{"id":3509,"date":"2019-12-29T22:35:24","date_gmt":"2019-12-29T22:35:24","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforlibscoreq\/?post_type=chapter&#038;p=3509"},"modified":"2021-02-05T23:47:59","modified_gmt":"2021-02-05T23:47:59","slug":"adding-mixed-numbers-with-common-denominators","status":"web-only","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/chapter\/adding-mixed-numbers-with-common-denominators\/","title":{"raw":"Adding Mixed Numbers with Common Denominators","rendered":"Adding Mixed Numbers with Common Denominators"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Use a model to add two mixed numbers with like denominators<\/li>\r\n \t<li>Use two different methods to add mixed numbers with like denominators<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2>Model addition of two mixed numbers with like denominators<\/h2>\r\nSo far, we\u2019ve added and subtracted proper and improper fractions, but not mixed numbers. Let\u2019s begin by thinking about addition of mixed numbers using money.\r\n<p style=\"text-align: center;\">If Ron has [latex]1[\/latex] dollar and [latex]1[\/latex] quarter, he has [latex]1\\Large\\frac{1}{4}[\/latex] dollars.<\/p>\r\n<p style=\"text-align: center;\">If Don has [latex]2[\/latex] dollars and [latex]1[\/latex] quarter, he has [latex]2\\Large\\frac{1}{4}[\/latex] dollars.<\/p>\r\nWhat if Ron and Don put their money together? They would have [latex]3[\/latex] dollars and [latex]2[\/latex] quarters. They add the dollars and add the quarters. This makes [latex]3\\Large\\frac{2}{4}[\/latex] dollars. Because two quarters is half a dollar, they would have [latex]3[\/latex] and a half dollars, or [latex]3\\Large\\frac{1}{2}[\/latex] dollars.\r\n<p style=\"text-align: center;\">[latex]1\\Large\\frac{1}{4}[\/latex]+[latex]2\\Large\\frac{1}{4}[\/latex]\r\n[latex]\\text{________}[\/latex]\r\n[latex]3\\Large\\frac{2}{4}=\\normalsize3\\Large\\frac{1}{2}[\/latex]<\/p>\r\nWhen you added the dollars and then added the quarters, you were adding the whole numbers and then adding the fractions.\r\n<p style=\"text-align: center;\">[latex]1\\Large\\frac{1}{4}+\\normalsize2\\Large\\frac{1}{4}[\/latex]<\/p>\r\nWe can use fraction circles to model this same example:\r\n<table id=\"eip-id1168467438800\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\"The first line says, \">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td><\/td>\r\n<td>[latex]1\\Large\\frac{1}{4}+\\normalsize2\\Large\\frac{1}{4}[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Start with [latex]1\\Large\\frac{1}{4}[\/latex]<\/td>\r\n<td>one whole and one [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\/24221117\/CNX_BMath_Figure_04_06_002_img-01.png\" alt=\".\" \/><\/td>\r\n<td>[latex]1\\Large\\frac{1}{4}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add [latex]2\\Large\\frac{1}{4}[\/latex] more.<\/td>\r\n<td>two wholes and one [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\/24221120\/CNX_BMath_Figure_04_06_002_img-02.png\" alt=\".\" \/><\/td>\r\n<td>[latex]+ 2\\Large\\frac{1}{4}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The sum is:<\/td>\r\n<td>three wholes and two [latex]\\Large\\frac{1}{4}[\/latex] 's<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221123\/CNX_BMath_Figure_04_06_002_img-03.png\" alt=\".\" \/><\/td>\r\n<td>[latex]3\\Large\\frac{2}{4} = \\normalsize 3\\Large\\frac{1}{2}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nModel [latex]2\\Large\\frac{1}{3}+\\normalsize1\\Large\\frac{2}{3}[\/latex] and give the sum.\r\n\r\nSolution:\r\nWe will use fraction circles, whole circles for the whole numbers and [latex]\\Large\\frac{1}{3}[\/latex] pieces for the fractions.\r\n<table id=\"eip-id1168467250924\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\"The top line says, \">\r\n<tbody>\r\n<tr>\r\n<td>two wholes and one [latex]\\Large\\frac{1}{3}[\/latex]<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221126\/CNX_BMath_Figure_04_06_003_img-01.png\" alt=\".