{"id":9551,"date":"2017-05-03T15:40:55","date_gmt":"2017-05-03T15:40:55","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=9551"},"modified":"2024-04-29T23:03:54","modified_gmt":"2024-04-29T23:03:54","slug":"modeling-subtraction-of-mixed-numbers","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/chapter\/modeling-subtraction-of-mixed-numbers\/","title":{"raw":"Subtracting Mixed Numbers With a Common Denominator","rendered":"Subtracting Mixed Numbers With a Common Denominator"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Model subtraction of mixed numbers with a common denominator<\/li>\r\n \t<li>Subtract mixed numbers with a common denominator<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2>Modeling subtraction of mixed numbers<\/h2>\r\nLet\u2019s think of pizzas again to model subtraction of mixed numbers with a common denominator. Suppose you just baked a whole pizza and want to give your brother half of the pizza. What do you have to do to the pizza to give him half? You have to cut it into at least two pieces. Then you can give him half.\r\n\r\nWe will use fraction circles (pizzas!) to help us visualize the process.\r\n\r\nStart with one whole.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221155\/CNX_BMath_Figure_04_06_018_img.png\" alt=\"A shaded circle is shown. Below it is a 1. There are arrows pointing to a shaded circle divided into 2 equal parts. Below it is 2 over 2. Next to this are two circles, each divided into 2 equal parts. The top circle has the right half shaded and the bottom circle has the left half shaded.\" \/>\r\nAlgebraically, you would write:\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221158\/CNX_BMath_Figure_04_06_019_img.png\" alt=\"On the left, it says 1 minus 1 half. There is an arrow pointing to 2 over 2 minus 1 over 2. There is another arrow pointing to 2 over 2 minus 1 over 2 equals 1 over 2.\" \/>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nUse a model to subtract: [latex]1-\\Large\\frac{1}{3}[\/latex].\r\n\r\nSolution:\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221159\/CNX_BMath_Figure_04_06_020_img.png\" alt=\"Step 1: Rewrite vertically, start with one whole. The model is a circle fully filed in. The math notation is 1 minus one third. Step 2: Since one third has a denominator of 3, cut the whole into 3 pieces. The 1 whole becomes three thirds. The model shows the circle divided into third. The math notation is three thirds minus one third. Step 3: Take away one third. There are two thirds left. The model shows the circle divided into thirds with one third gone. The math notation is three thirds minus one third equals two thirds.\" width=\"631\" height=\"484\" \/>\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n[ohm_question]146391[\/ohm_question]\r\n\r\n<\/div>\r\nWhat if we start with more than one whole? Let\u2019s find out.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nUse a model to subtract: [latex]2-\\Large\\frac{3}{4}[\/latex].\r\n[reveal-answer q=\"767805\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"767805\"]\r\n\r\nSolution:\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221202\/CNX_BMath_Figure_04_06_021_img.png\" alt=\"Step 1: Rewrite vertically, start with two wholes. The model is 2 circles fully filed in. The math notation is 2 minus three quarters. Step 2: Since three quarters has a denominator of 4, cut one of the wholes into 4 pieces. You have 1 whole and four fourths. The model shows a whole circle and the second circle divided into fourhts. The math notation is 1 and four fourths minus three fourths. Step 3: Take away three quarters. There are one and one quarter left. The model shows a whole circle and the second circle divided into quarters with three quarters gone. The math notation is one and four fourths minus three fourths equals one and one fourth.\" width=\"663\" height=\"483\" \/>\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]146392[\/ohm_question]\r\n\r\n<\/div>\r\nIn the next example, we\u2019ll subtract more than one whole.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nUse a model to subtract: [latex]2 - 1\\Large\\frac{2}{5}[\/latex].