{"id":4626,"date":"2020-04-21T00:19:11","date_gmt":"2020-04-21T00:19:11","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/chapter\/simplifying-fractions\/"},"modified":"2024-06-26T17:40:19","modified_gmt":"2024-06-26T17:40:19","slug":"simplifying-fractions","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/chapter\/simplifying-fractions\/","title":{"raw":"Simplifying Fractions","rendered":"Simplifying Fractions"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Simplify fractions by finding common factors between the numerator and denominator<\/li>\r\n \t<li>Simplify fractions containing variables<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2>Simplify Fractions<\/h2>\r\nIn working with equivalent fractions, you saw that there are many ways to write fractions that have the same value, or represent the same part of the whole. How do you know which one to use? Often, we\u2019ll use the fraction that is in <em>simplified<\/em> form.\r\n\r\nA fraction is considered simplified if there are no common factors, other than [latex]1[\/latex], in the numerator and denominator. If a fraction does have common factors in the numerator and denominator, we can reduce the fraction to its simplified form by removing the common factors.\r\n<div class=\"textbox shaded\">\r\n<h3>Simplified Fraction<\/h3>\r\nA fraction is considered simplified if there are no common factors in the numerator and denominator.\r\n\r\n<\/div>\r\nFor example,\r\n<ul id=\"fs-id1302300\">\r\n \t<li>[latex]\\Large\\frac{2}{3}[\/latex] is simplified because there are no common factors of [latex]2[\/latex] and [latex]3[\/latex].<\/li>\r\n \t<li>[latex]\\Large\\frac{10}{15}[\/latex] is not simplified because [latex]5[\/latex] is a common factor of [latex]10[\/latex] and [latex]15[\/latex].<\/li>\r\n<\/ul>\r\nThe process of simplifying a fraction is often called <em>reducing the fraction<\/em>. In the previous section, we used the Equivalent Fractions Property to find equivalent fractions. We can also use the Equivalent Fractions Property in reverse to simplify fractions. We rewrite the property to show both forms together.\r\n<div class=\"textbox shaded\">\r\n<h3>Equivalent Fractions Property<\/h3>\r\nIf [latex]a,b,c[\/latex] are numbers where [latex]b\\ne 0,c\\ne 0[\/latex], then\r\n\r\n[latex]{\\Large\\frac{a}{b}}={\\Large\\frac{a\\cdot c}{b\\cdot c}}\\text{ and }{\\Large\\frac{a\\cdot c}{b\\cdot c}}={\\Large\\frac{a}{b}}[\/latex].\r\n\r\n<\/div>\r\nNotice that [latex]c[\/latex] is a common factor in the numerator and denominator. Anytime we have a common factor in the numerator and denominator, it can be removed.\r\n<div class=\"textbox shaded\">\r\n<h3>Simplify a fraction.<\/h3>\r\n<ol id=\"eip-id1168467382990\" class=\"stepwise\">\r\n \t<li>Rewrite the numerator and denominator to show the common factors. If needed, factor the numerator and denominator into prime numbers.<\/li>\r\n \t<li>Simplify, using the equivalent fractions property, by removing common factors.<\/li>\r\n \t<li>Multiply any remaining factors.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nSimplify: [latex]\\Large\\frac{10}{15}[\/latex]\r\n\r\nSolution:\r\nTo simplify the fraction, we look for any common factors in the numerator and the denominator.\r\n<table id=\"eip-id1168468231694\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\"The first line says, \">\r\n<tbody>\r\n<tr>\r\n<td>Notice that [latex]5[\/latex] is a factor of both [latex]10[\/latex] and [latex]15[\/latex].<\/td>\r\n<td>[latex]\\Large\\frac{10}{15}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Factor the numerator and denominator.<\/td>\r\n<td>[latex]\\Large\\frac{2\\cdot5}{3\\cdot5}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Remove the common factors.<\/td>\r\n<td>[latex]\\Large\\frac{2\\cdot\\color{red}{5}}{3\\cdot\\color{red}{5}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]\\Large\\frac{2}{3}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question height=\"400\"]146014[\/ohm_question]\r\n\r\n<\/div>\r\nTo simplify a negative fraction, we use the same process as in the previous example. Remember to keep the negative sign.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nSimplify: [latex]\\Large-\\frac{18}{24}[\/latex]\r\n[reveal-answer q=\"270732\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"270732\"]\r\n\r\nSolution:\r\n<table id=\"eip-id1168469841089\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\"We notice that 18 and 24 both have factors,\">\r\n<tbody>\r\n<tr>\r\n<td>We notice that 18 and 24 both have factors of 6.<\/td>\r\n<td>[latex]\\Large-\\frac{18}{24}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rewrite the numerator and denominator showing the common factor.<\/td>\r\n<td>[latex]\\Large\\frac{3\\cdot6}{4\\cdot6}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Remove common factors.<\/td>\r\n<td>[latex]\\Large-\\frac{3\\cdot\\color{red}{6}}{4\\cdot\\color{red}{6}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]\\Large-\\frac{3}{4}[\/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=\"400\"]146015[\/ohm_question]\r\n\r\n<\/div>\r\nWatch the following video to see another example of how to simplify a fraction.