{"id":9542,"date":"2017-05-03T15:38:04","date_gmt":"2017-05-03T15:38:04","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=9542"},"modified":"2020-09-03T10:51:25","modified_gmt":"2020-09-03T10:51:25","slug":"adding-and-subtracting-fractions-with-different-denominators","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/chapter\/adding-and-subtracting-fractions-with-different-denominators\/","title":{"raw":"2.5.b - Adding and Subtracting Fractions With Different Denominators","rendered":"2.5.b &#8211; Adding and Subtracting Fractions With Different Denominators"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Add and subtract fractions with different denominators<\/li>\r\n \t<li>Add and subtract fractions with different denominators that contain variables<\/li>\r\n \t<li>Identify and use fraction operations<\/li>\r\n<\/ul>\r\n<\/div>\r\nOnce we have converted two fractions to equivalent forms with common denominators, we can add or subtract them by adding or subtracting the numerators.\r\n<div class=\"textbox shaded\">\r\n<h3>Add or subtract fractions with different denominators<\/h3>\r\n<ol id=\"eip-id1168468303196\" class=\"stepwise\">\r\n \t<li>Find the LCD.<\/li>\r\n \t<li>Convert each fraction to an equivalent form with the LCD as the denominator.<\/li>\r\n \t<li>Add or subtract the fractions.<\/li>\r\n \t<li>Write the result in simplified form.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nAdd: [latex]\\Large\\frac{1}{2}+\\Large\\frac{1}{3}[\/latex]\r\n\r\nSolution:\r\n<table id=\"eip-id1168466144855\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\"The first line says 1 half plus 1 third. The next line says, \">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]\\Large\\frac{1}{2}+\\Large\\frac{1}{3}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Find the LCD of [latex]2[\/latex], [latex]3[\/latex].<\/td>\r\n<td><img class=\"\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221040\/CNX_BMath_Figure_04_05_029_img-01.png\" alt=\".\" width=\"81\" height=\"110\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Change into equivalent fractions with the LCD [latex]6[\/latex].<\/td>\r\n<td>[latex]\\Large\\frac{1\\cdot\\color{red}{3}}{2\\cdot\\color{red}{3}} +\\Large\\frac{1\\cdot\\color{red}{2}}{3\\cdot\\color{red}{2}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify the numerators and denominators.<\/td>\r\n<td>[latex]\\Large\\frac{3}{6}+\\Large\\frac{2}{6}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add.<\/td>\r\n<td>[latex]\\Large\\frac{5}{6}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\nRemember, always check to see if the answer can be simplified. Since [latex]5[\/latex] and [latex]6[\/latex] have no common factors, the fraction [latex]\\Large\\frac{5}{6}[\/latex] cannot be reduced.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n[ohm_question height=\"230\"]146262[\/ohm_question]\r\n\r\n<\/div>\r\nWatch the following video to see more examples and explanation about how to add two fractions with unlike denominators.\r\n\r\nhttps:\/\/youtu.be\/zV4q7j1-89I\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n[ohm_question height=\"230\"]146264[\/ohm_question]\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nAdd: [latex]\\Large\\frac{7}{12}+\\Large\\frac{5}{18}[\/latex]\r\n[reveal-answer q=\"826911\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"826911\"]\r\n\r\nSolution:\r\n<table id=\"eip-id1168468285390\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\"The first line says 7 over 12 plus 5 over 18. The next line says, \">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]\\Large\\frac{7}{12}+\\Large\\frac{5}{18}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Find the LCD of [latex]12[\/latex] and [latex]18[\/latex].<\/td>\r\n<td><img class=\"\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221043\/CNX_BMath_Figure_04_05_031_img-01.png\" alt=\".\" width=\"146\" height=\"75\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rewrite as equivalent fractions with the LCD.<\/td>\r\n<td>[latex]\\Large\\frac{7\\cdot\\color{red}{3}}{12\\cdot\\color{red}{3}} +\\Large\\frac{5\\cdot\\color{red}{2}}{18\\cdot\\color{red}{2}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify the numerators and denominators.<\/td>\r\n<td>[latex]\\Large\\frac{21}{36}+\\Large\\frac{10}{36}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add.