{"id":9533,"date":"2017-05-03T15:32:31","date_gmt":"2017-05-03T15:32:31","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=9533"},"modified":"2020-07-02T02:46:31","modified_gmt":"2020-07-02T02:46:31","slug":"adding-fractions-with-common-denominators","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/cpcc-algebra-trig-I-support\/chapter\/adding-fractions-with-common-denominators\/","title":{"raw":"Adding Fractions With Common Denominators","rendered":"Adding Fractions With Common Denominators"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Model fraction addition<\/li>\r\n \t<li>Add fractions with a common denominator<\/li>\r\n \t<li>Add fractions with a common denominator that contain variables<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2>Model Fraction Addition<\/h2>\r\nHow many quarters are pictured? One quarter plus [latex]2[\/latex] quarters equals [latex]3[\/latex] quarters.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220949\/CNX_BMath_Figure_04_04_001.png\" alt=\"Three U.S. quarters are shown. One is shown on the left, and two are shown on the right.\" \/>\r\nRemember, quarters are really fractions of a dollar. Quarters are another way to say fourths. So the picture of the coins shows that\r\n<p style=\"text-align: center;\">[latex]{\\Large\\frac{1}{4}}+{\\Large\\frac{2}{4}}=\\Large{\\frac{3}{4}}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]\\text{one quarter }+\\text{ two quarters }=\\text{ three quarters} [\/latex]<\/p>\r\nLet\u2019s use fraction circles to model the same example, [latex]\\Large\\frac{1}{4}\\normalsize+\\Large\\frac{2}{4}[\/latex].\r\n<table id=\"eip-id1168467352669\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\"The first line says, \">\r\n<tbody>\r\n<tr>\r\n<td>Start with one [latex]\\Large\\frac{1}{4}[\/latex] piece.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220951\/CNX_BMath_Figure_04_04_002_img-01.png\" alt=\".\" \/><\/td>\r\n<td>[latex]\\Large\\frac{1}{4}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add two more [latex]\\Large\\frac{1}{4}[\/latex] pieces.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220953\/CNX_BMath_Figure_04_04_002_img-02.png\" alt=\".\" \/><\/td>\r\n<td>[latex]+\\Large\\frac{2}{4}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The result is [latex]\\Large\\frac{3}{4}[\/latex] .<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220954\/CNX_BMath_Figure_04_04_002_img-03.png\" alt=\".\" \/><\/td>\r\n<td>[latex]\\Large\\frac{3}{4}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nSo again, we see that\r\n\r\n[latex]\\Large\\frac{1}{4}\\normalsize+\\Large\\frac{2}{4}\\normalsize=\\Large\\frac{3}{4}[\/latex]\r\nDoing the Manipulative Mathematics activity \"Model Fraction Addition\" will help you develop a better understanding of adding fractions\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nUse a model to find the sum [latex]\\Large\\frac{3}{8}\\normalsize+\\Large\\frac{2}{8}[\/latex].\r\n\r\nSolution:\r\n<table id=\"eip-id1168468316426\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\"The first line says, \">\r\n<tbody>\r\n<tr>\r\n<td>Start with three [latex]\\Large\\frac{1}{8}[\/latex] pieces.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220957\/CNX_BMath_Figure_04_04_003_img-01.png\" alt=\".\" \/><\/td>\r\n<td>[latex]\\Large\\frac{3}{8}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add two [latex]\\Large\\frac{1}{8}[\/latex] pieces.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220959\/CNX_BMath_Figure_04_04_003_img-02.png\" alt=\".\" \/><\/td>\r\n<td>[latex]+\\Large\\frac{2}{8}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>How many [latex]\\Large\\frac{1}{8}[\/latex] pieces are there?<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221002\/CNX_BMath_Figure_04_04_003_img-03.png\" alt=\".\" \/><\/td>\r\n<td>[latex]\\Large\\frac{5}{8}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\nThere are five [latex]\\Large\\frac{1}{8}[\/latex] pieces, or five-eighths. The model shows that [latex]\\Large\\frac{3}{8}\\normalsize+\\Large\\frac{2}{8}\\normalsize=\\Large\\frac{5}{8}[\/latex].\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\nUse a model to find each sum. Show a diagram to illustrate your model.\r\n\r\n[latex]\\Large\\frac{1}{8}\\normalsize+\\Large\\frac{4}{8}[\/latex]\r\n[reveal-answer q=\"304582\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"304582\"]\r\n\r\n[latex]\\frac{5}{8}[\/latex]\r\n\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221004\/CNX_BMath_Figure_04_04_004_img.png\" alt=\"A circle divided into 8 sections, 5 of which are shaded.