{"id":3513,"date":"2019-12-29T22:36:15","date_gmt":"2019-12-29T22:36:15","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforlibscoreq\/?post_type=chapter&#038;p=3513"},"modified":"2021-02-05T23:48:03","modified_gmt":"2021-02-05T23:48:03","slug":"adding-and-subtracting-mixed-numbers-with-different-denominators","status":"web-only","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/chapter\/adding-and-subtracting-mixed-numbers-with-different-denominators\/","title":{"raw":"Adding and Subtracting Mixed Numbers with Different Denominators","rendered":"Adding and Subtracting Mixed Numbers 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 mixed numbers with unlike denominators<\/li>\r\n<\/ul>\r\n<\/div>\r\nTo add or subtract mixed numbers with different denominators, we first convert the fractions to equivalent fractions with the LCD. Then we can follow all the steps we have learned for adding or subtracting fractions with like denominators.\r\n\r\nIn our first video, we show the process of adding mixed numbers with different denominators using pattern blocks.\r\n\r\nhttps:\/\/youtu.be\/SngHXtqs_UE\r\n\r\nNow let's try adding mixed numbers with different denominators without the help of pattern blocks.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nAdd: [latex]2\\Large\\frac{1}{2}+\\normalsize5\\Large\\frac{2}{3}[\/latex]\r\n\r\nSolution:\r\nSince the denominators are different, we rewrite the fractions as equivalent fractions with the LCD, [latex]6[\/latex]. Then we will add and simplify.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221220\/CNX_BMath_Figure_04_06_015_img.png\" alt=\"There are three vertical addition problems. The first shows 2 and 1 half plus 5 and 2 thirds. There is an arrow pointing to the next. This one shows 2 and 1 times a red 3 over 2 times a red 3, with an arrow pointing to the top red 3 that says, \" \/>\r\nWe write the answer as a mixed number because we were given mixed numbers in the problem.\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n[ohm_question]146566[\/ohm_question]\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nSubtract: [latex]4\\Large\\frac{3}{4}-\\normalsize2\\Large\\frac{7}{8}[\/latex]\r\n[reveal-answer q=\"287927\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"287927\"]\r\n\r\nSolution\r\nSince the denominators of the fractions are different, we will rewrite them as equivalent fractions with the LCD [latex]8[\/latex]. Once in that form, we will subtract. But we will need to borrow [latex]1[\/latex] first.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221222\/CNX_BMath_Figure_04_06_016_img.png\" alt=\"There are four vertical subtraction problems. The first shows 4 and 3 fourths minus 2 and 7 eighths. There is an arrow pointing to the next. This shows 4 and 3 times a red 2 over 4 times a red 2, with an arrow above saying, \" \/>\r\nWe were given mixed numbers, so we leave the answer 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]146396[\/ohm_question]\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nSubtract: [latex]3\\Large\\frac{5}{11}-\\normalsize4\\Large\\frac{3}{4}[\/latex]\r\n[reveal-answer q=\"86800\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"86800\"]\r\n\r\nSolution:\r\nWe can see the answer will be negative since we are subtracting [latex]4[\/latex] from [latex]3[\/latex]. Generally, when we know the answer will be negative it is easier to subtract with improper fractions rather than mixed numbers.\r\n<table id=\"eip-id1168466307254\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]3\\Large\\frac{5}{11}-\\normalsize4\\Large\\frac{3}{4}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Change to equivalent fractions with the LCD.<\/td>\r\n<td>[latex]3\r\n\r\n\\Large\\frac{5\\cdot 4}{11\\cdot 4}-\\normalsize4\r\n\r\n\\Large\\frac{3\\cdot 11}{4\\cdot 11}[\/latex]\r\n\r\n[latex]3\r\n\r\n\\Large\\frac{20}{44}-\\normalsize4\r\n\r\n\\Large\\frac{33}{44}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rewrite as improper fractions.<\/td>\r\n<td>[latex]\\Large\\frac{152}{44}-\\Large\\frac{209}{44}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Subtract.<\/td>\r\n<td>[latex]-\\Large\\frac{57}{44}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rewrite as a mixed number.<\/td>\r\n<td>[latex]-1\\Large\\frac{13}{44}[\/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]146367[\/ohm_question]\r\n\r\n<\/div>\r\nIn the following video we show four more examples of adding and subtracting mixed numbers that have both like and unlike denominators. The method used for these examples employs improper fractions.\r\n\r\nhttps:\/\/youtu.be\/jgvJWbUDTno","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Add and subtract mixed numbers with unlike denominators<\/li>\n<\/ul>\n<\/div>\n<p>To add or subtract mixed numbers with different denominators, we first convert the fractions to equivalent fractions with the LCD. Then we can follow all the steps we have learned for adding or subtracting fractions with like denominators.