\r\n\r\nhttps:\/\/youtu.be\/_2Wk7jXf3Ok\r\n\r\nAfter simplifying a fraction, it is always important to check the result to make sure that the numerator and denominator do not have any more factors in common. Remember, the definition of a simplified fraction: <em>a fraction is considered simplified if there are no common factors in the numerator and denominator<\/em>.\r\n\r\nWhen we simplify an improper fraction, there is no need to change it to a mixed number.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nSimplify: [latex]\\Large-\\frac{56}{32}[\/latex]\r\n[reveal-answer q=\"877414\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"877414\"]\r\n\r\nSolution:\r\n<table id=\"eip-id1168466600046\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\"The first line shows negative 56 over 32. The next line says, \">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]\\Large-\\frac{56}{32}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rewrite the numerator and denominator, showing the common factors, 8.<\/td>\r\n<td>[latex]\\Large\\frac{7\\cdot8}{4\\cdot8}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Remove common factors.<\/td>\r\n<td>[latex]\\Large\\frac{7\\cdot\\color{red}{8}}{4\\cdot\\color{red}{8}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]\\Large-\\frac{7}{4}[\/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=\"400\"]146017[\/ohm_question]\r\n\r\n<\/div>\r\nSometimes it may not be easy to find common factors of the numerator and denominator. A good idea, then, is to factor the numerator and the denominator into prime numbers. (You may want to use the factor tree method to identify the prime factors.) Then divide out the common factors using the Equivalent Fractions Property.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nSimplify: [latex]\\Large\\frac{210}{385}[\/latex]\r\n[reveal-answer q=\"721590\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"721590\"]\r\n\r\nSolution:\r\n<table id=\"eip-id1168467251049\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\"The fraction 210 over 385 is shown. The next line says, \">\r\n<tbody>\r\n<tr>\r\n<td>Use factor trees to factor the numerator and denominator.<\/td>\r\n<td>[latex]\r\n\r\n\\Large\\frac{210}{385}[\/latex]\r\n\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220913\/CNX_BMath_Figure_04_02_028_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rewrite the numerator and denominator as the product of the primes.<\/td>\r\n<td>[latex]{\\Large\\frac{210}{385}}={\\Large\\frac{2\\cdot 3\\cdot 5\\cdot 7}{5\\cdot 7\\cdot 11}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Remove the common factors.<\/td>\r\n<td>[latex]\\Large\\frac{2\\cdot 3\\cdot\\color{blue}{5}\\cdot\\color{red}{7}}{\\color{blue}{5}\\cdot\\color{red}{7}\\cdot 11}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]\\Large\\frac{2\\cdot 3}{11}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply any remaining factors.<\/td>\r\n<td>[latex]\\Large\\frac{6}{11}[\/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=\"400\"]146018[\/ohm_question]\r\n\r\n<\/div>\r\nWe can also simplify fractions containing variables. If a variable is a common factor in the numerator and denominator, we remove it just as we do with an integer factor.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nSimplify: [latex]\\Large\\frac{5xy}{15x}[\/latex]\r\n[reveal-answer q=\"283612\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"283612\"]\r\n\r\nSolution:\r\n<table id=\"eip-id1168469401986\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]\\Large\\frac{5xy}{15x}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rewrite numerator and denominator showing common factors.<\/td>\r\n<td>[latex]\\Large\\frac{5\\cdot x\\cdot y}{3\\cdot 5\\cdot x}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Remove common factors.<\/td>\r\n<td>[latex]\\Large\\frac{\\overline{)5}\\cdot \\overline{)x}\\cdot y}{3\\cdot \\overline{)5}\\cdot \\overline{)x}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]\\Large\\frac{y}{3}[\/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=\"400\"]146019[\/ohm_question]\r\n\r\n<\/div>\r\nHere's a video with another example of how to simplify a fraction that contains variables.\r\n\r\nhttps:\/\/youtu.be\/tLgfPeecGe0","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Simplify fractions by finding common factors between the numerator and denominator<\/li>\n<li>Simplify fractions containing variables<\/li>\n<\/ul>\n<\/div>\n<h2>Simplify Fractions<\/h2>\n<p>In working with equivalent fractions, you saw that there are many ways to write fractions that have the same value, or represent the same part of the whole. How do you know which one to use? Often, we\u2019ll use the fraction that is in <em>simplified<\/em> form.<\/p>\n<p>A fraction is considered simplified if there are no common factors, other than [latex]1[\/latex], in the numerator and denominator. If a fraction does have common factors in the numerator and denominator, we can reduce the fraction to its simplified form by removing the common factors.