\" \/>\r\n\r\n[\/hidden-answer]\r\n\r\nUse a model to find each sum. Show a diagram to illustrate your model.\r\n[latex]\\Large\\frac{1}{6}\\normalsize+\\Large\\frac{4}{6}[\/latex]\r\n[reveal-answer q=\"297291\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"297291\"]\r\n\r\n[latex]\\frac{5}{6}[\/latex]\r\n\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221004\/CNX_BMath_Figure_04_04_005_img.png\" alt=\"A circle divided into 6 sections, 5 of which are shaded.\" \/>\r\n\r\n[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\n[ohm_question height=\"270\"]146178[\/ohm_question]\r\n\r\n<\/div>\r\nThe following video shows more examples of how to use models to add fractions with like denominators.\r\n\r\nhttps:\/\/youtu.be\/GTkY34kl6Kw\r\n<h2>Add Fractions with a Common Denominator<\/h2>\r\nThe example above shows that to add the same-size pieces\u2014meaning that the fractions have the same denominator\u2014we just add the number of pieces.\r\n<div class=\"textbox shaded\">\r\n<h3>Fraction Addition<\/h3>\r\nIf [latex]a,b,\\text{ and }c[\/latex] are numbers where [latex]c\\ne 0[\/latex], then\r\n\r\n[latex]\\Large\\frac{a}{c}\\normalsize+\\Large\\frac{b}{c}\\normalsize=\\Large\\frac{a+b}{c}[\/latex]\r\nTo add fractions with a common denominators, add the numerators and place the sum over the common denominator.\r\n\r\n<\/div>\r\n<h3><\/h3>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nFind the sum: [latex]\\Large\\frac{3}{5}\\normalsize+\\Large\\frac{1}{5}[\/latex]\r\n[reveal-answer q=\"250553\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"250553\"]\r\n\r\nSolution:\r\n<table id=\"eip-id1168468585410\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>[latex]\\Large\\frac{3}{5}\\normalsize+\\Large\\frac{1}{5}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add the numerators and place the sum over the common denominator.<\/td>\r\n<td>[latex]\\Large\\frac{3+1}{5}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]\\Large\\frac{4}{5}[\/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\"]146182[\/ohm_question]\r\n\r\n<\/div>\r\n<h3><\/h3>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nFind the sum: [latex]\\Large\\frac{x}{3}\\normalsize+\\Large\\frac{2}{3}[\/latex]\r\n[reveal-answer q=\"75083\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"75083\"]\r\n\r\nSolution:\r\n<table id=\"eip-id1168466426764\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>[latex]\\Large\\frac{x}{3}\\normalsize+\\Large\\frac{2}{3}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add the numerators and place the sum over the common denominator.<\/td>\r\n<td>[latex]\\Large\\frac{x+2}{3}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nNote that we cannot simplify this fraction any more. Since [latex]x\\text{ and }2[\/latex] are not like terms, we cannot combine them.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n[ohm_question height=\"270\"]146183[\/ohm_question]\r\n\r\n<\/div>\r\n<h3><\/h3>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nFind the sum: [latex]-\\Large\\frac{9}{d}\\normalsize+\\Large\\frac{3}{d}[\/latex]\r\n[reveal-answer q=\"15194\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"15194\"]\r\n\r\nSolution:\r\nWe will begin by rewriting the first fraction with the negative sign in the numerator.\r\n[latex]-\\Large\\frac{a}{b}\\normalsize=\\Large\\frac{-a}{b}[\/latex]\r\n<table id=\"eip-id1168466196770\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>[latex]-\\Large\\frac{9}{d}\\normalsize+\\Large\\frac{3}{d}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rewrite the first fraction with the negative in the numerator.<\/td>\r\n<td>[latex]\\Large\\frac{-9}{d}\\normalsize+\\Large\\frac{3}{d}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add the numerators and place the sum over the common denominator.<\/td>\r\n<td>[latex]\\Large\\frac{-9+3}{d}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify the numerator.<\/td>\r\n<td>[latex]\\Large\\frac{-6}{d}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rewrite with negative sign in front of the fraction.<\/td>\r\n<td>[latex]-\\Large\\frac{6}{d}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<h3>\u00a0Tip:\u00a0 A negative sign on a fraction can be written in the following locations: by the numerator, by the denominator or out in front of the fraction bar.\u00a0 It is your choice!