<\/td>\r\n<td>[latex]\\Large\\frac{31}{36}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nBecause [latex]31[\/latex] is a prime number, it has no factors in common with [latex]36[\/latex]. The answer is simplified.\r\n\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=\"230\"]146265[\/ohm_question]\r\n\r\n<\/div>\r\nYou can also add more than two fractions as long as you first find a common denominator for all of them. An example of a sum of three fractions is shown below. In this example, you will use the prime factorization method to find the LCM.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Think About It<\/h3>\r\nAdd [latex]\\Large\\frac{3}{4}+\\Large\\frac{1}{6}+\\Large\\frac{5}{8}[\/latex].\u00a0 Simplify the answer and write as a mixed number.\r\n\r\nWhat makes this example different than the previous ones? Use the box below to write down a few thoughts about how you would add three fractions with different denominators together.\r\n\r\n[practice-area rows=\"2\"][\/practice-area]\r\n\r\n[reveal-answer q=\"680977\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"680977\"]Since the denominators are not alike, find the least common denominator by finding the least common multiple (LCM) of 4, 6, and 8.\r\n<p style=\"text-align: center\">[latex]4=2\\cdot2\\\\6=3\\cdot2\\\\8=2\\cdot2\\cdot2\\\\\\text{LCM}:\\,\\,2\\cdot2\\cdot2\\cdot3=24[\/latex]<\/p>\r\nRewrite each fraction with a denominator of 24.\r\n<p style=\"text-align: center\">[latex]\\begin{array}{c}\\Large\\frac{3}{4}\\cdot\\Large\\frac{6}{6}=\\Large\\frac{18}{24}\\\\\\\\\\Large\\frac{1}{6}\\cdot\\Large\\frac{4}{4}=\\Large\\frac{4}{24}\\\\\\\\\\Large\\frac{5}{8}\\cdot\\Large\\frac{3}{3}=\\Large\\frac{15}{24}\\end{array}[\/latex]<\/p>\r\nAdd the fractions by adding the numerators and keeping the denominator the same.\r\n<p style=\"text-align: center\">[latex]\\Large\\frac{18}{24}+\\Large\\frac{4}{24}+\\Large\\frac{15}{24}=\\Large\\frac{37}{24}[\/latex]<\/p>\r\nWrite the improper fraction as a mixed number and simplify the fraction.\r\n<p style=\"text-align: center\">[latex]\\Large\\frac{37}{24}\\normalsize=1\\,\\,\\Large\\frac{13}{24}[\/latex]<\/p>\r\n\r\n<h4>Answer<\/h4>\r\n[latex]\\Large\\frac{3}{4}+\\Large\\frac{1}{6}+\\Large\\frac{5}{8}\\normalsize=1\\Large\\frac{13}{24}[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<h2>Subtracting Fractions<\/h2>\r\nWhen you subtract fractions, you must think about whether they have a common denominator, just like with adding fractions. Below are some examples of subtracting fractions whose denominators are not alike.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nSubtract: [latex]\\Large\\frac{7}{15}-\\Large\\frac{19}{24}[\/latex]\r\n[reveal-answer q=\"169999\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"169999\"]\r\n\r\nSolution:\r\n<table id=\"eip-id1168466319808\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\"The first line says 7 over 15 minus 19 over 24. The next line says \">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]\\Large\\frac{7}{15}-\\Large\\frac{19}{24}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Find the LCD.\r\n\r\n&nbsp;<\/td>\r\n<td><img class=\"\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221046\/CNX_BMath_Figure_04_05_032_img-01.png\" alt=\".\" width=\"170\" height=\"80\" \/>\r\n\r\n[latex]15[\/latex] is 'missing' three factors of [latex]2[\/latex]\r\n\r\n[latex]24[\/latex] is 'missing' a factor of [latex]5[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rewrite as equivalent fractions with the LCD.<\/td>\r\n<td>[latex]\\Large\\frac{7\\cdot\\color{red}{8}}{15\\cdot\\color{red}{8}} -\\Large\\frac{19\\cdot\\color{red}{5}}{24\\cdot\\color{red}{5}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify each numerator and denominator.<\/td>\r\n<td>[latex]\\Large\\frac{56}{120}-\\Large\\frac{95}{120}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Subtract.<\/td>\r\n<td>[latex]-\\Large\\frac{39}{120}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rewrite showing the common factor of [latex]3[\/latex].<\/td>\r\n<td>[latex]-\\Large\\frac{13\\cdot 3}{40\\cdot 3}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Remove the common factor to simplify.