\r\n[reveal-answer q=\"5274\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"5274\"]\r\n\r\nSolution:\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221204\/CNX_BMath_Figure_04_06_022_img.png\" alt=\"Step 1: Rewrite vertically, start with two wholes. The model is 2 circles fully filed in. The math notation is 2 minus one and two fifths. Step 2: Since two fifths has a denominator of 5, cut one of the wholes into 5 pieces. You have 1 whole and five fifths. The model shows a whole circle and the second circle divided into fifths. The math notation is 1 and five fifths minus one and two fifths. Step 3: Take away one and two fifths. There are three fifths left. The model shows an empty circle and the second circle divided into fifths with three fifths remaining. The math notation is one and five fifths minus one and two fifths equals 3 fifths.\" width=\"631\" height=\"483\" \/>\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]146393[\/ohm_question]\r\n\r\n<\/div>\r\nWhat if you start with a mixed number and need to subtract a fraction? Think about this situation: You need to put three quarters in a parking meter, but you have only a [latex]$1[\/latex] bill and one quarter. What could you do? You could change the dollar bill into [latex]4[\/latex] quarters. The value of [latex]4[\/latex] quarters is the same as one dollar bill, but the [latex]4[\/latex] quarters are more useful for the parking meter. Now, instead of having a [latex]$1[\/latex] bill and one quarter, you have [latex]5[\/latex] quarters and can put [latex]3[\/latex] quarters in the meter.\r\n\r\nThis models what happens when we subtract a fraction from a mixed number. We subtracted three quarters from one dollar and one quarter.\r\n\r\nWe can also model this using fraction circles, much like we did for addition of mixed numbers.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nUse a model to subtract: [latex]1\\Large\\frac{1}{4}-\\Large\\frac{3}{4}[\/latex]\r\n[reveal-answer q=\"569499\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"569499\"]\r\n\r\nSolution:\r\n<table id=\"eip-id1168468516648\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\"The top row says, \">\r\n<tbody>\r\n<tr>\r\n<td>Rewrite vertically. Start with one whole and one fourth.<\/td>\r\n<td><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221207\/CNX_BMath_Figure_04_06_010_img-01.png\" alt=\"1 whole and 1 fourth fraction circles\" width=\"190\" height=\"111\" \/><\/td>\r\n<td>[latex]\\color{red}{1\r\n\r\n\\Large\\frac{1}{4}}[\/latex]\r\n\r\n[latex]--\r\n\r\n\\Large\\frac{3}{4}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Since the fractions have denominator 4, cut the whole into 4 pieces.\r\n\r\nYou now have [latex]\r\n\r\n\\Large\\frac{4}{4}[\/latex] and [latex]\r\n\r\n\\Large\\frac{1}{4}[\/latex] which is [latex]\r\n\r\n\\Large\\frac{5}{4}[\/latex] .<\/td>\r\n<td><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221209\/CNX_BMath_Figure_04_06_010_img-02.png\" alt=\"four fourths and 1 fourth fraction circlesg\" width=\"190\" height=\"111\" \/><\/td>\r\n<td>[latex]\\color{red}{\r\n\r\n\\Large\\frac{5}{4}}[\/latex]\r\n\r\n[latex]--\r\n\r\n\\Large\\frac{3}{4}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Take away [latex]\r\n\r\n\\Large\\frac{3}{4}[\/latex] .\r\n\r\nThere is [latex]\r\n\r\n\\Large\\frac{1}{2}[\/latex] left.<\/td>\r\n<td><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221211\/CNX_BMath_Figure_04_06_010_img-03.png\" alt=\"Subtract three fourths and you're left with two fourths\" width=\"190\" height=\"137\" \/><\/td>\r\n<td>[latex]\r\n\r\n\\Large\\frac{5}{4}[\/latex]\r\n\r\n[latex]\r\n\r\n\\Large\\frac{\\color{red}{--\r\n\r\n\\LARGE\\frac{3}{4}}}{\r\n\r\n\\LARGE\\frac{2}{4}=\r\n\r\n\\LARGE\\frac{1}{2}}[\/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\nUse a model to subtract. Draw a picture to illustrate or model your answer.\r\n\r\n[latex]1\\Large\\frac{1}{3}-\\Large\\frac{2}{3}[\/latex]\r\n[reveal-answer q=\"468617\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"468617\"]\r\n\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221212\/CNX_BMath_Figure_04_06_012_img.png\" alt=\"A circle divided into three sections, two of which are shaded.\" \/>\r\n\r\n[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\nUse a model to subtract. Draw a picture to illustrate your model.