{"id":3517,"date":"2019-12-29T22:38:36","date_gmt":"2019-12-29T22:38:36","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforlibscoreq\/?post_type=chapter&#038;p=3517"},"modified":"2020-04-27T19:53:42","modified_gmt":"2020-04-27T19:53:42","slug":"converting-between-improper-fractions-and-mixed-numbers","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/chapter\/converting-between-improper-fractions-and-mixed-numbers\/","title":{"raw":"Converting Between Improper Fractions and Mixed Numbers","rendered":"Converting Between Improper Fractions and Mixed Numbers"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Convert mixed numbers to improper fractions<\/li>\r\n \t<li>Convert improper fractions to mixed numbers<\/li>\r\n<\/ul>\r\n<\/div>\r\nIn an example in the previous module's review section, we converted the improper fraction [latex]{\\Large\\frac{11}{6}}[\/latex] to the mixed number [latex]1{\\Large\\frac{5}{6}}[\/latex] using fraction circles. We did this by grouping six sixths together to make a whole; then we looked to see how many of the [latex]11[\/latex] pieces were left. We saw that [latex]{\\Large\\frac{11}{6}}[\/latex] made one whole group of six sixths plus five more sixths, showing that [latex]{\\Large\\frac{11}{6}}=1{\\Large\\frac{5}{6}}[\/latex].\r\n\r\nThe division expression [latex]{\\Large\\frac{11}{6}}[\/latex] (which can also be written as [latex]6\\overline{)11}[\/latex] ) tells us to find how many groups of [latex]6[\/latex] are in [latex]11[\/latex]. To convert an improper fraction to a mixed number without fraction circles, we divide.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nConvert [latex]{\\Large\\frac{11}{6}}[\/latex] to a mixed number.\r\n\r\nSolution:\r\n<table id=\"eip-id1168469636042\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\"A division symbol is shown with an 11 on the inside. A 6 is on the outside and is labeled as the divisor. A 6 is below the 11. Below the 6 is a 5 that is labeled as the remainder. Above the division sign, a 1 is labeled as the quotient.\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]{\\Large\\frac{11}{6}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide the denominator into the numerator.<\/td>\r\n<td>Remember [latex]{\\Large\\frac{11}{6}}[\/latex] means [latex]11\\div 6[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220740\/CNX_BMath_Figure_04_01_031_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Identify the quotient, remainder and divisor.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write the mixed number as [latex]\\text{quotient }({\\Large\\frac{\\text{remainder}}{\\text{divisor}}})[\/latex] .<\/td>\r\n<td>[latex]1{\\Large\\frac{5}{6}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>So, [latex]{\\Large\\frac{11}{6}}=1{\\Large\\frac{5}{6}}[\/latex]<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try it<\/h3>\r\n&nbsp;\r\n\r\n[ohm_question]145979[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox shaded\">\r\n<h3>Convert an improper fraction to a mixed number.<\/h3>\r\n<ol id=\"eip-241\" class=\"stepwise\">\r\n \t<li>Divide the denominator into the numerator.<\/li>\r\n \t<li>Identify the quotient, remainder, and divisor.<\/li>\r\n \t<li>Write the mixed number as quotient [latex]{\\Large\\frac{\\text{remainder}}{\\text{divisor}}}[\/latex] .<\/li>\r\n<\/ol>\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nConvert the improper fraction [latex]{\\Large\\frac{33}{8}}[\/latex] to a mixed number.\r\n[reveal-answer q=\"584602\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"584602\"]\r\n\r\nSolution:\r\n<table id=\"eip-id1168469862094\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\"A division symbol is shown with a 33 on the inside. An 8 is on the outside and is labeled as the divisor. A 32 is below the 33. Below the 32 is a 1 that is labeled as the remainder. Above the division sign, a 4 is labeled as the quotient.\">\r\n<tbody>\r\n<tr>\r\n<td>[latex]{\\Large\\frac{33}{8}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide the denominator into the numerator.<\/td>\r\n<td>Remember, [latex]{\\Large\\frac{33}{8}}[\/latex] means [latex]8\\overline{)33}[\/latex] .<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Identify the quotient, remainder, and divisor.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220741\/CNX_BMath_Figure_04_01_032_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write the mixed number as quotient [latex]{\\Large\\frac{\\text{remainder}}{\\text{divisor}}}[\/latex] .<\/td>\r\n<td>[latex]4{\\Large\\frac{1}{8}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>So, [latex]{\\Large\\frac{33}{8}}=4{\\Large\\frac{1}{8}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\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 height=\"270\"]145979[\/ohm_question]\r\n\r\n<\/div>\r\nNow you can watch worked examples of how to convert an improper fraction to a mixed number in the following video.