<\/td>\r\n<td>[latex]-\\Large\\frac{13}{40}[\/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=\"230\"]146266[\/ohm_question]\r\n\r\n<\/div>\r\nThe following video provides two more examples of how to subtract two fractions with unlike denominators.\r\n\r\nhttps:\/\/youtu.be\/aXlkygPPzQ8\r\n<h3><\/h3>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nAdd: [latex]-\\Large\\frac{11}{30}+\\Large\\frac{23}{42}[\/latex]\r\n[reveal-answer q=\"808641\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"808641\"]\r\n\r\nSolution:\r\n<table id=\"eip-id1168466855270\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\"The first line says negative 11 over 30 plus 23 over 42. The next line says, \">\r\n<tbody>\r\n<tr>\r\n<td>[latex]-\\Large\\frac{11}{30}+\\Large\\frac{23}{42}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Find the LCD.\r\n\r\n<img class=\"\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221049\/CNX_BMath_Figure_04_05_033_img-01.png\" alt=\".\" width=\"151\" height=\"82\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rewrite as equivalent fractions with the LCD.<\/td>\r\n<td>[latex]-\\Large\\frac{11\\cdot\\color{red}{7}}{30\\cdot\\color{red}{7}} +\\Large\\frac{23\\cdot\\color{red}{5}}{42\\cdot\\color{red}{5}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify each numerator and denominator.<\/td>\r\n<td>[latex]-\\Large\\frac{77}{210}+\\Large\\frac{115}{210}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add.<\/td>\r\n<td>[latex]\\Large\\frac{38}{210}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rewrite showing the common factor of [latex]2[\/latex].<\/td>\r\n<td>[latex]\\Large\\frac{19\\cdot 2}{105\\cdot 2}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Remove the common factor to simplify.<\/td>\r\n<td>[latex]\\Large\\frac{19}{105}[\/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=\"230\"]146267[\/ohm_question]\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nSubtract: [latex]\\Large\\frac{1}{2}-\\left(-\\Large\\frac{1}{4}\\right)[\/latex]\r\n[reveal-answer q=\"841760\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"841760\"]\r\n\r\nSolution:\r\n<table id=\"eip-id1168466426391\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\"The first line says 1 half minus negative 1 fourth. The next line says, \">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]\\Large\\frac{1}{2}-\\left(-\\Large\\frac{1}{4}\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Find the LCD of [latex]2[\/latex] and [latex]4[\/latex].<\/td>\r\n<td><img class=\"\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221041\/CNX_BMath_Figure_04_05_030_img-01.png\" alt=\".\" width=\"100\" height=\"76\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rewrite as equivalent fractions using the LCD [latex]4[\/latex].<\/td>\r\n<td>[latex]\\Large\\frac{1\\cdot\\color{red}{2}}{2\\cdot\\color{red}{2}} - (--\\Large\\frac{1}{4})[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify the first fraction.<\/td>\r\n<td>[latex]\\Large\\frac{2}{4}-\\left(-\\Large\\frac{1}{4}\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Subtract.<\/td>\r\n<td>[latex]\\Large\\frac{2-\\left(-1\\right)}{4}[\/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\nOne of the fractions already had the least common denominator, so we only had to convert the other fraction.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<h2>Adding and Subtracting Fractions that Contain Variables<\/h2>\r\nIn the next example, one of the fractions has a variable in its numerator. We follow the same steps as when both numerators are numbers.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nAdd: [latex]\\Large\\frac{3}{5}+\\Large\\frac{x}{8}[\/latex]\r\n[reveal-answer q=\"840732\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"840732\"]\r\n\r\nSolution:\r\nThe fractions have different denominators.\r\n<table id=\"eip-id1168467320994\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\"The first line says 3 over 5 plus x over 8. The next line says, \">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]\\Large\\frac{3}{5}+\\Large\\frac{x}{8}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Find the LCD.<\/td>\r\n<td><img class=\"\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221052\/CNX_BMath_Figure_04_05_034_img-01.png\" alt=\".\" width=\"143\" height=\"77\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rewrite as equivalent fractions with the LCD.