{"id":1062,"date":"2018-07-09T16:59:04","date_gmt":"2018-07-09T16:59:04","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/?post_type=chapter&#038;p=1062"},"modified":"2024-04-26T22:01:02","modified_gmt":"2024-04-26T22:01:02","slug":"convert-between-types-of-fractions","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/chapter\/convert-between-types-of-fractions\/","title":{"raw":"Convert Between Types of Fractions","rendered":"Convert Between Types of Fractions"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Identify different types of fractions and convert between them&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:13185,&quot;3&quot;:[null,0],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;,&quot;16&quot;:10}\">Identify different types of fractions and convert between them<\/span><\/li>\r\n<\/ul>\r\n<\/div>\r\nAndy and Bobby love pizza. On Tuesday night, Andy and Bobby share a pizza with their parents, Fred and Christy, with each person getting an equal amount of the whole pizza. How much of the pizza does each person get? There is one whole pizza, divided evenly into four equal parts. Each person has one of the four equal parts, so each has [latex]\\Large{\\frac{1}{4}}[\/latex] of the pizza.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220652\/CNX_BMath_Figure_04_01_002_img.png\" alt=\"An image of a round pizza sliced vertically and horizontally, creating four equal pieces. Each piece is labeled as one fourth.\" width=\"200\" height=\"200\" \/>\r\nOn Wednesday, the family invites some friends over for a pizza dinner. There are a total of [latex]12[\/latex] people. If they share the pizza equally, each person would get [latex]\\Large{\\frac{1}{12}}[\/latex] of the pizza.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220653\/CNX_BMath_Figure_04_01_003_img.png\" alt=\"An image of a round pizza sliced into twelve equal wedges. Each piece is labeled as one twelfth.\" width=\"200\" height=\"200\" \/>\r\n<div class=\"textbox shaded\">\r\n<h3>Fractions<\/h3>\r\nA fraction is written [latex]\\Large{\\frac{a}{b}}[\/latex], where [latex]a[\/latex] and [latex]b[\/latex] are integers and [latex]b\\ne 0[\/latex]. In a fraction, [latex]a[\/latex] is called the numerator and [latex]b[\/latex] is called the denominator.\r\n\r\n<\/div>\r\nA fraction is a way to represent parts of a whole. The denominator [latex]b[\/latex] represents the number of equal parts the whole has been divided into, and the numerator [latex]a[\/latex] represents how many parts are included. The denominator, [latex]b[\/latex], cannot equal zero because division by zero is undefined.\r\n\r\nIn the image below, the circle has been divided into three parts of equal size. Each part represents [latex]\\Large{\\frac{1}{3}}[\/latex] of the circle. This type of model is called a fraction circle. Other shapes, such as rectangles, can also be used to model fractions.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220654\/CNX_BMath_Figure_04_01_004.png\" alt=\"A circle is divided into three equal wedges. Each piece is labeled as one third.\" \/>\r\n\r\nWhat does the fraction [latex]\\Large{\\frac{2}{3}}[\/latex] represent? The fraction [latex]\\Large{\\frac{2}{3}}[\/latex] means two of three equal parts.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220656\/CNX_BMath_Figure_04_01_005_img.png\" alt=\"A circle is divided into three equal wedges. Two of the wedges are shaded.\" \/>\r\n\r\nWatch the following video to see more examples of how to write fractions given a model.\r\n\r\nhttps:\/\/youtu.be\/c_yIA4OQ4qA\r\n<h2>Mixed Numbers and Improper Fractions<\/h2>\r\nWhat would happen if you have eight equal fifth pieces. You can use five of them to make one whole, but you'll have three fifths left over. Let us use fraction notation to show what happened. You had eight pieces, each of them one fifth, [latex]{\\Large\\frac{1}{5}}[\/latex], so altogether you had eight fifths, which we can write as [latex]{\\Large\\frac{8}{5}}[\/latex]. The fraction [latex]{\\Large\\frac{8}{5}}[\/latex] is one whole, [latex]1[\/latex], plus three fifths, [latex]{\\Large\\frac{3}{5}}[\/latex], or [latex]1{\\Large\\frac{3}{5}}[\/latex], which is read as <em>one and three-fifths<\/em>.\r\n\r\nThe number [latex]1{\\Large\\frac{3}{5}}[\/latex] is called a mixed number.\r\n<div class=\"textbox shaded\">\r\n<h3>Mixed Numbers<\/h3>\r\nA mixed number consists of a whole number [latex]a[\/latex] and a fraction [latex]{\\Large\\frac{b}{c}}[\/latex] where [latex]c\\ne 0[\/latex]. It is written as follows.