<\/p>\n<p>In our first video, we show the process of adding mixed numbers with different denominators using pattern blocks.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Ex: Find the Sum of Two Mixed Numbers Using Pattern Blocks\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/SngHXtqs_UE?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>Now let&#8217;s try adding mixed numbers with different denominators without the help of pattern blocks.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Add: [latex]2\\Large\\frac{1}{2}+\\normalsize5\\Large\\frac{2}{3}[\/latex]<\/p>\n<p>Solution:<br \/>\nSince the denominators are different, we rewrite the fractions as equivalent fractions with the LCD, [latex]6[\/latex]. Then we will add and simplify.<\/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\/24221220\/CNX_BMath_Figure_04_06_015_img.png\" alt=\"There are three vertical addition problems. The first shows 2 and 1 half plus 5 and 2 thirds. There is an arrow pointing to the next. This one shows 2 and 1 times a red 3 over 2 times a red 3, with an arrow pointing to the top red 3 that says,\" \/><br \/>\nWe write the answer as a mixed number because we were given mixed numbers in the problem.<\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146566\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146566&theme=oea&iframe_resize_id=ohm146566&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Subtract: [latex]4\\Large\\frac{3}{4}-\\normalsize2\\Large\\frac{7}{8}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q287927\">Show Solution<\/span><\/p>\n<div id=\"q287927\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<br \/>\nSince the denominators of the fractions are different, we will rewrite them as equivalent fractions with the LCD [latex]8[\/latex]. Once in that form, we will subtract. But we will need to borrow [latex]1[\/latex] first.<\/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\/24221222\/CNX_BMath_Figure_04_06_016_img.png\" alt=\"There are four vertical subtraction problems. The first shows 4 and 3 fourths minus 2 and 7 eighths. There is an arrow pointing to the next. This shows 4 and 3 times a red 2 over 4 times a red 2, with an arrow above saying,\" \/><br \/>\nWe were given mixed numbers, so we leave the answer 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=\"ohm146396\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146396&theme=oea&iframe_resize_id=ohm146396&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Subtract: [latex]3\\Large\\frac{5}{11}-\\normalsize4\\Large\\frac{3}{4}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q86800\">Show Solution<\/span><\/p>\n<div id=\"q86800\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<br \/>\nWe can see the answer will be negative since we are subtracting [latex]4[\/latex] from [latex]3[\/latex]. Generally, when we know the answer will be negative it is easier to subtract with improper fractions rather than mixed numbers.<\/p>\n<table id=\"eip-id1168466307254\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]3\\Large\\frac{5}{11}-\\normalsize4\\Large\\frac{3}{4}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Change to equivalent fractions with the LCD.<\/td>\n<td>[latex]3    \\Large\\frac{5\\cdot 4}{11\\cdot 4}-\\normalsize4    \\Large\\frac{3\\cdot 11}{4\\cdot 11}[\/latex]<\/p>\n<p>[latex]3    \\Large\\frac{20}{44}-\\normalsize4    \\Large\\frac{33}{44}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Rewrite as improper fractions.<\/td>\n<td>[latex]\\Large\\frac{152}{44}-\\Large\\frac{209}{44}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Subtract.<\/td>\n<td>[latex]-\\Large\\frac{57}{44}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Rewrite as a mixed number.<\/td>\n<td>[latex]-1\\Large\\frac{13}{44}[\/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=\"ohm146367\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146367&theme=oea&iframe_resize_id=ohm146367&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the following video we show four more examples of adding and subtracting mixed numbers that have both like and unlike denominators. The method used for these examples employs improper fractions.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Ex:  Add and Subtract Mixed Numbers Using Improper Fractions\" width=\"500\" height=\"375\" src=\"https:\/\/www.youtube.com\/embed\/jgvJWbUDTno?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-3513\">\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: 146566, 146396, 146367. <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 and Subtract Mixed Numbers Using Improper Fractions. <strong>Authored by<\/strong>: James Sousa (mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/jgvJWbUDTno\">https:\/\/youtu.be\/jgvJWbUDTno<\/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":10,"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 and Subtract Mixed Numbers Using Improper 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