<\/td>\r\n<td>[latex]\\Large\\frac{3\\cdot\\color{red}{8}}{5\\cdot\\color{red}{8}} +\\Large\\frac{x\\cdot\\color{red}{5}}{8\\cdot\\color{red}{5}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify the numerators and denominators.<\/td>\r\n<td>[latex]\\Large\\frac{24}{40}+\\Large\\frac{5x}{8}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add.<\/td>\r\n<td>[latex]\\Large\\frac{24+5x}{40}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nWe cannot add [latex]24[\/latex] and [latex]5x[\/latex] since they are not like terms, so we cannot simplify the expression any further.\r\n\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=\"230\"]146268[\/ohm_question]\r\n\r\n<\/div>\r\nWatch the following video to see more examples of how to add and subtract fractions with unlike denominators that contain variables.\r\n\r\nhttps:\/\/youtu.be\/ac88_8vBEuc","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Add and subtract fractions with different denominators<\/li>\n<li>Add and subtract fractions with different denominators that contain variables<\/li>\n<li>Identify and use fraction operations<\/li>\n<\/ul>\n<\/div>\n<p>Once we have converted two fractions to equivalent forms with common denominators, we can add or subtract them by adding or subtracting the numerators.<\/p>\n<div class=\"textbox shaded\">\n<h3>Add or subtract fractions with different denominators<\/h3>\n<ol id=\"eip-id1168468303196\" class=\"stepwise\">\n<li>Find the LCD.<\/li>\n<li>Convert each fraction to an equivalent form with the LCD as the denominator.<\/li>\n<li>Add or subtract the fractions.<\/li>\n<li>Write the result in simplified form.<\/li>\n<\/ol>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Add: [latex]\\Large\\frac{1}{2}+\\Large\\frac{1}{3}[\/latex]<\/p>\n<p>Solution:<\/p>\n<table id=\"eip-id1168466144855\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\"The first line says 1 half plus 1 third. The next line says,\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]\\Large\\frac{1}{2}+\\Large\\frac{1}{3}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Find the LCD of [latex]2[\/latex], [latex]3[\/latex].<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221040\/CNX_BMath_Figure_04_05_029_img-01.png\" alt=\".\" width=\"81\" height=\"110\" \/><\/td>\n<\/tr>\n<tr>\n<td>Change into equivalent fractions with the LCD [latex]6[\/latex].<\/td>\n<td>[latex]\\Large\\frac{1\\cdot\\color{red}{3}}{2\\cdot\\color{red}{3}} +\\Large\\frac{1\\cdot\\color{red}{2}}{3\\cdot\\color{red}{2}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify the numerators and denominators.<\/td>\n<td>[latex]\\Large\\frac{3}{6}+\\Large\\frac{2}{6}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td>[latex]\\Large\\frac{5}{6}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>Remember, always check to see if the answer can be simplified. Since [latex]5[\/latex] and [latex]6[\/latex] have no common factors, the fraction [latex]\\Large\\frac{5}{6}[\/latex] cannot be reduced.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146262\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146262&theme=oea&iframe_resize_id=ohm146262&show_question_numbers\" width=\"100%\" height=\"230\"><\/iframe><\/p>\n<\/div>\n<p>Watch the following video to see more examples and explanation about how to add two fractions with unlike denominators.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Ex: Add Fractions with Unlike Denominators (Basic with Model)\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/zV4q7j1-89I?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146264\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146264&theme=oea&iframe_resize_id=ohm146264&show_question_numbers\" width=\"100%\" height=\"230\"><\/iframe><\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Add: [latex]\\Large\\frac{7}{12}+\\Large\\frac{5}{18}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q826911\">Show Solution<\/span><\/p>\n<div id=\"q826911\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168468285390\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\"The first line says 7 over 12 plus 5 over 18. The next line says,\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]\\Large\\frac{7}{12}+\\Large\\frac{5}{18}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Find the LCD of [latex]12[\/latex] and [latex]18[\/latex].