\" \/><\/td>\r\n<td>[latex]2\\Large\\frac{1}{3}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>plus one whole and two [latex]\\Large\\frac{1}{3}[\/latex] s<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221129\/CNX_BMath_Figure_04_06_003_img-02.png\" alt=\".\" \/><\/td>\r\n<td>[latex]+ 1\\Large\\frac{2}{3}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>sum is three wholes and three [latex]\\Large\\frac{1}{3}[\/latex] s<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221132\/CNX_BMath_Figure_04_06_003_img-03.png\" alt=\".\" \/><\/td>\r\n<td>[latex]3\\Large\\frac{3}{3} = 4[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nThis is the same as [latex]4[\/latex] wholes. So, [latex]2\\Large\\frac{1}{3}+\\normalsize1\\Large\\frac{2}{3}=4[\/latex].\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n[ohm_question height=\"270\"]146357[\/ohm_question]\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nModel [latex]1\\Large\\frac{3}{5}+\\normalsize2\\Large\\frac{3}{5}[\/latex] and give the sum as a mixed number.\r\n[reveal-answer q=\"207730\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"207730\"]\r\n\r\nSolution:\r\nWe will use fraction circles, whole circles for the whole numbers and [latex]\\Large\\frac{1}{5}[\/latex] pieces for the fractions.\r\n<table id=\"eip-id1168469468861\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\"The top line says, \">\r\n<tbody>\r\n<tr>\r\n<td>one whole and three [latex]\\Large\\frac{1}{5}\\normalsize\\text{s}[\/latex]<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221139\/CNX_BMath_Figure_04_06_006_img-01.png\" alt=\".\" \/><\/td>\r\n<td>[latex]1\\Large\\frac{3}{5}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>plus two wholes and three [latex]\\Large\\frac{1}{5}\\normalsize\\text{s}[\/latex] .<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221143\/CNX_BMath_Figure_04_06_006_img-02.png\" alt=\".\" \/><\/td>\r\n<td>[latex]+ 2\\Large\\frac{3}{5}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>sum is three wholes and six [latex]\\Large\\frac{1}{5}\\normalsize\\text{s}[\/latex]<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221146\/CNX_BMath_Figure_04_06_006_img-03.png\" alt=\".\" \/><\/td>\r\n<td>[latex]3\\Large\\frac{6}{5} = \\normalsize4\\Large\\frac{1}{5}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nAdding the whole circles and fifth pieces, we got a sum of [latex]3\\Large\\frac{6}{5}[\/latex]. We can see that [latex]\\Large\\frac{6}{5}[\/latex] is equivalent to [latex]1\\Large\\frac{1}{5}[\/latex], so we add that to the [latex]3[\/latex] to get [latex]4\\Large\\frac{1}{5}[\/latex].\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\nModel, and give the sum as a mixed number. Draw a picture to illustrate your model.\r\n\r\n[latex]2\\Large\\frac{5}{6}+\\normalsize1\\Large\\frac{5}{6}[\/latex]\r\n[reveal-answer q=\"299932\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"299932\"]\r\n\r\n[latex]4\\Large\\frac{2}{3}[\/latex]\r\n\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221149\/CNX_BMath_Figure_04_06_007_img.png\" alt=\"The figure shows five circles. The last two are divided into six equal sections. Two sections of the last circle are white.\" \/>\r\n\r\n[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\nModel, and give the sum as a mixed number. Draw a picture to illustrate your model.\r\n[latex]1\\Large\\frac{5}{8}+\\normalsize1\\Large\\frac{7}{8}[\/latex]\r\n[reveal-answer q=\"691025\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"691025\"]\r\n\r\n[latex]3\\Large\\frac{1}{2}[\/latex]\r\n\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221150\/CNX_BMath_Figure_04_06_008_img.png\" alt=\"The figure shows four circles. The last two are divided into eight equal sections. Four sections of the last circle are white.\" \/>\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<h2>Add mixed numbers with like denominators<\/h2>\r\nModeling with fraction circles helps illustrate the process for adding mixed numbers: We add the whole numbers and add the fractions, and then we simplify the result, if possible.