<\/h3>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n[ohm_question height=\"270\"]146185[\/ohm_question]\r\n\r\n<\/div>\r\n<h3><\/h3>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nFind the sum: [latex]\\Large\\frac{2n}{11}\\normalsize+\\Large\\frac{5n}{11}[\/latex]\r\n[reveal-answer q=\"178713\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"178713\"]\r\n\r\nSolution:\r\n<table id=\"eip-id1168467203824\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>[latex]\\Large\\frac{2n}{11}\\normalsize+\\Large\\frac{5n}{11}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add the numerators and place the sum over the common denominator.<\/td>\r\n<td>[latex]\\Large\\frac{2n+5n}{11}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Combine like terms.<\/td>\r\n<td>[latex]\\Large\\frac{7n}{11}[\/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\"]146186[\/ohm_question]\r\n\r\n<\/div>\r\n<h3><\/h3>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nFind the sum: [latex]\\Large-\\frac{3}{12}+\\left(-\\frac{5}{12}\\right)[\/latex]\r\n[reveal-answer q=\"855499\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"855499\"]\r\n\r\nSolution:\r\n<table id=\"eip-id1168467276148\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>[latex]\\Large-\\frac{3}{12}+\\left(-\\frac{5}{12}\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add the numerators and place the sum over the common denominator.<\/td>\r\n<td>[latex]\\Large\\frac{-3+\\left(-5\\right)}{12}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add.<\/td>\r\n<td>[latex]\\Large\\frac{-8}{12}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify the fraction.<\/td>\r\n<td>[latex]\\Large-\\frac{2}{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\"]146187[\/ohm_question]\r\n\r\n<\/div>\r\n<span style=\"color: #000000;\">in the next video we show three more examples of adding fractions with common denominators. Pay close attention to the second example, it addresses a common mistake made by students when simplifying fractions with variables.<\/span>\r\n\r\nhttps:\/\/youtu.be\/V6N0ZYB6Pu8\r\n<h2>Contribute!<\/h2><div style=\"margin-bottom: 8px;\">Did you have an idea for improving this content? We\u2019d love your input.<\/div><a href=\"https:\/\/docs.google.com\/document\/d\/1j1cMOGNKRxhRqAc73jugrR3_CDfTw0IJFH-EmEjKz5U\" target=\"_blank\" style=\"font-size: 10pt; font-weight: 600; color: #077fab; text-decoration: none; border: 2px solid #077fab; border-radius: 7px; padding: 5px 25px; text-align: center; cursor: pointer; line-height: 1.5em;\">Improve this page<\/a><a style=\"margin-left: 16px;\" target=\"_blank\" href=\"https:\/\/docs.google.com\/document\/d\/1vy-T6DtTF-BbMfpVEI7VP_R7w2A4anzYZLXR8Pk4Fu4\">Learn More<\/a>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Model fraction addition<\/li>\n<li>Add fractions with a common denominator<\/li>\n<li>Add fractions with a common denominator that contain variables<\/li>\n<\/ul>\n<\/div>\n<h2>Model Fraction Addition<\/h2>\n<p>How many quarters are pictured? One quarter plus [latex]2[\/latex] quarters equals [latex]3[\/latex] quarters.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220949\/CNX_BMath_Figure_04_04_001.png\" alt=\"Three U.S. quarters are shown. One is shown on the left, and two are shown on the right.\" \/><br \/>\nRemember, quarters are really fractions of a dollar. Quarters are another way to say fourths. So the picture of the coins shows that<\/p>\n<p style=\"text-align: center;\">[latex]{\\Large\\frac{1}{4}}+{\\Large\\frac{2}{4}}=\\Large{\\frac{3}{4}}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\text{one quarter }+\\text{ two quarters }=\\text{ three quarters}[\/latex]<\/p>\n<p>Let\u2019s use fraction circles to model the same example, [latex]\\Large\\frac{1}{4}\\normalsize+\\Large\\frac{2}{4}[\/latex].<\/p>\n<table id=\"eip-id1168467352669\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\"The first line says,\">\n<tbody>\n<tr>\n<td>Start with one [latex]\\Large\\frac{1}{4}[\/latex] piece.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220951\/CNX_BMath_Figure_04_04_002_img-01.png\" alt=\".\" \/><\/td>\n<td>[latex]\\Large\\frac{1}{4}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add two more [latex]\\Large\\frac{1}{4}[\/latex] pieces.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220953\/CNX_BMath_Figure_04_04_002_img-02.png\" alt=\".\" \/><\/td>\n<td>[latex]+\\Large\\frac{2}{4}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>The result is [latex]\\Large\\frac{3}{4}[\/latex] .<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220954\/CNX_BMath_Figure_04_04_002_img-03.png\" alt=\".