\r\n[latex]1\\Large\\frac{1}{5}-\\Large\\frac{4}{5}[\/latex]\r\n[reveal-answer q=\"468189\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"468189\"]\r\n\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221213\/CNX_BMath_Figure_04_06_013_img.png\" alt=\"A circle divided into 5 sections, 2 of which are shaded.\" \/>\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<h2>Subtract mixed numbers with a common denominator<\/h2>\r\nNow we will subtract mixed numbers without using a model. But it may help to picture the model in your mind as you read the steps.\r\n<div class=\"textbox shaded\">\r\n<h3>Subtract mixed numbers with common denominators<\/h3>\r\n<ol class=\"stepwise\">\r\n \t<li>Rewrite the problem in vertical form.<\/li>\r\n \t<li>Compare the two fractions.\r\n<ul id=\"eip-id1170322757770\">\r\n \t<li>If the top fraction is larger than the bottom fraction, go to Step 3.<\/li>\r\n \t<li>If not, in the top mixed number, take one whole and add it to the fraction part, making a mixed number with an improper fraction.<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>Subtract the fractions.<\/li>\r\n \t<li>Subtract the whole numbers.<\/li>\r\n \t<li>Simplify, if possible.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nFind the difference: [latex]5\\Large\\frac{3}{5}-\\normalsize2\\Large\\frac{4}{5}[\/latex]\r\n\r\nSolution:\r\n<table id=\"eip-id1168468520831\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\"The top line says 5 and 3 fifths minus 2 and 4 fifths. The next line says to rewrite the problem in vertical form and shows 5 and 3 fifths above 2 and 4 fifths. The next line says, \">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]5\\Large\\frac{3}{5}-\\normalsize2\\Large\\frac{4}{5}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rewrite the problem in vertical form.<\/td>\r\n<td><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221215\/CNX_BMath_Figure_04_06_014_img-02.png\" alt=\"5 and 3 fifths minus two and four fifths.\" width=\"162\" height=\"98\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Since [latex]\\Large\\frac{3}{5}[\/latex] is less than [latex]\\Large\\frac{4}{5}[\/latex] , take 1 from the 5 and add it to the [latex]\\Large\\frac{3}{5}:\\left(\\Large\\frac{5}{5}+\\Large\\frac{3}{5}=\\Large\\frac{8}{5}\\right)[\/latex]<\/td>\r\n<td><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221217\/CNX_BMath_Figure_04_06_014_img-03.png\" alt=\"5 and 3 fifths minus two and four fifths can be converted into 4 and 8 fifths minus two and four fifths.\" width=\"162\" height=\"92\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Subtract the fractions.<\/td>\r\n<td><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221217\/CNX_BMath_Figure_04_06_014_img-04.png\" alt=\"Ignoring the whole number values, subtract the fractions. 4 and 8 fifths minus two and four fifths equals four fifths\" width=\"162\" height=\"128\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Subtract the whole parts.\r\n\r\nThe result is in simplest form.<\/td>\r\n<td><img class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221219\/CNX_BMath_Figure_04_06_014_img-05.png\" alt=\"Subtract the whole parts. 4 minus two is two. The answer is two and four fifths. 4 and 8 fifths minus two and four fifths equals 2 and four fifths.\" width=\"161\" height=\"136\" \/><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nSince the problem was given with mixed numbers, we leave the result as mixed numbers.\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n[ohm_question]146395[\/ohm_question]\r\n\r\n<\/div>\r\nWatch the following video to see two more examples of how to subtract mixed numbers with like denominators.\r\n\r\nhttps:\/\/youtu.be\/Et84c52ipX0\r\n\r\nJust as we did with addition, we could subtract mixed numbers by converting them first to improper fractions. We should write the answer in the form it was given, so if we are given mixed numbers to subtract we will write the answer as a mixed number.\r\n<div class=\"textbox shaded\">\r\n<h3>Subtract mixed numbers with common denominators as improper fractions<\/h3>\r\nStep 1. Rewrite the mixed numbers as improper fractions.