\r\n<div class=\"textbox shaded\">\r\n<h3>Add mixed numbers with a common denominator<\/h3>\r\nStep 1. Add the whole numbers.\r\nStep 2. Add the fractions.\r\nStep 3. Simplify, if possible.\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nAdd: [latex]3\\Large\\frac{4}{9}+\\normalsize2\\Large\\frac{2}{9}[\/latex]\r\n\r\nSolution:\r\n<table id=\"eip-id1168467315461\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\"The top line says 3 and four-ninths plus 2 and two-ninths. The next line says, \">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]3\\Large\\frac{4}{9}+\\normalsize2\\Large\\frac{2}{9}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add the whole numbers.<\/td>\r\n<td>[latex]\\color{red}{3}\r\n\r\n\\Large\\frac{4}{9}[\/latex]\r\n\r\n[latex]\r\n\r\n\\Large\\frac{+\\color{red}{2}\\frac{2}{9}}{\\color{red}{5}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add the fractions.<\/td>\r\n<td>[latex]3\\color{red}{\r\n\r\n\\Large\\frac{4}{9}}[\/latex]\r\n\r\n[latex]\r\n\r\n\\Large\\frac{+2\\color{red}{\r\n\r\n\\Large\\frac{2}{9}}}{5\\color{red}{\r\n\r\n\\Large\\frac{6}{9}}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify the fraction.<\/td>\r\n<td>[latex]\\color{red}{5\\Large\\frac{6}{9}}=5\\Large\\frac{2}{3}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n[ohm_question height=\"270\"]146367[\/ohm_question]\r\n\r\n<\/div>\r\nIn the example above, the sum of the fractions was a proper fraction. Now we will work through an example where the sum is an improper fraction.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nFind the sum: [latex]9\\Large\\frac{5}{9}+\\normalsize5\\Large\\frac{7}{9}[\/latex]\r\n[reveal-answer q=\"697129\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"697129\"]\r\n\r\nSolution:\r\n<table id=\"eip-id1168467368769\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]9\\Large\\frac{5}{9}+\\normalsize5\\Large\\frac{7}{9}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add the whole numbers and then add the fractions.<\/td>\r\n<td>[latex]\\begin{array}{}\\\\ \\hfill 9\\Large\\frac{5}{9}\\\\ \\hfill \\underset{\\text{_____}}{+5\\Large\\frac{7}{9}}\\\\ \\hfill 14\\Large\\frac{12}{9}\\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rewrite [latex]\\Large\\frac{12}{9}[\/latex] as an improper fraction.<\/td>\r\n<td>[latex]14+1\\Large\\frac{3}{9}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add.<\/td>\r\n<td>[latex]15\\Large\\frac{3}{9}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]15\\Large\\frac{1}{3}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n[ohm_question height=\"270\"]146368[\/ohm_question]\r\n\r\n<\/div>\r\nIn the following video we show another example of how to add two mixed numbers.\r\n\r\nhttps:\/\/youtu.be\/2iHExOrBUvw\r\n\r\nAn alternate method for adding mixed numbers is to convert the mixed numbers to improper fractions and then add the improper fractions. This method is usually written horizontally.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nAdd by converting the mixed numbers to improper fractions: [latex]3\\Large\\frac{7}{8}+4\\Large\\frac{3}{8}[\/latex].\r\n[reveal-answer q=\"112316\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"112316\"]\r\n\r\nSolution:\r\n<table id=\"eip-id1168467375736\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]3\\Large\\frac{7}{8}+\\normalsize4\\Large\\frac{3}{8}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Convert to improper fractions.<\/td>\r\n<td>[latex]\\Large\\frac{31}{8}+\\Large\\frac{35}{8}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add the fractions.<\/td>\r\n<td>[latex]\\Large\\frac{31+35}{8}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify the numerator.<\/td>\r\n<td>[latex]\\Large\\frac{66}{8}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rewrite as a mixed number.<\/td>\r\n<td>[latex]8\\Large\\frac{2}{8}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify the fraction.