_id=ohm146101&show_question_numbers\" width=\"100%\" height=\"270\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Translate the phrase into an algebraic expression: the quotient of the difference of [latex]m[\/latex] and [latex]n[\/latex], and [latex]p[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q123871\">Show Solution<\/span><\/p>\n<div id=\"q123871\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<br \/>\nWe are looking for the <em>quotient<\/em> of the <em>difference<\/em> of [latex]m[\/latex] and [latex]n[\/latex], and [latex]p[\/latex]. This means we want to divide the difference of <em> [latex]m[\/latex] <\/em> and [latex]n[\/latex] by [latex]p[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\Large\\frac{m-n}{p}[\/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=\"ohm146103\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146103&theme=oea&iframe_resize_id=ohm146103&show_question_numbers\" width=\"100%\" height=\"270\"><\/iframe><\/p>\n<\/div>\n<p>In the following video we show more examples of translating English expressions into algebraic expressions.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"The Language of Division\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/WxJxY4aJ9Vk?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h3>Simplify Complex Fractions<\/h3>\n<p>Our work with fractions so far has included proper fractions, improper fractions, and mixed numbers. Another kind of fraction is called complex fraction, which is a fraction in which the numerator or the denominator contains a fraction.<br \/>\nSome examples of complex fractions are:<\/p>\n<p style=\"text-align: center;\">[latex]\\LARGE\\frac{\\frac{6}{7}}{ 3}, \\frac{\\frac{3}{4}}{\\frac{5}{8}}, \\frac{\\frac{x}{2}}{\\frac{5}{6}}[\/latex]<br \/>\nTo simplify a complex fraction, remember that the fraction bar means division. So the complex fraction [latex]\\LARGE\\frac{\\frac{3}{4}}{\\frac{5}{8}}[\/latex] can be written as [latex]\\Large\\frac{3}{4}\\normalsize\\div\\Large\\frac{5}{8}[\/latex].<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Simplify: [latex]\\LARGE\\frac{\\frac{3}{4}}{\\frac{5}{8}}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q853762\">Show Solution<\/span><\/p>\n<div id=\"q853762\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168468527734\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]\\LARGE\\frac{\\frac{3}{4}}{\\frac{5}{8}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Rewrite as division.<\/td>\n<td>[latex]\\Large\\frac{3}{4}\\normalsize\\div\\Large\\frac{5}{8}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply the first fraction by the reciprocal of the second.<\/td>\n<td>[latex]\\Large\\frac{3}{4}\\cdot \\frac{8}{5}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]\\Large\\frac{3\\cdot 8}{4\\cdot 5}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Look for common factors.<\/td>\n<td>[latex]\\Large\\frac{3\\cdot\\color{red}{4}\\cdot 2}{\\color{red}{4} \\cdot 5}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Remove common factors and simplify.<\/td>\n<td>[latex]\\Large\\frac{6}{5}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146109\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146109&theme=oea&iframe_resize_id=ohm146109&show_question_numbers\" width=\"100%\" height=\"270\"><\/iframe><\/p>\n<\/div>\n<p>The following video shows another example of how to simplify a complex fraction.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Ex:  Evaluate a Complex Fraction\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/CLmWfkeKBg0?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<div class=\"textbox shaded\">\n<h3>Simplify a complex fraction.<\/h3>\n<ol id=\"eip-id1168468756479\" class=\"stepwise\">\n<li>Rewrite the complex fraction as a division problem.<\/li>\n<li>Follow the rules for dividing fractions.<\/li>\n<li>Simplify if possible.<\/li>\n<\/ol>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Simplify: [latex]\\LARGE\\frac{-\\frac{6}{7}}{ 3}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q652451\">Show Solution<\/span><\/p>\n<div id=\"q652451\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168466330347\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\">\n<tbody>\n<tr>\n<td>[latex]\\LARGE\\frac{-\\frac{6}{7}}{ 3}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Rewrite as division.<\/td>\n<td>[latex]\\Large-\\frac{6}{7}\\normalsize\\div 3[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply the first fraction by the reciprocal of the second.<\/td>\n<td>[latex]\\Large-\\frac{6}{7}\\cdot \\frac{1}{3}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply; the product will be negative.<\/td>\n<td>[latex]\\Large-\\frac{6\\cdot 1}{7\\cdot 3}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Look for common factors.<\/td>\n<td>[latex]\\Large-\\frac{\\color{red}{3} \\cdot 2\\cdot 1}{7\\cdot \\color{red}{3} }[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Remove common factors and simplify.<\/td>\n<td>[latex]\\Large-\\frac{2}{7}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146110\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146110&theme=oea&iframe_resize_id=ohm146110&show_question_numbers\" width=\"100%\" height=\"270\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146111\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146111&theme=oea&iframe_resize_id=ohm146111&show_question_numbers\" width=\"100%\" height=\"270\"><\/iframe><\/p>\n<\/div>\n<p><iframe loading=\"lazy\" id=\"oembed-3\" title=\"Simplify Complex Fractions (2\/3)\/(5\/6) and (-8\/7)\/4\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/T1PIfrU3NTw?