<\/p>\n<div class=\"textbox shaded\">\n<h3>Simplified Fraction<\/h3>\n<p>A fraction is considered simplified if there are no common factors in the numerator and denominator.<\/p>\n<\/div>\n<p>For example,<\/p>\n<ul id=\"fs-id1302300\">\n<li>[latex]\\Large\\frac{2}{3}[\/latex] is simplified because there are no common factors of [latex]2[\/latex] and [latex]3[\/latex].<\/li>\n<li>[latex]\\Large\\frac{10}{15}[\/latex] is not simplified because [latex]5[\/latex] is a common factor of [latex]10[\/latex] and [latex]15[\/latex].<\/li>\n<\/ul>\n<p>The process of simplifying a fraction is often called <em>reducing the fraction<\/em>. In the previous section, we used the Equivalent Fractions Property to find equivalent fractions. We can also use the Equivalent Fractions Property in reverse to simplify fractions. We rewrite the property to show both forms together.<\/p>\n<div class=\"textbox shaded\">\n<h3>Equivalent Fractions Property<\/h3>\n<p>If [latex]a,b,c[\/latex] are numbers where [latex]b\\ne 0,c\\ne 0[\/latex], then<\/p>\n<p>[latex]{\\Large\\frac{a}{b}}={\\Large\\frac{a\\cdot c}{b\\cdot c}}\\text{ and }{\\Large\\frac{a\\cdot c}{b\\cdot c}}={\\Large\\frac{a}{b}}[\/latex].<\/p>\n<\/div>\n<p>Notice that [latex]c[\/latex] is a common factor in the numerator and denominator. Anytime we have a common factor in the numerator and denominator, it can be removed.<\/p>\n<div class=\"textbox shaded\">\n<h3>Simplify a fraction.<\/h3>\n<ol id=\"eip-id1168467382990\" class=\"stepwise\">\n<li>Rewrite the numerator and denominator to show the common factors. If needed, factor the numerator and denominator into prime numbers.<\/li>\n<li>Simplify, using the equivalent fractions property, by removing common factors.<\/li>\n<li>Multiply any remaining factors.<\/li>\n<\/ol>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Simplify: [latex]\\Large\\frac{10}{15}[\/latex]<\/p>\n<p>Solution:<br \/>\nTo simplify the fraction, we look for any common factors in the numerator and the denominator.<\/p>\n<table id=\"eip-id1168468231694\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\"The first line says,\">\n<tbody>\n<tr>\n<td>Notice that [latex]5[\/latex] is a factor of both [latex]10[\/latex] and [latex]15[\/latex].<\/td>\n<td>[latex]\\Large\\frac{10}{15}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Factor the numerator and denominator.<\/td>\n<td>[latex]\\Large\\frac{2\\cdot5}{3\\cdot5}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Remove the common factors.<\/td>\n<td>[latex]\\Large\\frac{2\\cdot\\color{red}{5}}{3\\cdot\\color{red}{5}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]\\Large\\frac{2}{3}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146014\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146014&theme=oea&iframe_resize_id=ohm146014&show_question_numbers\" width=\"100%\" height=\"400\"><\/iframe><\/p>\n<\/div>\n<p>To simplify a negative fraction, we use the same process as in the previous example. Remember to keep the negative sign.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Simplify: [latex]\\Large-\\frac{18}{24}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q270732\">Show Solution<\/span><\/p>\n<div id=\"q270732\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168469841089\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\"We notice that 18 and 24 both have factors,\">\n<tbody>\n<tr>\n<td>We notice that 18 and 24 both have factors of 6.<\/td>\n<td>[latex]\\Large-\\frac{18}{24}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Rewrite the numerator and denominator showing the common factor.<\/td>\n<td>[latex]\\Large\\frac{3\\cdot6}{4\\cdot6}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Remove common factors.<\/td>\n<td>[latex]\\Large-\\frac{3\\cdot\\color{red}{6}}{4\\cdot\\color{red}{6}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]\\Large-\\frac{3}{4}[\/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=\"ohm146015\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146015&theme=oea&iframe_resize_id=ohm146015&show_question_numbers\" width=\"100%\" height=\"400\"><\/iframe><\/p>\n<\/div>\n<p>Watch the following video to see another example of how to simplify a fraction.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Ex 1:  Simplify Fractions\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/_2Wk7jXf3Ok?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>After simplifying a fraction, it is always important to check the result to make sure that the numerator and denominator do not have any more factors in common. Remember, the definition of a simplified fraction: <em>a fraction is considered simplified if there are no common factors in the numerator and denominator<\/em>.<\/p>\n<p>When we simplify an improper fraction, there is no need to change it to a mixed number.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Simplify: [latex]\\Large-\\frac{56}{32}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q877414\">Show Solution<\/span><\/p>\n<div id=\"q877414\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168466600046\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\"The first line shows negative 56 over 32. The next line says,\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]\\Large-\\frac{56}{32}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Rewrite the numerator and denominator, showing the common factors, 8.