<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221043\/CNX_BMath_Figure_04_05_031_img-01.png\" alt=\".\" width=\"146\" height=\"75\" \/><\/td>\n<\/tr>\n<tr>\n<td>Rewrite as equivalent fractions with the LCD.<\/td>\n<td>[latex]\\Large\\frac{7\\cdot\\color{red}{3}}{12\\cdot\\color{red}{3}} +\\Large\\frac{5\\cdot\\color{red}{2}}{18\\cdot\\color{red}{2}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify the numerators and denominators.<\/td>\n<td>[latex]\\Large\\frac{21}{36}+\\Large\\frac{10}{36}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td>[latex]\\Large\\frac{31}{36}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Because [latex]31[\/latex] is a prime number, it has no factors in common with [latex]36[\/latex]. The answer is simplified.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146265\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146265&theme=oea&iframe_resize_id=ohm146265&show_question_numbers\" width=\"100%\" height=\"230\"><\/iframe><\/p>\n<\/div>\n<p>You can also add more than two fractions as long as you first find a common denominator for all of them. An example of a sum of three fractions is shown below. In this example, you will use the prime factorization method to find the LCM.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Think About It<\/h3>\n<p>Add [latex]\\Large\\frac{3}{4}+\\Large\\frac{1}{6}+\\Large\\frac{5}{8}[\/latex].\u00a0 Simplify the answer and write as a mixed number.<\/p>\n<p>What makes this example different than the previous ones? Use the box below to write down a few thoughts about how you would add three fractions with different denominators together.<\/p>\n<p><textarea aria-label=\"Your Answer\" rows=\"2\"><\/textarea><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q680977\">Show Solution<\/span><\/p>\n<div id=\"q680977\" class=\"hidden-answer\" style=\"display: none\">Since the denominators are not alike, find the least common denominator by finding the least common multiple (LCM) of 4, 6, and 8.<\/p>\n<p style=\"text-align: center\">[latex]4=2\\cdot2\\\\6=3\\cdot2\\\\8=2\\cdot2\\cdot2\\\\\\text{LCM}:\\,\\,2\\cdot2\\cdot2\\cdot3=24[\/latex]<\/p>\n<p>Rewrite each fraction with a denominator of 24.<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{c}\\Large\\frac{3}{4}\\cdot\\Large\\frac{6}{6}=\\Large\\frac{18}{24}\\\\\\\\\\Large\\frac{1}{6}\\cdot\\Large\\frac{4}{4}=\\Large\\frac{4}{24}\\\\\\\\\\Large\\frac{5}{8}\\cdot\\Large\\frac{3}{3}=\\Large\\frac{15}{24}\\end{array}[\/latex]<\/p>\n<p>Add the fractions by adding the numerators and keeping the denominator the same.<\/p>\n<p style=\"text-align: center\">[latex]\\Large\\frac{18}{24}+\\Large\\frac{4}{24}+\\Large\\frac{15}{24}=\\Large\\frac{37}{24}[\/latex]<\/p>\n<p>Write the improper fraction as a mixed number and simplify the fraction.<\/p>\n<p style=\"text-align: center\">[latex]\\Large\\frac{37}{24}\\normalsize=1\\,\\,\\Large\\frac{13}{24}[\/latex]<\/p>\n<h4>Answer<\/h4>\n<p>[latex]\\Large\\frac{3}{4}+\\Large\\frac{1}{6}+\\Large\\frac{5}{8}\\normalsize=1\\Large\\frac{13}{24}[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<h2>Subtracting Fractions<\/h2>\n<p>When you subtract fractions, you must think about whether they have a common denominator, just like with adding fractions. Below are some examples of subtracting fractions whose denominators are not alike.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Subtract: [latex]\\Large\\frac{7}{15}-\\Large\\frac{19}{24}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q169999\">Show Solution<\/span><\/p>\n<div id=\"q169999\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168466319808\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\"The first line says 7 over 15 minus 19 over 24. The next line says\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]\\Large\\frac{7}{15}-\\Large\\frac{19}{24}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Find the LCD.<\/p>\n<p>&nbsp;<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221046\/CNX_BMath_Figure_04_05_032_img-01.png\" alt=\".\" width=\"170\" height=\"80\" \/><\/p>\n<p>[latex]15[\/latex] is &#8216;missing&#8217; three factors of [latex]2[\/latex]<\/p>\n<p>[latex]24[\/latex] is &#8216;missing&#8217; a factor of [latex]5[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Rewrite as equivalent fractions with the LCD.