\r\n\r\nhttps:\/\/youtu.be\/e6uoYVg5Q30\r\n\r\nIn an earlier example, we changed [latex]1{\\Large\\frac{4}{5}}[\/latex] to an improper fraction by first seeing that the whole is a set of five fifths. So we had five fifths and four more fifths.\r\n<p style=\"text-align: center\">[latex]{\\Large\\frac{5}{5}}+{\\Large\\frac{4}{5}}={\\Large\\frac{9}{5}}[\/latex]<\/p>\r\nWhere did the nine come from? There are nine fifths\u2014one whole (five fifths) plus four fifths. Let us use this idea to see how to convert a mixed number to an improper fraction.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nConvert the mixed number [latex]4{\\Large\\frac{2}{3}}[\/latex] to an improper fraction.\r\n[reveal-answer q=\"486918\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"486918\"]\r\n\r\nSolution:\r\n<table id=\"eip-id1168466233262\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\"The mixed number 4 and 2 thirds is shown. The first step says, \">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]4{\\Large\\frac{2}{3}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply the whole number by the denominator.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The whole number is 4 and the denominator is 3.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220743\/CNX_BMath_Figure_04_01_068_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220744\/CNX_BMath_Figure_04_01_068_img-02.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add the numerator to the product.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The numerator of the mixed number is 2.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220745\/CNX_BMath_Figure_04_01_068_img-03.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220745\/CNX_BMath_Figure_04_01_068_img-04.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write the final sum over the original denominator.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The denominator is 3.<\/td>\r\n<td>[latex]{\\Large\\frac{14}{3}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\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 height=\"270\"]145980[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox shaded\">\r\n<h3>Convert a mixed number to an improper fraction.<\/h3>\r\n<ol id=\"eip-id1168467427407\" class=\"stepwise\">\r\n \t<li>Multiply the whole number by the denominator.<\/li>\r\n \t<li>Add the numerator to the product found in Step 1.<\/li>\r\n \t<li>Write the final sum over the original denominator.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nConvert the mixed number [latex]10{\\Large\\frac{2}{7}}[\/latex] to an improper fraction.\r\n[reveal-answer q=\"474296\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"474296\"]\r\n\r\nSolution:\r\n<table id=\"eip-id1168466244930\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\"The mixed number 10 and 2 sevenths is shown. The first step says, \">\r\n<tbody>\r\n<tr>\r\n<td>[latex]10{\\Large\\frac{2}{7}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply the whole number by the denominator.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The whole number is 10 and the denominator is 7.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220746\/CNX_BMath_Figure_04_01_069_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220747\/CNX_BMath_Figure_04_01_069_img-02.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add the numerator to the product.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The numerator of the mixed number is 2.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220748\/CNX_BMath_Figure_04_01_069_img-03.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220749\/CNX_BMath_Figure_04_01_069_img-04.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write the final sum over the original denominator.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>The denominator is 7.<\/td>\r\n<td>[latex]{\\Large\\frac{72}{7}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\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 height=\"270\"]145980[\/ohm_question]\r\n\r\n<\/div>\r\nIn the following video we show more example of how to convert a mixed number to an improper fraction.\r\n\r\nhttps:\/\/youtu.be\/p_YRBcZ4u4g","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Convert mixed numbers to improper fractions<\/li>\n<li>Convert improper fractions to mixed numbers<\/li>\n<\/ul>\n<\/div>\n<p>In an example in the previous module&#8217;s review section, we converted the improper fraction [latex]{\\Large\\frac{11}{6}}[\/latex] to the mixed number [latex]1{\\Large\\frac{5}{6}}[\/latex] using fraction circles. We did this by grouping six sixths together to make a whole; then we looked to see how many of the [latex]11[\/latex] pieces were left. We saw that [latex]{\\Large\\frac{11}{6}}[\/latex] made one whole group of six sixths plus five more sixths, showing that [latex]{\\Large\\frac{11}{6}}=1{\\Large\\frac{5}{6}}[\/latex].