\r\nStep 2. Subtract the numerators.\r\nStep 3. Write the answer as a mixed number, simplifying the fraction part, if possible.\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nFind the difference by converting to improper fractions:\r\n[latex]9\\Large\\frac{6}{11}-\\normalsize7\\Large\\frac{10}{11}[\/latex]\r\n[reveal-answer q=\"958067\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"958067\"]\r\n\r\nSolution:\r\n<table id=\"eip-id1168466312849\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]9\\Large\\frac{6}{11}-\\normalsize7\\Large\\frac{10}{11}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rewrite as improper fractions.<\/td>\r\n<td>[latex]\\Large\\frac{105}{11}-\\Large\\frac{87}{11}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Subtract the numerators.<\/td>\r\n<td>[latex]\\Large\\frac{18}{11}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rewrite as a mixed number. The result is in simplest form.<\/td>\r\n<td>[latex]1\\Large\\frac{7}{11}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n[ohm_question height=\"270\"]146395[\/ohm_question]\r\n\r\n<\/div>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Model subtraction of mixed numbers with a common denominator<\/li>\n<li>Subtract mixed numbers with a common denominator<\/li>\n<\/ul>\n<\/div>\n<h2>Modeling subtraction of mixed numbers<\/h2>\n<p>Let\u2019s think of pizzas again to model subtraction of mixed numbers with a common denominator. Suppose you just baked a whole pizza and want to give your brother half of the pizza. What do you have to do to the pizza to give him half? You have to cut it into at least two pieces. Then you can give him half.<\/p>\n<p>We will use fraction circles (pizzas!) to help us visualize the process.<\/p>\n<p>Start with one whole.<\/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\/24221155\/CNX_BMath_Figure_04_06_018_img.png\" alt=\"A shaded circle is shown. Below it is a 1. There are arrows pointing to a shaded circle divided into 2 equal parts. Below it is 2 over 2. Next to this are two circles, each divided into 2 equal parts. The top circle has the right half shaded and the bottom circle has the left half shaded.\" \/><br \/>\nAlgebraically, you would write:<\/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\/24221158\/CNX_BMath_Figure_04_06_019_img.png\" alt=\"On the left, it says 1 minus 1 half. There is an arrow pointing to 2 over 2 minus 1 over 2. There is another arrow pointing to 2 over 2 minus 1 over 2 equals 1 over 2.\" \/><\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Use a model to subtract: [latex]1-\\Large\\frac{1}{3}[\/latex].<\/p>\n<p>Solution:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221159\/CNX_BMath_Figure_04_06_020_img.png\" alt=\"Step 1: Rewrite vertically, start with one whole. The model is a circle fully filed in. The math notation is 1 minus one third. Step 2: Since one third has a denominator of 3, cut the whole into 3 pieces. The 1 whole becomes three thirds. The model shows the circle divided into third. The math notation is three thirds minus one third. Step 3: Take away one third. There are two thirds left. The model shows the circle divided into thirds with one third gone. The math notation is three thirds minus one third equals two thirds.\" width=\"631\" height=\"484\" \/><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146391\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146391&theme=oea&iframe_resize_id=ohm146391&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>What if we start with more than one whole? Let\u2019s find out.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Use a model to subtract: [latex]2-\\Large\\frac{3}{4}[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q767805\">Show Solution<\/span><\/p>\n<div id=\"q767805\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221202\/CNX_BMath_Figure_04_06_021_img.png\" alt=\"Step 1: Rewrite vertically, start with two wholes. The model is 2 circles fully filed in. The math notation is 2 minus three quarters. Step 2: Since three quarters has a denominator of 4, cut one of the wholes into 4 pieces. You have 1 whole and four fourths. The model shows a whole circle and the second circle divided into fourhts. The math notation is 1 and four fourths minus three fourths. Step 3: Take away three quarters. There are one and one quarter left. The model shows a whole circle and the second circle divided into quarters with three quarters gone. The math notation is one and four fourths minus three fourths equals one and one fourth.