<\/td>\n<td>[latex]\\Large\\frac{7\\cdot\\color{red}{8}}{15\\cdot\\color{red}{8}} -\\Large\\frac{19\\cdot\\color{red}{5}}{24\\cdot\\color{red}{5}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify each numerator and denominator.<\/td>\n<td>[latex]\\Large\\frac{56}{120}-\\Large\\frac{95}{120}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Subtract.<\/td>\n<td>[latex]-\\Large\\frac{39}{120}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Rewrite showing the common factor of [latex]3[\/latex].<\/td>\n<td>[latex]-\\Large\\frac{13\\cdot 3}{40\\cdot 3}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Remove the common factor to simplify.<\/td>\n<td>[latex]-\\Large\\frac{13}{40}[\/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=\"ohm146266\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146266&theme=oea&iframe_resize_id=ohm146266&show_question_numbers\" width=\"100%\" height=\"230\"><\/iframe><\/p>\n<\/div>\n<p>The following video provides two more examples of how to subtract two fractions with unlike denominators.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Example:  Subtract Fractions with Unlike Denominators\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/aXlkygPPzQ8?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h3><\/h3>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Add: [latex]-\\Large\\frac{11}{30}+\\Large\\frac{23}{42}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q808641\">Show Solution<\/span><\/p>\n<div id=\"q808641\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168466855270\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\"The first line says negative 11 over 30 plus 23 over 42. The next line says,\">\n<tbody>\n<tr>\n<td>[latex]-\\Large\\frac{11}{30}+\\Large\\frac{23}{42}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Find the LCD.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221049\/CNX_BMath_Figure_04_05_033_img-01.png\" alt=\".\" width=\"151\" height=\"82\" \/><\/td>\n<\/tr>\n<tr>\n<td>Rewrite as equivalent fractions with the LCD.<\/td>\n<td>[latex]-\\Large\\frac{11\\cdot\\color{red}{7}}{30\\cdot\\color{red}{7}} +\\Large\\frac{23\\cdot\\color{red}{5}}{42\\cdot\\color{red}{5}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify each numerator and denominator.<\/td>\n<td>[latex]-\\Large\\frac{77}{210}+\\Large\\frac{115}{210}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td>[latex]\\Large\\frac{38}{210}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Rewrite showing the common factor of [latex]2[\/latex].<\/td>\n<td>[latex]\\Large\\frac{19\\cdot 2}{105\\cdot 2}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Remove the common factor to simplify.<\/td>\n<td>[latex]\\Large\\frac{19}{105}[\/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=\"ohm146267\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146267&theme=oea&iframe_resize_id=ohm146267&show_question_numbers\" width=\"100%\" height=\"230\"><\/iframe><\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Subtract: [latex]\\Large\\frac{1}{2}-\\left(-\\Large\\frac{1}{4}\\right)[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q841760\">Show Solution<\/span><\/p>\n<div id=\"q841760\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168466426391\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\"The first line says 1 half minus negative 1 fourth. The next line says,\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]\\Large\\frac{1}{2}-\\left(-\\Large\\frac{1}{4}\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Find the LCD of [latex]2[\/latex] and [latex]4[\/latex].<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221041\/CNX_BMath_Figure_04_05_030_img-01.png\" alt=\".\" width=\"100\" height=\"76\" \/><\/td>\n<\/tr>\n<tr>\n<td>Rewrite as equivalent fractions using the LCD [latex]4[\/latex].<\/td>\n<td>[latex]\\Large\\frac{1\\cdot\\color{red}{2}}{2\\cdot\\color{red}{2}} - (--\\Large\\frac{1}{4})[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify the first fraction.<\/td>\n<td>[latex]\\Large\\frac{2}{4}-\\left(-\\Large\\frac{1}{4}\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Subtract.