<\/p>\n<p>The division expression [latex]{\\Large\\frac{11}{6}}[\/latex] (which can also be written as [latex]6\\overline{)11}[\/latex] ) tells us to find how many groups of [latex]6[\/latex] are in [latex]11[\/latex]. To convert an improper fraction to a mixed number without fraction circles, we divide.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Convert [latex]{\\Large\\frac{11}{6}}[\/latex] to a mixed number.<\/p>\n<p>Solution:<\/p>\n<table id=\"eip-id1168469636042\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\"A division symbol is shown with an 11 on the inside. A 6 is on the outside and is labeled as the divisor. A 6 is below the 11. Below the 6 is a 5 that is labeled as the remainder. Above the division sign, a 1 is labeled as the quotient.\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]{\\Large\\frac{11}{6}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Divide the denominator into the numerator.<\/td>\n<td>Remember [latex]{\\Large\\frac{11}{6}}[\/latex] means [latex]11\\div 6[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220740\/CNX_BMath_Figure_04_01_031_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Identify the quotient, remainder and divisor.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Write the mixed number as [latex]\\text{quotient }({\\Large\\frac{\\text{remainder}}{\\text{divisor}}})[\/latex] .<\/td>\n<td>[latex]1{\\Large\\frac{5}{6}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>So, [latex]{\\Large\\frac{11}{6}}=1{\\Large\\frac{5}{6}}[\/latex]<\/td>\n<td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Try it<\/h3>\n<p>&nbsp;<\/p>\n<p><iframe loading=\"lazy\" id=\"ohm145979\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145979&theme=oea&iframe_resize_id=ohm145979&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox shaded\">\n<h3>Convert an improper fraction to a mixed number.<\/h3>\n<ol id=\"eip-241\" class=\"stepwise\">\n<li>Divide the denominator into the numerator.<\/li>\n<li>Identify the quotient, remainder, and divisor.<\/li>\n<li>Write the mixed number as quotient [latex]{\\Large\\frac{\\text{remainder}}{\\text{divisor}}}[\/latex] .<\/li>\n<\/ol>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Convert the improper fraction [latex]{\\Large\\frac{33}{8}}[\/latex] to a mixed number.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q584602\">Show Solution<\/span><\/p>\n<div id=\"q584602\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168469862094\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\"A division symbol is shown with a 33 on the inside. An 8 is on the outside and is labeled as the divisor. A 32 is below the 33. Below the 32 is a 1 that is labeled as the remainder. Above the division sign, a 4 is labeled as the quotient.\">\n<tbody>\n<tr>\n<td>[latex]{\\Large\\frac{33}{8}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Divide the denominator into the numerator.<\/td>\n<td>Remember, [latex]{\\Large\\frac{33}{8}}[\/latex] means [latex]8\\overline{)33}[\/latex] .<\/td>\n<\/tr>\n<tr>\n<td>Identify the quotient, remainder, and divisor.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220741\/CNX_BMath_Figure_04_01_032_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Write the mixed number as quotient [latex]{\\Large\\frac{\\text{remainder}}{\\text{divisor}}}[\/latex] .<\/td>\n<td>[latex]4{\\Large\\frac{1}{8}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>So, [latex]{\\Large\\frac{33}{8}}=4{\\Large\\frac{1}{8}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm145979\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145979&theme=oea&iframe_resize_id=ohm145979&show_question_numbers\" width=\"100%\" height=\"270\"><\/iframe><\/p>\n<\/div>\n<p>Now you can watch worked examples of how to convert an improper fraction to a mixed number in the following video.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Examples: Convert an Improper Fraction to a Mixed Number\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/e6uoYVg5Q30?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>In an earlier example, we changed [latex]1{\\Large\\frac{4}{5}}[\/latex] to an improper fraction by first seeing that the whole is a set of five fifths. So we had five fifths and four more fifths.<\/p>\n<p style=\"text-align: center\">[latex]{\\Large\\frac{5}{5}}+{\\Large\\frac{4}{5}}={\\Large\\frac{9}{5}}[\/latex]<\/p>\n<p>Where did the nine come from? There are nine fifths\u2014one whole (five fifths) plus four fifths. Let us use this idea to see how to convert a mixed number to an improper fraction.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Convert the mixed number [latex]4{\\Large\\frac{2}{3}}[\/latex] to an improper fraction.