\r\n<p style=\"text-align: center;\">[latex]a{\\Large\\frac{b}{c}}\\text{, }c\\ne 0[\/latex]<\/p>\r\n\r\n<\/div>\r\nThe number\u00a0[latex]{\\Large\\frac{8}{5}}[\/latex] is called an improper fraction.\r\n<div class=\"textbox shaded\">\r\n<h3>Proper and Improper Fractions<\/h3>\r\nThe fraction [latex]{\\Large\\frac{a}{b}}[\/latex] is a proper fraction if [latex]a&lt;b[\/latex] and an improper fraction if [latex]a\\ge b[\/latex].\r\n\r\n<\/div>\r\nFractions such as [latex]{\\Large\\frac{5}{4}},{\\Large\\frac{3}{2}},{\\Large\\frac{5}{5}}[\/latex], and [latex]{\\Large\\frac{7}{3}}[\/latex] are called improper fractions. In an improper fraction, the numerator is greater than or equal to the denominator, so its value is greater than or equal to one. When a fraction has a numerator that is smaller than the denominator, it is called a proper fraction, and its value is less than one. Fractions such as [latex]{\\Large\\frac{1}{2}},{\\Large\\frac{3}{7}}[\/latex], and [latex]{\\Large\\frac{11}{18}}[\/latex] are proper fractions.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nDraw a figure to model [latex]{\\Large\\frac{11}{8}}[\/latex].\r\n[reveal-answer q=\"992194\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"992194\"]\r\n\r\nSolution:\r\nThe denominator of the improper fraction is [latex]8[\/latex]. Draw a circle divided into eight pieces and shade all of them. This takes care of eight eighths, but we have [latex]11[\/latex] eighths. We must shade three of the eight parts of another circle.\r\n\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220730\/CNX_BMath_Figure_04_01_026_img.png\" alt=\"Two circles are shown, both divided into eight equal pieces. The circle on the left has all eight pieces shaded and is labeled as eight eighths. The circle on the right has three pieces shaded and is labeled as three eighths. The diagram indicates that eight eighths plus three eighths is one plus three eighths.\" \/>\r\nSo, [latex]{\\Large\\frac{11}{8}}=1{\\Large\\frac{3}{8}}[\/latex].\r\n\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\nDraw a figure to model [latex]{\\Large\\frac{7}{6}}[\/latex]\r\n[reveal-answer q=\"924546\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"924546\"]\r\n\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220732\/CNX_BMath_Figure_04_01_027_img.png\" alt=\"Two circles are shown. Each is divided into six sections. All of the first circle is shaded and one section of the second circle is shaded.\" \/>\r\n\r\n[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\nDraw a figure to model [latex]{\\Large\\frac{6}{5}}[\/latex]\r\n[reveal-answer q=\"203648\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"203648\"]\r\n\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220733\/CNX_BMath_Figure_04_01_028_img.png\" alt=\"Two circles are shown. Each is divided into five sections. All of the first circle is shaded and one section of the second circle is shaded.\" \/>\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nName the improper fraction modeled. Then write the improper fraction as a mixed number.\r\n\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220725\/CNX_BMath_Figure_04_01_023_img.png\" alt=\"Two circles are shown, both divided into three equal pieces. The circle on the left has all three pieces shaded. The circle on the right has one piece shaded.\" \/>\r\n\r\n[reveal-answer q=\"670905\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"670905\"]\r\n\r\nSolution:\r\nEach circle is divided into three pieces, so each piece is [latex]{\\Large\\frac{1}{3}}[\/latex] of the circle. There are four pieces shaded, so there are four thirds or [latex]{\\Large\\frac{4}{3}}[\/latex]. The figure shows that we also have one whole circle and one third, which is [latex]1{\\Large\\frac{1}{3}}[\/latex]. So, [latex]{\\Large\\frac{4}{3}}=1{\\Large\\frac{1}{3}}[\/latex].[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]145976[\/ohm_question]\r\n\r\n[ohm_question]145977[\/ohm_question]\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nUse a model to rewrite the improper fraction [latex]{\\Large\\frac{11}{6}}[\/latex] as a mixed number.\r\n[reveal-answer q=\"121702\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"121702\"]\r\n\r\nSolution:\r\nWe start with [latex]11[\/latex] sixths [latex]\\left({\\Large\\frac{11}{6}}\\right)[\/latex]. We know that six sixths makes one whole.\r\n<p style=\"padding-left: 30px;\">[latex]{\\Large\\frac{6}{6}}=1[\/latex]<\/p>\r\nThat leaves us with five more sixths, which is [latex]{\\Large\\frac{5}{6}}[\/latex] (11 sixths minus 6 sixths is 5 sixths).