<\/td>\r\n<td>[latex]8\\Large\\frac{1}{4}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nSince the problem was given in mixed number form, we will write the sum as a mixed number.\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=\"270\"]146380[\/ohm_question]\r\n\r\n<\/div>\r\nThe table below compares the two methods of addition, using the expression [latex]3\\Large\\frac{2}{5}+\\normalsize6\\Large\\frac{4}{5}[\/latex] as an example. Which way do you prefer?\r\n<table id=\"fs-id1951781\" style=\"width: 85%;\" summary=\"Table with two columns. The first one is labeled \">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th>Mixed Numbers<\/th>\r\n<th>Improper Fractions<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td>[latex]\\begin{array}{}\\\\ \\\\ \\hfill 3\\frac{2}{5}\\hfill \\\\ \\hfill \\frac{+6\\frac{4}{5}}{9\\frac{6}{5}}\\hfill \\\\ \\hfill 9+\\frac{6}{5}\\hfill \\\\ \\hfill 9+1\\frac{1}{5}\\hfill \\\\ \\hfill 10\\frac{1}{5}\\hfill \\end{array}[\/latex]<\/td>\r\n<td>[latex]\\begin{array}{}\\\\ \\hfill 3\\frac{2}{5}+6\\frac{4}{5}\\hfill \\\\ \\hfill \\frac{17}{5}+\\frac{34}{5}\\hfill \\\\ \\hfill \\frac{51}{5}\\hfill \\\\ \\hfill 10\\frac{1}{5}\\hfill \\end{array}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Use a model to add two mixed numbers with like denominators<\/li>\n<li>Use two different methods to add mixed numbers with like denominators<\/li>\n<\/ul>\n<\/div>\n<h2>Model addition of two mixed numbers with like denominators<\/h2>\n<p>So far, we\u2019ve added and subtracted proper and improper fractions, but not mixed numbers. Let\u2019s begin by thinking about addition of mixed numbers using money.<\/p>\n<p style=\"text-align: center;\">If Ron has [latex]1[\/latex] dollar and [latex]1[\/latex] quarter, he has [latex]1\\Large\\frac{1}{4}[\/latex] dollars.<\/p>\n<p style=\"text-align: center;\">If Don has [latex]2[\/latex] dollars and [latex]1[\/latex] quarter, he has [latex]2\\Large\\frac{1}{4}[\/latex] dollars.<\/p>\n<p>What if Ron and Don put their money together? They would have [latex]3[\/latex] dollars and [latex]2[\/latex] quarters. They add the dollars and add the quarters. This makes [latex]3\\Large\\frac{2}{4}[\/latex] dollars. Because two quarters is half a dollar, they would have [latex]3[\/latex] and a half dollars, or [latex]3\\Large\\frac{1}{2}[\/latex] dollars.<\/p>\n<p style=\"text-align: center;\">[latex]1\\Large\\frac{1}{4}[\/latex]+[latex]2\\Large\\frac{1}{4}[\/latex]<br \/>\n[latex]\\text{________}[\/latex]<br \/>\n[latex]3\\Large\\frac{2}{4}=\\normalsize3\\Large\\frac{1}{2}[\/latex]<\/p>\n<p>When you added the dollars and then added the quarters, you were adding the whole numbers and then adding the fractions.<\/p>\n<p style=\"text-align: center;\">[latex]1\\Large\\frac{1}{4}+\\normalsize2\\Large\\frac{1}{4}[\/latex]<\/p>\n<p>We can use fraction circles to model this same example:<\/p>\n<table id=\"eip-id1168467438800\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\"The first line says,\">\n<tbody>\n<tr>\n<td><\/td>\n<td><\/td>\n<td>[latex]1\\Large\\frac{1}{4}+\\normalsize2\\Large\\frac{1}{4}[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Start with [latex]1\\Large\\frac{1}{4}[\/latex]<\/td>\n<td>one whole and one [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\/24221117\/CNX_BMath_Figure_04_06_002_img-01.png\" alt=\".\" \/><\/td>\n<td>[latex]1\\Large\\frac{1}{4}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add [latex]2\\Large\\frac{1}{4}[\/latex] more.<\/td>\n<td>two wholes and one [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\/24221120\/CNX_BMath_Figure_04_06_002_img-02.png\" alt=\".\" \/><\/td>\n<td>[latex]+ 2\\Large\\frac{1}{4}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>The sum is:<\/td>\n<td>three wholes and two [latex]\\Large\\frac{1}{4}[\/latex] &#8216;s<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221123\/CNX_BMath_Figure_04_06_002_img-03.png\" alt=\".