\" \/><\/td>\n<td>[latex]\\Large\\frac{3}{4}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>So again, we see that<\/p>\n<p>[latex]\\Large\\frac{1}{4}\\normalsize+\\Large\\frac{2}{4}\\normalsize=\\Large\\frac{3}{4}[\/latex]<br \/>\nDoing the Manipulative Mathematics activity &#8220;Model Fraction Addition&#8221; will help you develop a better understanding of adding fractions<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Use a model to find the sum [latex]\\Large\\frac{3}{8}\\normalsize+\\Large\\frac{2}{8}[\/latex].<\/p>\n<p>Solution:<\/p>\n<table id=\"eip-id1168468316426\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\"The first line says,\">\n<tbody>\n<tr>\n<td>Start with three [latex]\\Large\\frac{1}{8}[\/latex] pieces.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220957\/CNX_BMath_Figure_04_04_003_img-01.png\" alt=\".\" \/><\/td>\n<td>[latex]\\Large\\frac{3}{8}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add two [latex]\\Large\\frac{1}{8}[\/latex] pieces.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220959\/CNX_BMath_Figure_04_04_003_img-02.png\" alt=\".\" \/><\/td>\n<td>[latex]+\\Large\\frac{2}{8}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>How many [latex]\\Large\\frac{1}{8}[\/latex] pieces are there?<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221002\/CNX_BMath_Figure_04_04_003_img-03.png\" alt=\".\" \/><\/td>\n<td>[latex]\\Large\\frac{5}{8}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>There are five [latex]\\Large\\frac{1}{8}[\/latex] pieces, or five-eighths. The model shows that [latex]\\Large\\frac{3}{8}\\normalsize+\\Large\\frac{2}{8}\\normalsize=\\Large\\frac{5}{8}[\/latex].<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p>Use a model to find each sum. Show a diagram to illustrate your model.<\/p>\n<p>[latex]\\Large\\frac{1}{8}\\normalsize+\\Large\\frac{4}{8}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q304582\">Show Solution<\/span><\/p>\n<div id=\"q304582\" class=\"hidden-answer\" style=\"display: none\">\n<p>[latex]\\frac{5}{8}[\/latex]<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221004\/CNX_BMath_Figure_04_04_004_img.png\" alt=\"A circle divided into 8 sections, 5 of which are shaded.\" \/><\/p>\n<\/div>\n<\/div>\n<p>Use a model to find each sum. Show a diagram to illustrate your model.<br \/>\n[latex]\\Large\\frac{1}{6}\\normalsize+\\Large\\frac{4}{6}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q297291\">Show Solution<\/span><\/p>\n<div id=\"q297291\" class=\"hidden-answer\" style=\"display: none\">\n<p>[latex]\\frac{5}{6}[\/latex]<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221004\/CNX_BMath_Figure_04_04_005_img.png\" alt=\"A circle divided into 6 sections, 5 of which are shaded.\" \/><\/p>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146178\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146178&theme=oea&iframe_resize_id=ohm146178&show_question_numbers\" width=\"100%\" height=\"270\"><\/iframe><\/p>\n<\/div>\n<p>The following video shows more examples of how to use models to add fractions with like denominators.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Ex:  Add Fractions with Like Denominators\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/GTkY34kl6Kw?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h2>Add Fractions with a Common Denominator<\/h2>\n<p>The example above shows that to add the same-size pieces\u2014meaning that the fractions have the same denominator\u2014we just add the number of pieces.<\/p>\n<div class=\"textbox shaded\">\n<h3>Fraction Addition<\/h3>\n<p>If [latex]a,b,\\text{ and }c[\/latex] are numbers where [latex]c\\ne 0[\/latex], then<\/p>\n<p>[latex]\\Large\\frac{a}{c}\\normalsize+\\Large\\frac{b}{c}\\normalsize=\\Large\\frac{a+b}{c}[\/latex]<br \/>\nTo add fractions with a common denominators, add the numerators and place the sum over the common denominator.<\/p>\n<\/div>\n<h3><\/h3>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Find the sum: [latex]\\Large\\frac{3}{5}\\normalsize+\\Large\\frac{1}{5}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q250553\">Show Solution<\/span><\/p>\n<div id=\"q250553\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168468585410\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\">\n<tbody>\n<tr>\n<td>[latex]\\Large\\frac{3}{5}\\normalsize+\\Large\\frac{1}{5}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add the numerators and place the sum over the common denominator.