\" width=\"663\" height=\"483\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146392\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146392&theme=oea&iframe_resize_id=ohm146392&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the next example, we\u2019ll subtract more than one whole.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Use a model to subtract: [latex]2 - 1\\Large\\frac{2}{5}[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q5274\">Show Solution<\/span><\/p>\n<div id=\"q5274\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221204\/CNX_BMath_Figure_04_06_022_img.png\" alt=\"Step 1: Rewrite vertically, start with two wholes. The model is 2 circles fully filed in. The math notation is 2 minus one and two fifths. Step 2: Since two fifths has a denominator of 5, cut one of the wholes into 5 pieces. You have 1 whole and five fifths. The model shows a whole circle and the second circle divided into fifths. The math notation is 1 and five fifths minus one and two fifths. Step 3: Take away one and two fifths. There are three fifths left. The model shows an empty circle and the second circle divided into fifths with three fifths remaining. The math notation is one and five fifths minus one and two fifths equals 3 fifths.\" width=\"631\" height=\"483\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146393\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146393&theme=oea&iframe_resize_id=ohm146393&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>What if you start with a mixed number and need to subtract a fraction? Think about this situation: You need to put three quarters in a parking meter, but you have only a [latex]$1[\/latex] bill and one quarter. What could you do? You could change the dollar bill into [latex]4[\/latex] quarters. The value of [latex]4[\/latex] quarters is the same as one dollar bill, but the [latex]4[\/latex] quarters are more useful for the parking meter. Now, instead of having a [latex]$1[\/latex] bill and one quarter, you have [latex]5[\/latex] quarters and can put [latex]3[\/latex] quarters in the meter.<\/p>\n<p>This models what happens when we subtract a fraction from a mixed number. We subtracted three quarters from one dollar and one quarter.<\/p>\n<p>We can also model this using fraction circles, much like we did for addition of mixed numbers.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Use a model to subtract: [latex]1\\Large\\frac{1}{4}-\\Large\\frac{3}{4}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q569499\">Show Solution<\/span><\/p>\n<div id=\"q569499\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168468516648\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\"The top row says,\">\n<tbody>\n<tr>\n<td>Rewrite vertically. Start with one whole and one fourth.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221207\/CNX_BMath_Figure_04_06_010_img-01.png\" alt=\"1 whole and 1 fourth fraction circles\" width=\"190\" height=\"111\" \/><\/td>\n<td>[latex]\\color{red}{1    \\Large\\frac{1}{4}}[\/latex]<\/p>\n<p>[latex]--    \\Large\\frac{3}{4}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Since the fractions have denominator 4, cut the whole into 4 pieces.<\/p>\n<p>You now have [latex]\\Large\\frac{4}{4}[\/latex] and [latex]\\Large\\frac{1}{4}[\/latex] which is [latex]\\Large\\frac{5}{4}[\/latex] .<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221209\/CNX_BMath_Figure_04_06_010_img-02.png\" alt=\"four fourths and 1 fourth fraction circlesg\" width=\"190\" height=\"111\" \/><\/td>\n<td>[latex]\\color{red}{    \\Large\\frac{5}{4}}[\/latex]<\/p>\n<p>[latex]--    \\Large\\frac{3}{4}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Take away [latex]\\Large\\frac{3}{4}[\/latex] .<\/p>\n<p>There is [latex]\\Large\\frac{1}{2}[\/latex] left.