<\/td>\n<td>[latex]\\Large\\frac{2-\\left(-1\\right)}{4}[\/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<p>One of the fractions already had the least common denominator, so we only had to convert the other fraction.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<h2>Adding and Subtracting Fractions that Contain Variables<\/h2>\n<p>In the next example, one of the fractions has a variable in its numerator. We follow the same steps as when both numerators are numbers.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Add: [latex]\\Large\\frac{3}{5}+\\Large\\frac{x}{8}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q840732\">Show Solution<\/span><\/p>\n<div id=\"q840732\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<br \/>\nThe fractions have different denominators.<\/p>\n<table id=\"eip-id1168467320994\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\"The first line says 3 over 5 plus x over 8. The next line says,\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]\\Large\\frac{3}{5}+\\Large\\frac{x}{8}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Find the LCD.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221052\/CNX_BMath_Figure_04_05_034_img-01.png\" alt=\".\" width=\"143\" height=\"77\" \/><\/td>\n<\/tr>\n<tr>\n<td>Rewrite as equivalent fractions with the LCD.<\/td>\n<td>[latex]\\Large\\frac{3\\cdot\\color{red}{8}}{5\\cdot\\color{red}{8}} +\\Large\\frac{x\\cdot\\color{red}{5}}{8\\cdot\\color{red}{5}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify the numerators and denominators.<\/td>\n<td>[latex]\\Large\\frac{24}{40}+\\Large\\frac{5x}{8}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td>[latex]\\Large\\frac{24+5x}{40}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>We cannot add [latex]24[\/latex] and [latex]5x[\/latex] since they are not like terms, so we cannot simplify the expression any further.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146268\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146268&theme=oea&iframe_resize_id=ohm146268&show_question_numbers\" width=\"100%\" height=\"230\"><\/iframe><\/p>\n<\/div>\n<p>Watch the following video to see more examples of how to add and subtract fractions with unlike denominators that contain variables.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-3\" title=\"Ex:  Add and Subtract Fractions Containing Variables\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/ac88_8vBEuc?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-9542\">\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: 146262, 146264, 146265, 146266, 146267, 146268. <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: Add Fractions with Unlike Denominators (Basic with Model). <strong>Authored by<\/strong>: James Sousa (mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/zV4q7j1-89I\">https:\/\/youtu.be\/zV4q7j1-89I<\/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>Example: Subtract Fractions with Unlike Denominators. <strong>Authored by<\/strong>: James Sousa (mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/aXlkygPPzQ8\">https:\/\/youtu.be\/aXlkygPPzQ8<\/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: Add and Subtract Fractions Containing Variables. <strong>Authored by<\/strong>: James Sousa (mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/ac88_8vBEuc\">https:\/\/youtu.be\/ac88_8vBEuc<\/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":25,"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: Add Fractions with Unlike Denominators (Basic with Model)\",\"author\":\"James Sousa (mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/zV4q7j1-89I\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Example: Subtract Fractions with Unlike Denominators\",\"author\":\"James Sousa (mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/aXlkygPPzQ8\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Ex: Add and Subtract Fractions Containing Variables\",\"author\":\"James Sousa (mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/ac88_8vBEuc\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Question ID: 146262, 146264, 146265, 146266, 146267, 146268\",\"author\":\"Alyson Day\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"IMathAS Community License CC-BY + GPL\"}]","CANDELA_OUTCOMES_GUID":"1c3e903aceb94c409b819d5b184a24ef, f9ea9f7a9216423ea5ece82b36e8f3ae, 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