\r\n<p style=\"padding-left: 30px;\">So, [latex]{\\Large\\frac{11}{6}}=1{\\Large\\frac{5}{6}}[\/latex]<\/p>\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220735\/CNX_BMath_Figure_04_01_029_img.png\" alt=\"Two circles are shown, both divided into six equal pieces. The circle on the left has all six pieces shaded and is labeled as six sixths. The circle on the right has five pieces shaded and is labeled as five sixths. Below the circles, it says one plus five sixths, then six sixths plus five sixths equals eleven sixths, and one plus five sixths equals one and five sixths. It then says that eleven sixths equals one and five sixths.\" \/>\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]145982[\/ohm_question]\r\n\r\n<\/div>\r\nIn the next video we show another way to draw a model that represents a fraction. \u00a0You will see example of both proper and improper fractions shown.\r\n\r\nhttps:\/\/youtu.be\/akyByv80Uzc\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nUse a model to rewrite the mixed number [latex]1{\\Large\\frac{4}{5}}[\/latex] as an improper fraction.\r\n[reveal-answer q=\"852331\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"852331\"]\r\n\r\nSolution:\r\nThe mixed number [latex]1{\\Large\\frac{4}{5}}[\/latex] means one whole plus four fifths. The denominator is [latex]5[\/latex], so the whole is [latex]{\\Large\\frac{5}{5}}[\/latex]. Together five fifths and four fifths equals nine fifths.\r\nSo, [latex]1{\\Large\\frac{4}{5}}={\\Large\\frac{9}{5}}[\/latex]\r\n\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220738\/CNX_BMath_Figure_04_01_030_img.png\" alt=\"Two circles are shown, both divided into five equal pieces. The circle on the left has all five pieces shaded and is labeled as 5 fifths. The circle on the right has four pieces shaded and is labeled as 4 fifths. It then says that 5 fifths plus 4 fifths equals 9 fifths and that 9 fifths is equal to one plus 4 fifths.\" \/>\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]145981[\/ohm_question]\r\n\r\n<\/div>\r\nThere is another method to turning a mixed number into an improper fraction \u2014 it's just a shortcut to what you've been practicing above.\r\n<div>\r\n<div class=\"textbox shaded\">\r\n<h3>Mixed Numbers to Improper Fractions<\/h3>\r\n<ol>\r\n \t<li>Multiply the whole number by the denominator<\/li>\r\n \t<li>Add that value to the numerator (this becomes the numerator of the improper fraction)<\/li>\r\n \t<li>Place the denominator of the mixed number in the denominator of the improper fraction<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>EXAMPLE<\/h3>\r\nConvert [latex]5\\frac{2}{3}[\/latex] into an improper fraction using the shortcut\r\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"1\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 50%;\">1. Multiply the whole number by the denomimator<\/td>\r\n<td style=\"width: 50%;\">[latex]5\\cdot{3}=15[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%;\">2. Add that value to the numerator<\/td>\r\n<td style=\"width: 50%;\">[latex]15+2=17[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%;\">new numerator for improper fraction<\/td>\r\n<td style=\"width: 50%;\">[latex]\\Large\\frac{17}{?}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%;\">3. Place the denominator of the mixed number in the denominator of the improper fraction<\/td>\r\n<td style=\"width: 50%;\">[latex]\\Large\\frac{17}{3}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>TRY IT<\/h3>\r\n[ohm_question]156957[\/ohm_question]\r\n\r\n<\/div>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Identify different types of fractions and convert between them&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:13185,&quot;3&quot;:[null,0],&quot;10&quot;:0,&quot;11&quot;:4,&quot;12&quot;:0,&quot;15&quot;:&quot;Calibri&quot;,&quot;16&quot;:10}\">Identify different types of fractions and convert between them<\/span><\/li>\n<\/ul>\n<\/div>\n<p>Andy and Bobby love pizza. On Tuesday night, Andy and Bobby share a pizza with their parents, Fred and Christy, with each person getting an equal amount of the whole pizza. How much of the pizza does each person get? There is one whole pizza, divided evenly into four equal parts. Each person has one of the four equal parts, so each has [latex]\\Large{\\frac{1}{4}}[\/latex] of the pizza.<\/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\/24220652\/CNX_BMath_Figure_04_01_002_img.png\" alt=\"An image of a round pizza sliced vertically and horizontally, creating four equal pieces. Each piece is labeled as one fourth.