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221211\/CNX_BMath_Figure_04_06_010_img-03.png\" alt=\"Subtract three fourths and you're left with two fourths\" width=\"190\" height=\"137\" \/><\/td>\n<td>[latex]\\Large\\frac{5}{4}[\/latex]<\/p>\n<p>[latex]\\Large\\frac{\\color{red}{--    \\LARGE\\frac{3}{4}}}{    \\LARGE\\frac{2}{4}=    \\LARGE\\frac{1}{2}}[\/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>Use a model to subtract. Draw a picture to illustrate or model your answer.<\/p>\n<p>[latex]1\\Large\\frac{1}{3}-\\Large\\frac{2}{3}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q468617\">Show Solution<\/span><\/p>\n<div id=\"q468617\" class=\"hidden-answer\" style=\"display: none\">\n<p><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221212\/CNX_BMath_Figure_04_06_012_img.png\" alt=\"A circle divided into three sections, two of which are shaded.\" \/><\/p>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>Use a model to subtract. Draw a picture to illustrate your model.<br \/>\n[latex]1\\Large\\frac{1}{5}-\\Large\\frac{4}{5}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q468189\">Show Solution<\/span><\/p>\n<div id=\"q468189\" class=\"hidden-answer\" style=\"display: none\">\n<p><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221213\/CNX_BMath_Figure_04_06_013_img.png\" alt=\"A circle divided into 5 sections, 2 of which are shaded.\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<h2>Subtract mixed numbers with a common denominator<\/h2>\n<p>Now we will subtract mixed numbers without using a model. But it may help to picture the model in your mind as you read the steps.<\/p>\n<div class=\"textbox shaded\">\n<h3>Subtract mixed numbers with common denominators<\/h3>\n<ol class=\"stepwise\">\n<li>Rewrite the problem in vertical form.<\/li>\n<li>Compare the two fractions.\n<ul id=\"eip-id1170322757770\">\n<li>If the top fraction is larger than the bottom fraction, go to Step 3.<\/li>\n<li>If not, in the top mixed number, take one whole and add it to the fraction part, making a mixed number with an improper fraction.<\/li>\n<\/ul>\n<\/li>\n<li>Subtract the fractions.<\/li>\n<li>Subtract the whole numbers.<\/li>\n<li>Simplify, if possible.<\/li>\n<\/ol>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Find the difference: [latex]5\\Large\\frac{3}{5}-\\normalsize2\\Large\\frac{4}{5}[\/latex]<\/p>\n<p>Solution:<\/p>\n<table id=\"eip-id1168468520831\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\"The top line says 5 and 3 fifths minus 2 and 4 fifths. The next line says to rewrite the problem in vertical form and shows 5 and 3 fifths above 2 and 4 fifths. The next line says,\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]5\\Large\\frac{3}{5}-\\normalsize2\\Large\\frac{4}{5}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Rewrite the problem in vertical form.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221215\/CNX_BMath_Figure_04_06_014_img-02.png\" alt=\"5 and 3 fifths minus two and four fifths.\" width=\"162\" height=\"98\" \/><\/td>\n<\/tr>\n<tr>\n<td>Since [latex]\\Large\\frac{3}{5}[\/latex] is less than [latex]\\Large\\frac{4}{5}[\/latex] , take 1 from the 5 and add it to the [latex]\\Large\\frac{3}{5}:\\left(\\Large\\frac{5}{5}+\\Large\\frac{3}{5}=\\Large\\frac{8}{5}\\right)[\/latex]<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221217\/CNX_BMath_Figure_04_06_014_img-03.png\" alt=\"5 and 3 fifths minus two and four fifths can be converted into 4 and 8 fifths minus two and four fifths.\" width=\"162\" height=\"92\" \/><\/td>\n<\/tr>\n<tr>\n<td>Subtract the fractions.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221217\/CNX_BMath_Figure_04_06_014_img-04.png\" alt=\"Ignoring the whole number values, subtract the fractions. 4 and 8 fifths minus two and four fifths equals four fifths\" width=\"162\" height=\"128\" \/><\/td>\n<\/tr>\n<tr>\n<td>Subtract the whole parts.<\/p>\n<p>The result is in simplest form.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221219\/CNX_BMath_Figure_04_06_014_img-05.png\" alt=\"Subtract the whole parts. 4 minus two is two. The answer is two and four fifths. 4 and 8 fifths minus two and four fifths equals 2 and four fifths.\" width=\"161\" height=\"136\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Since the problem was given with mixed numbers, we leave the result as mixed numbers.