<\/td>\n<td>[latex]\\Large\\frac{3+1}{5}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]\\Large\\frac{4}{5}[\/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=\"ohm146182\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146182&theme=oea&iframe_resize_id=ohm146182&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>Find the sum: [latex]\\Large\\frac{x}{3}\\normalsize+\\Large\\frac{2}{3}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q75083\">Show Solution<\/span><\/p>\n<div id=\"q75083\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168466426764\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\">\n<tbody>\n<tr>\n<td>[latex]\\Large\\frac{x}{3}\\normalsize+\\Large\\frac{2}{3}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add the numerators and place the sum over the common denominator.<\/td>\n<td>[latex]\\Large\\frac{x+2}{3}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>Note that we cannot simplify this fraction any more. Since [latex]x\\text{ and }2[\/latex] are not like terms, we cannot combine them.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146183\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146183&theme=oea&iframe_resize_id=ohm146183&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>Find the sum: [latex]-\\Large\\frac{9}{d}\\normalsize+\\Large\\frac{3}{d}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q15194\">Show Solution<\/span><\/p>\n<div id=\"q15194\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<br \/>\nWe will begin by rewriting the first fraction with the negative sign in the numerator.<br \/>\n[latex]-\\Large\\frac{a}{b}\\normalsize=\\Large\\frac{-a}{b}[\/latex]<\/p>\n<table id=\"eip-id1168466196770\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\">\n<tbody>\n<tr>\n<td>[latex]-\\Large\\frac{9}{d}\\normalsize+\\Large\\frac{3}{d}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Rewrite the first fraction with the negative in the numerator.<\/td>\n<td>[latex]\\Large\\frac{-9}{d}\\normalsize+\\Large\\frac{3}{d}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add the numerators and place the sum over the common denominator.<\/td>\n<td>[latex]\\Large\\frac{-9+3}{d}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify the numerator.<\/td>\n<td>[latex]\\Large\\frac{-6}{d}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Rewrite with negative sign in front of the fraction.<\/td>\n<td>[latex]-\\Large\\frac{6}{d}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<h3>\u00a0Tip:\u00a0 A negative sign on a fraction can be written in the following locations: by the numerator, by the denominator or out in front of the fraction bar.\u00a0 It is your choice!<\/h3>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146185\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146185&theme=oea&iframe_resize_id=ohm146185&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>Find the sum: [latex]\\Large\\frac{2n}{11}\\normalsize+\\Large\\frac{5n}{11}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q178713\">Show Solution<\/span><\/p>\n<div id=\"q178713\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168467203824\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\">\n<tbody>\n<tr>\n<td>[latex]\\Large\\frac{2n}{11}\\normalsize+\\Large\\frac{5n}{11}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add the numerators and place the sum over the common denominator.<\/td>\n<td>[latex]\\Large\\frac{2n+5n}{11}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td>[latex]\\Large\\frac{7n}{11}[\/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=\"ohm146186\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146186&theme=oea&iframe_resize_id=ohm146186&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>Find the sum: [latex]\\Large-\\frac{3}{12}+\\left(-\\frac{5}{12}\\right)[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q855499\">Show Solution<\/span><\/p>\n<div id=\"q855499\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168467276148\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\">\n<tbody>\n<tr>\n<td>[latex]\\Large-\\frac{3}{12}+\\left(-\\frac{5}{12}\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add the numerators and place the sum over the common denominator.<\/td>\n<td>[latex]\\Large\\frac{-3+\\left(-5\\right)}{12}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td>[latex]\\Large\\frac{-8}{12}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify the fraction.<\/td>\n<td>[latex]\\Large-\\frac{2}{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=\"ohm146187\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146187&theme=oea&iframe_resize_id=ohm146187&show_question_numbers\" width=\"100%\" height=\"270\"><\/iframe><\/p>\n<\/div>\n<p><span style=\"color: #000000;\">in the next video we show three more examples of adding fractions with common denominators. Pay close attention to the second example, it addresses a common mistake made by students when simplifying fractions with variables.