\" width=\"200\" height=\"200\" \/><br \/>\nOn Wednesday, the family invites some friends over for a pizza dinner. There are a total of [latex]12[\/latex] people. If they share the pizza equally, each person would get [latex]\\Large{\\frac{1}{12}}[\/latex] of the pizza.<\/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\/24220653\/CNX_BMath_Figure_04_01_003_img.png\" alt=\"An image of a round pizza sliced into twelve equal wedges. Each piece is labeled as one twelfth.\" width=\"200\" height=\"200\" \/><\/p>\n<div class=\"textbox shaded\">\n<h3>Fractions<\/h3>\n<p>A fraction is written [latex]\\Large{\\frac{a}{b}}[\/latex], where [latex]a[\/latex] and [latex]b[\/latex] are integers and [latex]b\\ne 0[\/latex]. In a fraction, [latex]a[\/latex] is called the numerator and [latex]b[\/latex] is called the denominator.<\/p>\n<\/div>\n<p>A fraction is a way to represent parts of a whole. The denominator [latex]b[\/latex] represents the number of equal parts the whole has been divided into, and the numerator [latex]a[\/latex] represents how many parts are included. The denominator, [latex]b[\/latex], cannot equal zero because division by zero is undefined.<\/p>\n<p>In the image below, the circle has been divided into three parts of equal size. Each part represents [latex]\\Large{\\frac{1}{3}}[\/latex] of the circle. This type of model is called a fraction circle. Other shapes, such as rectangles, can also be used to model fractions.<\/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\/24220654\/CNX_BMath_Figure_04_01_004.png\" alt=\"A circle is divided into three equal wedges. Each piece is labeled as one third.\" \/><\/p>\n<p>What does the fraction [latex]\\Large{\\frac{2}{3}}[\/latex] represent? The fraction [latex]\\Large{\\frac{2}{3}}[\/latex] means two of three equal parts.<\/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\/24220656\/CNX_BMath_Figure_04_01_005_img.png\" alt=\"A circle is divided into three equal wedges. Two of the wedges are shaded.\" \/><\/p>\n<p>Watch the following video to see more examples of how to write fractions given a model.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Ex:  Determine the Fraction Modeled\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/c_yIA4OQ4qA?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h2>Mixed Numbers and Improper Fractions<\/h2>\n<p>What would happen if you have eight equal fifth pieces. You can use five of them to make one whole, but you&#8217;ll have three fifths left over. Let us use fraction notation to show what happened. You had eight pieces, each of them one fifth, [latex]{\\Large\\frac{1}{5}}[\/latex], so altogether you had eight fifths, which we can write as [latex]{\\Large\\frac{8}{5}}[\/latex]. The fraction [latex]{\\Large\\frac{8}{5}}[\/latex] is one whole, [latex]1[\/latex], plus three fifths, [latex]{\\Large\\frac{3}{5}}[\/latex], or [latex]1{\\Large\\frac{3}{5}}[\/latex], which is read as <em>one and three-fifths<\/em>.<\/p>\n<p>The number [latex]1{\\Large\\frac{3}{5}}[\/latex] is called a mixed number.<\/p>\n<div class=\"textbox shaded\">\n<h3>Mixed Numbers<\/h3>\n<p>A mixed number consists of a whole number [latex]a[\/latex] and a fraction [latex]{\\Large\\frac{b}{c}}[\/latex] where [latex]c\\ne 0[\/latex]. It is written as follows.<\/p>\n<p style=\"text-align: center;\">[latex]a{\\Large\\frac{b}{c}}\\text{, }c\\ne 0[\/latex]<\/p>\n<\/div>\n<p>The number\u00a0[latex]{\\Large\\frac{8}{5}}[\/latex] is called an improper fraction.<\/p>\n<div class=\"textbox shaded\">\n<h3>Proper and Improper Fractions<\/h3>\n<p>The fraction [latex]{\\Large\\frac{a}{b}}[\/latex] is a proper fraction if [latex]a<b[\/latex] and an improper fraction if [latex]a\\ge b[\/latex].\n\n<\/div>\n<p>Fractions such as [latex]{\\Large\\frac{5}{4}},{\\Large\\frac{3}{2}},{\\Large\\frac{5}{5}}[\/latex], and [latex]{\\Large\\frac{7}{3}}[\/latex] are called improper fractions. In an improper fraction, the numerator is greater than or equal to the denominator, so its value is greater than or equal to one. When a fraction has a numerator that is smaller than the denominator, it is called a proper fraction, and its value is less than one. Fractions such as [latex]{\\Large\\frac{1}{2}},{\\Large\\frac{3}{7}}[\/latex], and [latex]{\\Large\\frac{11}{18}}[\/latex] are proper fractions.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Draw a figure to model [latex]{\\Large\\frac{11}{8}}[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q992194\">Show Answer<\/span><\/p>\n<div id=\"q992194\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<br \/>\nThe denominator of the improper fraction is [latex]8[\/latex]. Draw a circle divided into eight pieces and shade all of them. This takes care of eight eighths, but we have [latex]11[\/latex] eighths. We must shade three of the eight parts of another circle.