\" \/><\/td>\n<td>[latex]3\\Large\\frac{2}{4} = \\normalsize 3\\Large\\frac{1}{2}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Model [latex]2\\Large\\frac{1}{3}+\\normalsize1\\Large\\frac{2}{3}[\/latex] and give the sum.<\/p>\n<p>Solution:<br \/>\nWe will use fraction circles, whole circles for the whole numbers and [latex]\\Large\\frac{1}{3}[\/latex] pieces for the fractions.<\/p>\n<table id=\"eip-id1168467250924\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\"The top line says,\">\n<tbody>\n<tr>\n<td>two wholes and one [latex]\\Large\\frac{1}{3}[\/latex]<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221126\/CNX_BMath_Figure_04_06_003_img-01.png\" alt=\".\" \/><\/td>\n<td>[latex]2\\Large\\frac{1}{3}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>plus one whole and two [latex]\\Large\\frac{1}{3}[\/latex] s<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221129\/CNX_BMath_Figure_04_06_003_img-02.png\" alt=\".\" \/><\/td>\n<td>[latex]+ 1\\Large\\frac{2}{3}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>sum is three wholes and three [latex]\\Large\\frac{1}{3}[\/latex] s<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221132\/CNX_BMath_Figure_04_06_003_img-03.png\" alt=\".\" \/><\/td>\n<td>[latex]3\\Large\\frac{3}{3} = 4[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>This is the same as [latex]4[\/latex] wholes. So, [latex]2\\Large\\frac{1}{3}+\\normalsize1\\Large\\frac{2}{3}=4[\/latex].<\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146357\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146357&theme=oea&iframe_resize_id=ohm146357&show_question_numbers\" width=\"100%\" height=\"270\"><\/iframe><\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Model [latex]1\\Large\\frac{3}{5}+\\normalsize2\\Large\\frac{3}{5}[\/latex] and give the sum as a mixed number.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q207730\">Show Solution<\/span><\/p>\n<div id=\"q207730\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<br \/>\nWe will use fraction circles, whole circles for the whole numbers and [latex]\\Large\\frac{1}{5}[\/latex] pieces for the fractions.<\/p>\n<table id=\"eip-id1168469468861\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\"The top line says,\">\n<tbody>\n<tr>\n<td>one whole and three [latex]\\Large\\frac{1}{5}\\normalsize\\text{s}[\/latex]<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221139\/CNX_BMath_Figure_04_06_006_img-01.png\" alt=\".\" \/><\/td>\n<td>[latex]1\\Large\\frac{3}{5}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>plus two wholes and three [latex]\\Large\\frac{1}{5}\\normalsize\\text{s}[\/latex] .<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221143\/CNX_BMath_Figure_04_06_006_img-02.png\" alt=\".\" \/><\/td>\n<td>[latex]+ 2\\Large\\frac{3}{5}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>sum is three wholes and six [latex]\\Large\\frac{1}{5}\\normalsize\\text{s}[\/latex]<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221146\/CNX_BMath_Figure_04_06_006_img-03.png\" alt=\".\" \/><\/td>\n<td>[latex]3\\Large\\frac{6}{5} = \\normalsize4\\Large\\frac{1}{5}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Adding the whole circles and fifth pieces, we got a sum of [latex]3\\Large\\frac{6}{5}[\/latex]. We can see that [latex]\\Large\\frac{6}{5}[\/latex] is equivalent to [latex]1\\Large\\frac{1}{5}[\/latex], so we add that to the [latex]3[\/latex] to get [latex]4\\Large\\frac{1}{5}[\/latex].<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p>Model, and give the sum as a mixed number. Draw a picture to illustrate your model.<\/p>\n<p>[latex]2\\Large\\frac{5}{6}+\\normalsize1\\Large\\frac{5}{6}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q299932\">Show Solution<\/span><\/p>\n<div id=\"q299932\" class=\"hidden-answer\" style=\"display: none\">\n<p>[latex]4\\Large\\frac{2}{3}[\/latex]<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221149\/CNX_BMath_Figure_04_06_007_img.png\" alt=\"The figure shows five circles. The last two are divided into six equal sections. Two sections of the last circle are white.