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Simplify: [latex]\\LARGE\\frac{\\frac{x}{2}}{\\frac{xy}{6}}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q663304\">Show Solution<\/span><\/p>\n<div id=\"q663304\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168468401740\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]\\LARGE\\frac{\\frac{x}{2}}{\\frac{xy}{6}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Rewrite as division.<\/td>\n<td>[latex]\\Large\\frac{x}{2}\\div \\frac{xy}{6}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply the first fraction by the reciprocal of the second.<\/td>\n<td>[latex]\\Large\\frac{x}{2}\\cdot \\frac{6}{xy}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]\\Large\\frac{x\\cdot 6}{2\\cdot xy}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Look for common factors.<\/td>\n<td>[latex]\\Large\\frac{\\color{red}{x}\\cdot 3\\cdot \\color{red}{2}}{\\color{red}{2}\\cdot \\color{red}{x}\\cdot y}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Remove common factors and simplify.<\/td>\n<td>[latex]\\Large\\frac{3}{y}[\/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=\"ohm146112\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146112&theme=oea&iframe_resize_id=ohm146112&show_question_numbers\" width=\"100%\" height=\"270\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Simplify: [latex]\\LARGE\\frac{2\\frac{3}{4}}{\\frac{1}{8}}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q216274\">Show Solution<\/span><\/p>\n<div id=\"q216274\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168467162804\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]\\LARGE\\frac{2\\frac{3}{4}}{\\frac{1}{8}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Rewrite as division.<\/td>\n<td>[latex]2\\Large\\frac{3}{4}\\normalsize\\div\\Large\\frac{1}{8}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Change the mixed number to an improper fraction.<\/td>\n<td>[latex]\\Large\\frac{11}{4}\\normalsize\\div\\Large\\frac{1}{8}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply the first fraction by the reciprocal of the second.<\/td>\n<td>[latex]\\Large\\frac{11}{4}\\cdot \\frac{8}{1}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]\\Large\\frac{11\\cdot 8}{4\\cdot 1}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Look for common factors.<\/td>\n<td>[latex]\\Large\\frac{11\\cdot \\color{red}{4} \\cdot 2}{\\color{red}{4} \\cdot 1}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Remove common factors and simplify.<\/td>\n<td>[latex]22[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146161\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146161&theme=oea&iframe_resize_id=ohm146161&show_question_numbers\" width=\"100%\" height=\"270\"><\/iframe><\/p>\n<\/div>\n<p><iframe loading=\"lazy\" id=\"oembed-4\" title=\"Simplify Complex Fractions (8\/5)\/(3 1\/2) and (a\/8)\/((ab)\/8)\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/H5K4ESHLBks?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/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-3503\">\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>Simplify Complex Fractions (2\/3)\/(5\/6) and (-8\/7)\/4. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/T1PIfrU3NTw\">https:\/\/youtu.be\/T1PIfrU3NTw<\/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>Simplify Complex Fractions (8\/5)\/(3 1\/2) and (a\/8)\/((ab)\/8). <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/H5K4ESHLBks\">https:\/\/youtu.be\/H5K4ESHLBks<\/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>Question ID: 146101, 146103, 146109, 146110, 146111, 146112, 146161. <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><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Ex: Evaluate a Complex Fraction. <strong>Authored by<\/strong>: Sousa, James(mathispower4u.com) . <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/CLmWfkeKBg0\">https:\/\/youtu.be\/CLmWfkeKBg0<\/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>The Language of Division. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/WxJxY4aJ9Vk\">https:\/\/youtu.be\/WxJxY4aJ9Vk<\/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: Evaluate a Complex Fraction\",\"author\":\"Sousa, James(mathispower4u.com) \",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/CLmWfkeKBg0\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Simplify Complex Fractions (2\/3)\/(5\/6) and (-8\/7)\/4\",\"author\":\"James Sousa (Mathispower4u.com) for Lumen Learning\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/T1PIfrU3NTw\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Simplify Complex Fractions (8\/5)\/(3 1\/2) and (a\/8)\/((ab)\/8)\",\"author\":\"James Sousa (Mathispower4u.com) for Lumen Learning\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/H5K4ESHLBks\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"The Language of Division\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/WxJxY4aJ9Vk\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Question ID: 146101, 146103, 146109, 146110, 146111, 146112, 146161\",\"author\":\"Alyson Day\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"IMathAS Community License CC-BY + GPL\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-3503","chapter","type-chapter","status-web-only","hentry"],"part":658,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/3503","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":6,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/3503\/revisions"}],"predecessor-version":[{"id":5292,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/3503\/revisions\/5292"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/parts\/658"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/3503\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/media?parent=3503"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=3503"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/contributor?post=3503"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/license?post=3503"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}