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q486918\">Show Solution<\/span><\/p>\n<div id=\"q486918\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168466233262\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\"The mixed number 4 and 2 thirds is shown. The first step says,\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]4{\\Large\\frac{2}{3}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply the whole number by the denominator.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>The whole number is 4 and the denominator is 3.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220743\/CNX_BMath_Figure_04_01_068_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220744\/CNX_BMath_Figure_04_01_068_img-02.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Add the numerator to the product.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>The numerator of the mixed number is 2.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220745\/CNX_BMath_Figure_04_01_068_img-03.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220745\/CNX_BMath_Figure_04_01_068_img-04.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Write the final sum over the original denominator.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>The denominator is 3.<\/td>\n<td>[latex]{\\Large\\frac{14}{3}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm145980\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145980&theme=oea&iframe_resize_id=ohm145980&show_question_numbers\" width=\"100%\" height=\"270\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox shaded\">\n<h3>Convert a mixed number to an improper fraction.<\/h3>\n<ol id=\"eip-id1168467427407\" class=\"stepwise\">\n<li>Multiply the whole number by the denominator.<\/li>\n<li>Add the numerator to the product found in Step 1.<\/li>\n<li>Write the final sum over the original denominator.<\/li>\n<\/ol>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Convert the mixed number [latex]10{\\Large\\frac{2}{7}}[\/latex] to an improper fraction.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q474296\">Show Solution<\/span><\/p>\n<div id=\"q474296\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<\/p>\n<table id=\"eip-id1168466244930\" class=\"unnumbered unstyled\" style=\"width: 85%\" summary=\"The mixed number 10 and 2 sevenths is shown. The first step says,\">\n<tbody>\n<tr>\n<td>[latex]10{\\Large\\frac{2}{7}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply the whole number by the denominator.<\/td>\n<\/tr>\n<tr>\n<td>The whole number is 10 and the denominator is 7.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220746\/CNX_BMath_Figure_04_01_069_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220747\/CNX_BMath_Figure_04_01_069_img-02.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Add the numerator to the product.<\/td>\n<\/tr>\n<tr>\n<td>The numerator of the mixed number is 2.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220748\/CNX_BMath_Figure_04_01_069_img-03.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220749\/CNX_BMath_Figure_04_01_069_img-04.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Write the final sum over the original denominator.<\/td>\n<\/tr>\n<tr>\n<td>The denominator is 7.<\/td>\n<td>[latex]{\\Large\\frac{72}{7}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm145980\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145980&theme=oea&iframe_resize_id=ohm145980&show_question_numbers\" width=\"100%\" height=\"270\"><\/iframe><\/p>\n<\/div>\n<p>In the following video we show more example of how to convert a mixed number to an improper fraction.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Examples:  Converting a Mixed Number to an Improper Fraction\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/p_YRBcZ4u4g?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-3517\">\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>Revision and Adaptation. <strong>Provided by<\/strong>: Lumen Learning. <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, Shared previously<\/div><ul class=\"citation-list\"><li>Examples: Convert an Improper Fraction to a Mixed Number. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/www.youtube.com\/watch?v=e6uoYVg5Q30&#038;feature=youtu.be\">https:\/\/www.youtube.com\/watch?v=e6uoYVg5Q30&#038;feature=youtu.be<\/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>Examples: Converting a Mixed Number to an Improper Fraction. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/p_YRBcZ4u4g\">https:\/\/youtu.be\/p_YRBcZ4u4g<\/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>Authored 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":3,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"OpenStax\",\"organization\":\"\",\"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\":\"Examples: Convert an Improper Fraction to a Mixed Number\",\"author\":\"James Sousa 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