\" \/><\/p>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>Model, and give the sum as a mixed number. Draw a picture to illustrate your model.<br \/>\n[latex]1\\Large\\frac{5}{8}+\\normalsize1\\Large\\frac{7}{8}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q691025\">Show Solution<\/span><\/p>\n<div id=\"q691025\" class=\"hidden-answer\" style=\"display: none\">\n<p>[latex]3\\Large\\frac{1}{2}[\/latex]<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221150\/CNX_BMath_Figure_04_06_008_img.png\" alt=\"The figure shows four circles. The last two are divided into eight equal sections. Four sections of the last circle are white.\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<h2>Add mixed numbers with like denominators<\/h2>\n<p>Modeling with fraction circles helps illustrate the process for adding mixed numbers: We add the whole numbers and add the fractions, and then we simplify the result, if possible.<\/p>\n<div class=\"textbox shaded\">\n<h3>Add mixed numbers with a common denominator<\/h3>\n<p>Step 1. Add the whole numbers.<br \/>\nStep 2. Add the fractions.<br \/>\nStep 3. Simplify, if possible.<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Add: [latex]3\\Large\\frac{4}{9}+\\normalsize2\\Large\\frac{2}{9}[\/latex]<\/p>\n<p>Solution:<\/p>\n<table id=\"eip-id1168467315461\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\"The top line says 3 and four-ninths plus 2 and two-ninths. The next line says,\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]3\\Large\\frac{4}{9}+\\normalsize2\\Large\\frac{2}{9}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add the whole numbers.<\/td>\n<td>[latex]\\color{red}{3}    \\Large\\frac{4}{9}[\/latex]<\/p>\n<p>[latex]\\Large\\frac{+\\color{red}{2}\\frac{2}{9}}{\\color{red}{5}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add the fractions.<\/td>\n<td>[latex]3\\color{red}{    \\Large\\frac{4}{9}}[\/latex]<\/p>\n<p>[latex]\\Large\\frac{+2\\color{red}{    \\Large\\frac{2}{9}}}{5\\color{red}{    \\Large\\frac{6}{9}}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify the fraction.<\/td>\n<td>[latex]\\color{red}{5\\Large\\frac{6}{9}}=5\\Large\\frac{2}{3}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146367\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146367&theme=oea&iframe_resize_id=ohm146367&show_question_numbers\" width=\"100%\" height=\"270\"><\/iframe><\/p>\n<\/div>\n<p>In the example above, the sum of the fractions was a proper fraction. Now we will work through an example where the sum is an improper fraction.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Find the sum: [latex]9\\Large\\frac{5}{9}+\\normalsize5\\Large\\frac{7}{9}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q697129\">Show Solution<\/span><\/p>\n<div id=\"q697129\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168467368769\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]9\\Large\\frac{5}{9}+\\normalsize5\\Large\\frac{7}{9}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add the whole numbers and then add the fractions.<\/td>\n<td>[latex]\\begin{array}{}\\\\ \\hfill 9\\Large\\frac{5}{9}\\\\ \\hfill \\underset{\\text{_____}}{+5\\Large\\frac{7}{9}}\\\\ \\hfill 14\\Large\\frac{12}{9}\\end{array}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Rewrite [latex]\\Large\\frac{12}{9}[\/latex] as an improper fraction.<\/td>\n<td>[latex]14+1\\Large\\frac{3}{9}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td>[latex]15\\Large\\frac{3}{9}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]15\\Large\\frac{1}{3}[\/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=\"ohm146368\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146368&theme=oea&iframe_resize_id=ohm146368&show_question_numbers\" width=\"100%\" height=\"270\"><\/iframe><\/p>\n<\/div>\n<p>In the following video we show another example of how to add two mixed numbers.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Ex:  Add Mixed Numbers with Like Denominators\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/2iHExOrBUvw?