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220730\/CNX_BMath_Figure_04_01_026_img.png\" alt=\"Two circles are shown, both divided into eight equal pieces. The circle on the left has all eight pieces shaded and is labeled as eight eighths. The circle on the right has three pieces shaded and is labeled as three eighths. The diagram indicates that eight eighths plus three eighths is one plus three eighths.\" \/><br \/>\nSo, [latex]{\\Large\\frac{11}{8}}=1{\\Large\\frac{3}{8}}[\/latex].<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Try it<\/h3>\n<p>Draw a figure to model [latex]{\\Large\\frac{7}{6}}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q924546\">Show Answer<\/span><\/p>\n<div id=\"q924546\" 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\/24220732\/CNX_BMath_Figure_04_01_027_img.png\" alt=\"Two circles are shown. Each is divided into six sections. All of the first circle is shaded and one section of the second circle is shaded.\" \/><\/p>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>Draw a figure to model [latex]{\\Large\\frac{6}{5}}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q203648\">Show Answer<\/span><\/p>\n<div id=\"q203648\" 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\/24220733\/CNX_BMath_Figure_04_01_028_img.png\" alt=\"Two circles are shown. Each is divided into five sections. All of the first circle is shaded and one section of the second circle is shaded.\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Name the improper fraction modeled. Then write the improper fraction as a mixed number.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220725\/CNX_BMath_Figure_04_01_023_img.png\" alt=\"Two circles are shown, both divided into three equal pieces. The circle on the left has all three pieces shaded. The circle on the right has one piece shaded.\" \/><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q670905\">Show Answer<\/span><\/p>\n<div id=\"q670905\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<br \/>\nEach circle is divided into three pieces, so each piece is [latex]{\\Large\\frac{1}{3}}[\/latex] of the circle. There are four pieces shaded, so there are four thirds or [latex]{\\Large\\frac{4}{3}}[\/latex]. The figure shows that we also have one whole circle and one third, which is [latex]1{\\Large\\frac{1}{3}}[\/latex]. So, [latex]{\\Large\\frac{4}{3}}=1{\\Large\\frac{1}{3}}[\/latex].<\/p><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm145976\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145976&theme=oea&iframe_resize_id=ohm145976&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm145977\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145977&theme=oea&iframe_resize_id=ohm145977&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Use a model to rewrite the improper fraction [latex]{\\Large\\frac{11}{6}}[\/latex] as a mixed number.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q121702\">Show Answer<\/span><\/p>\n<div id=\"q121702\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<br \/>\nWe start with [latex]11[\/latex] sixths [latex]\\left({\\Large\\frac{11}{6}}\\right)[\/latex]. We know that six sixths makes one whole.<\/p>\n<p style=\"padding-left: 30px;\">[latex]{\\Large\\frac{6}{6}}=1[\/latex]<\/p>\n<p>That leaves us with five more sixths, which is [latex]{\\Large\\frac{5}{6}}[\/latex] (11 sixths minus 6 sixths is 5 sixths).<\/p>\n<p style=\"padding-left: 30px;\">So, [latex]{\\Large\\frac{11}{6}}=1{\\Large\\frac{5}{6}}[\/latex]<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220735\/CNX_BMath_Figure_04_01_029_img.png\" alt=\"Two circles are shown, both divided into six equal pieces. The circle on the left has all six pieces shaded and is labeled as six sixths. The circle on the right has five pieces shaded and is labeled as five sixths. Below the circles, it says one plus five sixths, then six sixths plus five sixths equals eleven sixths, and one plus five sixths equals one and five sixths. It then says that eleven sixths equals one and five sixths.\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm145982\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145982&theme=oea&iframe_resize_id=ohm145982&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the next video we show another way to draw a model that represents a fraction. \u00a0You will see example of both proper and improper fractions shown.