<\/td>\n<td>[latex]\\Large\\frac{7\\cdot8}{4\\cdot8}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Remove common factors.<\/td>\n<td>[latex]\\Large\\frac{7\\cdot\\color{red}{8}}{4\\cdot\\color{red}{8}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]\\Large-\\frac{7}{4}[\/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=\"ohm146017\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146017&theme=oea&iframe_resize_id=ohm146017&show_question_numbers\" width=\"100%\" height=\"400\"><\/iframe><\/p>\n<\/div>\n<p>Sometimes it may not be easy to find common factors of the numerator and denominator. A good idea, then, is to factor the numerator and the denominator into prime numbers. (You may want to use the factor tree method to identify the prime factors.) Then divide out the common factors using the Equivalent Fractions Property.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Simplify: [latex]\\Large\\frac{210}{385}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q721590\">Show Solution<\/span><\/p>\n<div id=\"q721590\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168467251049\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\"The fraction 210 over 385 is shown. The next line says,\">\n<tbody>\n<tr>\n<td>Use factor trees to factor the numerator and denominator.<\/td>\n<td>[latex]\\Large\\frac{210}{385}[\/latex]<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220913\/CNX_BMath_Figure_04_02_028_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Rewrite the numerator and denominator as the product of the primes.<\/td>\n<td>[latex]{\\Large\\frac{210}{385}}={\\Large\\frac{2\\cdot 3\\cdot 5\\cdot 7}{5\\cdot 7\\cdot 11}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Remove the common factors.<\/td>\n<td>[latex]\\Large\\frac{2\\cdot 3\\cdot\\color{blue}{5}\\cdot\\color{red}{7}}{\\color{blue}{5}\\cdot\\color{red}{7}\\cdot 11}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]\\Large\\frac{2\\cdot 3}{11}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply any remaining factors.<\/td>\n<td>[latex]\\Large\\frac{6}{11}[\/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=\"ohm146018\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146018&theme=oea&iframe_resize_id=ohm146018&show_question_numbers\" width=\"100%\" height=\"400\"><\/iframe><\/p>\n<\/div>\n<p>We can also simplify fractions containing variables. If a variable is a common factor in the numerator and denominator, we remove it just as we do with an integer factor.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Simplify: [latex]\\Large\\frac{5xy}{15x}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q283612\">Show Solution<\/span><\/p>\n<div id=\"q283612\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168469401986\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]\\Large\\frac{5xy}{15x}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Rewrite numerator and denominator showing common factors.<\/td>\n<td>[latex]\\Large\\frac{5\\cdot x\\cdot y}{3\\cdot 5\\cdot x}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Remove common factors.<\/td>\n<td>[latex]\\Large\\frac{\\overline{)5}\\cdot \\overline{)x}\\cdot y}{3\\cdot \\overline{)5}\\cdot \\overline{)x}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]\\Large\\frac{y}{3}[\/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=\"ohm146019\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146019&theme=oea&iframe_resize_id=ohm146019&show_question_numbers\" width=\"100%\" height=\"400\"><\/iframe><\/p>\n<\/div>\n<p>Here&#8217;s a video with another example of how to simplify a fraction that contains variables.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Ex 3:  Simplify Fractions Containing Variables\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/tLgfPeecGe0?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-4626\">\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: 146014, 146015, 146017, 146018, 146019. <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 1: Simplify Fractions. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/_2Wk7jXf3Ok\">https:\/\/youtu.be\/_2Wk7jXf3Ok<\/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 3: Simplify Fractions Containing Variables. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/tLgfPeecGe0\">https:\/\/youtu.be\/tLgfPeecGe0<\/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":17533,"menu_order":3,"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 1: Simplify Fractions\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/_2Wk7jXf3Ok\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Ex 3: Simplify Fractions Containing Variables\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/tLgfPeecGe0\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Question ID: 146014, 146015, 146017, 146018, 146019\",\"author\":\"Alyson Day\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"IMathAS Community License CC-BY + 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