<\/span><\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Add Fractions with Variables and Common Denominators\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/V6N0ZYB6Pu8?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h2>Contribute!<\/h2>\n<div style=\"margin-bottom: 8px;\">Did you have an idea for improving this content? We\u2019d love your input.<\/div>\n<p><a href=\"https:\/\/docs.google.com\/document\/d\/1j1cMOGNKRxhRqAc73jugrR3_CDfTw0IJFH-EmEjKz5U\" target=\"_blank\" style=\"font-size: 10pt; font-weight: 600; color: #077fab; text-decoration: none; border: 2px solid #077fab; border-radius: 7px; padding: 5px 25px; text-align: center; cursor: pointer; line-height: 1.5em;\">Improve this page<\/a><a style=\"margin-left: 16px;\" target=\"_blank\" href=\"https:\/\/docs.google.com\/document\/d\/1vy-T6DtTF-BbMfpVEI7VP_R7w2A4anzYZLXR8Pk4Fu4\">Learn More<\/a><\/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-9533\">\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>Add Fractions with Variables and Common Denominators. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/V6N0ZYB6Pu8\">https:\/\/youtu.be\/V6N0ZYB6Pu8<\/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: 146178, 146182, 146183, 146185, 146186, 146187. <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 Like Denominators. <strong>Authored by<\/strong>: James Sousa (mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/GTkY34kl6Kw\">https:\/\/youtu.be\/GTkY34kl6Kw<\/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><strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/i5XHfiQ2Fe0\">https:\/\/youtu.be\/i5XHfiQ2Fe0<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/about\/pdm\">Public Domain: No Known Copyright<\/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":11,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757\"},{\"type\":\"cc\",\"description\":\"Ex: Add Fractions with Like Denominators\",\"author\":\"James Sousa (mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/GTkY34kl6Kw\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"\",\"author\":\"\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/i5XHfiQ2Fe0\",\"project\":\"\",\"license\":\"pd\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Add Fractions with Variables and Common Denominators\",\"author\":\"James Sousa (Mathispower4u.com) for Lumen Learning\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/V6N0ZYB6Pu8\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Question ID: 146178, 146182, 146183, 146185, 146186, 146187\",\"author\":\"Alyson Day\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"IMathAS Community License CC-BY + GPL\"}]","CANDELA_OUTCOMES_GUID":"0f680d3958dd41e08f6f5f208f58e3ea, d9de0a6cf0f4408c854856f914c06136","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-9533","chapter","type-chapter","status-publish","hentry"],"part":6633,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/cpcc-algebra-trig-I-support\/wp-json\/pressbooks\/v2\/chapters\/9533","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/cpcc-algebra-trig-I-support\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/cpcc-algebra-trig-I-support\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/cpcc-algebra-trig-I-support\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":34,"href":"https:\/\/courses.lumenlearning.com\/cpcc-algebra-trig-I-support\/wp-json\/pressbooks\/v2\/chapters\/9533\/revisions"}],"predecessor-version":[{"id":18607,"href":"https:\/\/courses.lumenlearning.com\/cpcc-algebra-trig-I-support\/wp-json\/pressbooks\/v2\/chapters\/9533\/revisions\/18607"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/cpcc-algebra-trig-I-support\/wp-json\/pressbooks\/v2\/parts\/6633"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/cpcc-algebra-trig-I-support\/wp-json\/pressbooks\/v2\/chapters\/9533\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/cpcc-algebra-trig-I-support\/wp-json\/wp\/v2\/media?parent=9533"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/cpcc-algebra-trig-I-support\/wp-json\/pressbooks\/v2\/chapter-type?post=9533"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/cpcc-algebra-trig-I-support\/wp-json\/wp\/v2\/contributor?post=9533"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/cpcc-algebra-trig-I-support\/wp-json\/wp\/v2\/license?post=9533"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}