<\/p>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146395\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146395&theme=oea&iframe_resize_id=ohm146395&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>Watch the following video to see two more examples of how to subtract mixed numbers with like denominators.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Ex:  Subtract Mixed Numbers with Like Denominators\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/Et84c52ipX0?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>Just as we did with addition, we could subtract mixed numbers by converting them first to improper fractions. We should write the answer in the form it was given, so if we are given mixed numbers to subtract we will write the answer as a mixed number.<\/p>\n<div class=\"textbox shaded\">\n<h3>Subtract mixed numbers with common denominators as improper fractions<\/h3>\n<p>Step 1. Rewrite the mixed numbers as improper fractions.<br \/>\nStep 2. Subtract the numerators.<br \/>\nStep 3. Write the answer as a mixed number, simplifying the fraction part, if possible.<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Find the difference by converting to improper fractions:<br \/>\n[latex]9\\Large\\frac{6}{11}-\\normalsize7\\Large\\frac{10}{11}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q958067\">Show Solution<\/span><\/p>\n<div id=\"q958067\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168466312849\" class=\"unnumbered unstyled\" style=\"width: 85%;\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]9\\Large\\frac{6}{11}-\\normalsize7\\Large\\frac{10}{11}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Rewrite as improper fractions.<\/td>\n<td>[latex]\\Large\\frac{105}{11}-\\Large\\frac{87}{11}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Subtract the numerators.<\/td>\n<td>[latex]\\Large\\frac{18}{11}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Rewrite as a mixed number. The result is in simplest form.<\/td>\n<td>[latex]1\\Large\\frac{7}{11}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146395\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146395&theme=oea&iframe_resize_id=ohm146395&show_question_numbers\" width=\"100%\" height=\"270\"><\/iframe><\/p>\n<\/div>\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-9551\">\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: 146391, 146392, 146393, 146395. <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: Subtract Mixed Numbers with Like Denominators. <strong>Authored by<\/strong>: James Sousa (mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/Et84c52ipX0\">https:\/\/youtu.be\/Et84c52ipX0<\/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":30,"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: Subtract Mixed Numbers with Like Denominators\",\"author\":\"James Sousa (mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/Et84c52ipX0\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Question ID: 146391, 146392, 146393, 146395\",\"author\":\"Alyson Day\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"IMathAS Community License CC-BY + GPL\"}]","CANDELA_OUTCOMES_GUID":"1ea1211951d34854b1fe47d7d4f4960f, 7832bf17f44e46d88de136d5b18ee1ca","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-9551","chapter","type-chapter","status-publish","hentry"],"part":6633,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/9551","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":27,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/9551\/revisions"}],"predecessor-version":[{"id":20363,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/9551\/revisions\/20363"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/parts\/6633"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/9551\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/wp\/v2\/media?parent=9551"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/pressbooks\/v2\/chapter-type?post=9551"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/wp\/v2\/contributor?post=9551"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/wp-json\/wp\/v2\/license?post=9551"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}