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Draw Models of Fractions and Explain the Meaning of the Fraction\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/akyByv80Uzc?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Use a model to rewrite the mixed number [latex]1{\\Large\\frac{4}{5}}[\/latex] as an improper fraction.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q852331\">Show Answer<\/span><\/p>\n<div id=\"q852331\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution:<br \/>\nThe mixed number [latex]1{\\Large\\frac{4}{5}}[\/latex] means one whole plus four fifths. The denominator is [latex]5[\/latex], so the whole is [latex]{\\Large\\frac{5}{5}}[\/latex]. Together five fifths and four fifths equals nine fifths.<br \/>\nSo, [latex]1{\\Large\\frac{4}{5}}={\\Large\\frac{9}{5}}[\/latex]<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220738\/CNX_BMath_Figure_04_01_030_img.png\" alt=\"Two circles are shown, both divided into five equal pieces. The circle on the left has all five pieces shaded and is labeled as 5 fifths. The circle on the right has four pieces shaded and is labeled as 4 fifths. It then says that 5 fifths plus 4 fifths equals 9 fifths and that 9 fifths is equal to one plus 4 fifths.\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm145981\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=145981&theme=oea&iframe_resize_id=ohm145981&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>There is another method to turning a mixed number into an improper fraction \u2014 it&#8217;s just a shortcut to what you&#8217;ve been practicing above.<\/p>\n<div>\n<div class=\"textbox shaded\">\n<h3>Mixed Numbers to Improper Fractions<\/h3>\n<ol>\n<li>Multiply the whole number by the denominator<\/li>\n<li>Add that value to the numerator (this becomes the numerator of the improper fraction)<\/li>\n<li>Place the denominator of the mixed number in the denominator of the improper fraction<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>EXAMPLE<\/h3>\n<p>Convert [latex]5\\frac{2}{3}[\/latex] into an improper fraction using the shortcut<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">1. Multiply the whole number by the denomimator<\/td>\n<td style=\"width: 50%;\">[latex]5\\cdot{3}=15[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">2. Add that value to the numerator<\/td>\n<td style=\"width: 50%;\">[latex]15+2=17[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">new numerator for improper fraction<\/td>\n<td style=\"width: 50%;\">[latex]\\Large\\frac{17}{?}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">3. Place the denominator of the mixed number in the denominator of the improper fraction<\/td>\n<td style=\"width: 50%;\">[latex]\\Large\\frac{17}{3}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<div>\n<div class=\"textbox key-takeaways\">\n<h3>TRY IT<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm156957\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=156957&theme=oea&iframe_resize_id=ohm156957&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\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-1062\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/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":7,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"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\"}]","CANDELA_OUTCOMES_GUID":"1f1dd0a7-dca2-43f3-9757-33d4e41a9363, 79edd5e0-59fc-40da-9aa4-25d5ddb683d1","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1062","chapter","type-chapter","status-publish","hentry"],"part":22,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/pressbooks\/v2\/chapters\/1062","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":13,"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/pressbooks\/v2\/chapters\/1062\/revisions"}],"predecessor-version":[{"id":3981,"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/pressbooks\/v2\/chapters\/1062\/revisions\/3981"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/pressbooks\/v2\/parts\/22"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/pressbooks\/v2\/chapters\/1062\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/wp\/v2\/media?parent=1062"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/pressbooks\/v2\/chapter-type?post=1062"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/wp\/v2\/contributor?post=1062"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-accountingformanagers\/wp-json\/wp\/v2\/license?post=1062"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}