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>An alternate method for adding mixed numbers is to convert the mixed numbers to improper fractions and then add the improper fractions. This method is usually written horizontally.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Add by converting the mixed numbers to improper fractions: [latex]3\\Large\\frac{7}{8}+4\\Large\\frac{3}{8}[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q112316\">Show Solution<\/span><\/p>\n<div id=\"q112316\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168467375736\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]3\\Large\\frac{7}{8}+\\normalsize4\\Large\\frac{3}{8}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Convert to improper fractions.<\/td>\n<td>[latex]\\Large\\frac{31}{8}+\\Large\\frac{35}{8}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add the fractions.<\/td>\n<td>[latex]\\Large\\frac{31+35}{8}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify the numerator.<\/td>\n<td>[latex]\\Large\\frac{66}{8}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Rewrite as a mixed number.<\/td>\n<td>[latex]8\\Large\\frac{2}{8}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify the fraction.<\/td>\n<td>[latex]8\\Large\\frac{1}{4}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Since the problem was given in mixed number form, we will write the sum as a mixed number.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146380\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146380&theme=oea&iframe_resize_id=ohm146380&show_question_numbers\" width=\"100%\" height=\"270\"><\/iframe><\/p>\n<\/div>\n<p>The table below compares the two methods of addition, using the expression [latex]3\\Large\\frac{2}{5}+\\normalsize6\\Large\\frac{4}{5}[\/latex] as an example. Which way do you prefer?<\/p>\n<table id=\"fs-id1951781\" style=\"width: 85%;\" summary=\"Table with two columns. The first one is labeled\">\n<thead>\n<tr valign=\"top\">\n<th>Mixed Numbers<\/th>\n<th>Improper Fractions<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td>[latex]\\begin{array}{}\\\\ \\\\ \\hfill 3\\frac{2}{5}\\hfill \\\\ \\hfill \\frac{+6\\frac{4}{5}}{9\\frac{6}{5}}\\hfill \\\\ \\hfill 9+\\frac{6}{5}\\hfill \\\\ \\hfill 9+1\\frac{1}{5}\\hfill \\\\ \\hfill 10\\frac{1}{5}\\hfill \\end{array}[\/latex]<\/td>\n<td>[latex]\\begin{array}{}\\\\ \\hfill 3\\frac{2}{5}+6\\frac{4}{5}\\hfill \\\\ \\hfill \\frac{17}{5}+\\frac{34}{5}\\hfill \\\\ \\hfill \\frac{51}{5}\\hfill \\\\ \\hfill 10\\frac{1}{5}\\hfill \\end{array}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\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-3509\">\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: 146357, 146367, 146368, 146380. <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 Mixed Numbers with Like Denominators. <strong>Authored by<\/strong>: James Sousa (mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/2iHExOrBUvw\">https:\/\/youtu.be\/2iHExOrBUvw<\/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: Find the Sum of Two Mixed Numbers Using Pattern Blocks. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/SngHXtqs_UE\">https:\/\/youtu.be\/SngHXtqs_UE<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>Prealgebra. <strong>Provided by<\/strong>: OpenStax. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":25777,"menu_order":8,"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 Mixed Numbers with Like Denominators\",\"author\":\"James Sousa (mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/2iHExOrBUvw\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Ex: Find the Sum of Two Mixed Numbers Using Pattern Blocks\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/SngHXtqs_UE\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Question ID: 146357, 146367, 146368, 146380\",\"author\":\"Alyson Day\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"IMathAS Community License CC-BY + 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