{"id":3515,"date":"2019-12-29T22:38:01","date_gmt":"2019-12-29T22:38:01","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforlibscoreq\/?post_type=chapter&#038;p=3515"},"modified":"2019-12-30T01:51:57","modified_gmt":"2019-12-30T01:51:57","slug":"locating-and-ordering-fractions-and-mixed-numbers-on-the-number-line","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/chapter\/locating-and-ordering-fractions-and-mixed-numbers-on-the-number-line\/","title":{"raw":"Locating and Ordering Fractions and Mixed Numbers on the Number Line","rendered":"Locating and Ordering Fractions and Mixed Numbers on the Number Line"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Locate and label improper and proper fractions on a number line<\/li>\r\n \t<li>Order fractions and mixed numbers on a number line<\/li>\r\n \t<li>Use inequality symbols to compare fractions and mixed numbers<\/li>\r\n<\/ul>\r\n<\/div>\r\nNow we are ready to plot fractions on a number line. This will help us visualize fractions and understand their values.\r\n\r\nLet us locate [latex]{\\Large\\frac{1}{5},\\frac{4}{5}},3,3{\\Large\\frac{1}{3},\\frac{7}{4},\\frac{9}{2}},5[\/latex], and [latex]{\\Large\\frac{8}{3}}[\/latex] on the number line.\r\n\r\nWe will start with the whole numbers [latex]3[\/latex] and [latex]5[\/latex] because they are the easiest to plot.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220803\/CNX_BMath_Figure_04_01_044_img.png\" alt=\"A number line is shown with the numbers 3, 4, and 5. There are red dots at 3 and at 5.\" \/>\r\nThe proper fractions listed are [latex]{\\Large\\frac{1}{5}}[\/latex] and [latex]{\\Large\\frac{4}{5}}[\/latex]. We know proper fractions have values less than one, so [latex]{\\Large\\frac{1}{5}}[\/latex] and [latex]{\\Large\\frac{4}{5}}[\/latex] are located between the whole numbers [latex]0[\/latex] and [latex]1[\/latex]. The denominators are both [latex]5[\/latex], so we need to divide the segment of the number line between [latex]0[\/latex] and [latex]1[\/latex] into five equal parts. We can do this by drawing four equally spaced marks on the number line, which we can then label as [latex]{\\Large\\frac{1}{5},\\frac{2}{5},\\frac{3}{5}}[\/latex], and [latex]{\\Large\\frac{4}{5}}[\/latex].\r\n\r\nNow plot points at [latex]{\\Large\\frac{1}{5}}[\/latex] and [latex]{\\Large\\frac{4}{5}}[\/latex].\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220805\/CNX_BMath_Figure_04_01_045_img.png\" alt=\"A number line is shown. It shows 0, 1 fifth, 2 fifths, 3 fifths, 4 fifths, and 1. There are red dots at 1 fifth and at 4 fifths.\" \/>\r\nThe only mixed number to plot is [latex]3{\\Large\\frac{1}{3}}[\/latex]. Between what two whole numbers is [latex]3{\\Large\\frac{1}{3}}[\/latex]? Remember that a mixed number is a whole number plus a proper fraction, so [latex]3{\\Large\\frac{1}{3}}&gt;3[\/latex]. Since it is greater than [latex]3[\/latex], but not a whole unit greater, [latex]3{\\Large\\frac{1}{3}}[\/latex] is between [latex]3[\/latex] and [latex]4[\/latex]. We need to divide the portion of the number line between [latex]3[\/latex] and [latex]4[\/latex] into three equal pieces (thirds) and plot [latex]3{\\Large\\frac{1}{3}}[\/latex] at the first mark.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220806\/CNX_BMath_Figure_04_01_046_img.png\" alt=\"A number line is shown with whole number 0 through 5. Between 3 and 4, 3 and 1 third and 3 and 2 thirds are labeled. There is a red dot at 3 and 1 third.\" \/>\r\nFinally, look at the improper fractions [latex]{\\Large\\frac{7}{4},\\frac{9}{2}}[\/latex], and [latex]{\\Large\\frac{8}{3}}[\/latex]. Locating these points will be easier if you change each of them to a mixed number.\r\n<p style=\"text-align: center\">[latex]{\\Large\\frac{7}{4}}=1{\\Large\\frac{3}{4}},{\\Large\\frac{9}{2}}=4{\\Large\\frac{1}{2}},{\\Large\\frac{8}{3}}=2{\\Large\\frac{2}{3}}[\/latex]<\/p>\r\nHere is the number line with all the points plotted.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220808\/CNX_BMath_Figure_04_01_047_img.png\" alt=\"A number line is shown with whole numbers 0 through 6. Between 0 and 1, 1 fifth and 4 fifths are labeled and shown with red dots. Between 1 and 2, 7 fourths is labeled and shown with a red dot. Between 2 and 3, 8 thirds is labeled and shown with a red dot. Between 3 and 4, 3 and 1 third is labeled and shown with a red dot. Between 4 and 5, 9 halves is labeled and shown with a red dot.\" \/>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nLocate and label the following on a number line: [latex]{\\Large\\frac{3}{4},\\frac{4}{3},\\frac{5}{3}},4{\\Large\\frac{1}{5}}[\/latex], and [latex]{\\Large\\frac{7}{2}}[\/latex].\r\n\r\nSolution:\r\nStart by locating the proper fraction [latex]{\\Large\\frac{3}{4}}[\/latex]. It is between [latex]0[\/latex] and [latex]1[\/latex]. To do this, divide the distance between [latex]0[\/latex] and [latex]1[\/latex] into four equal parts. Then plot [latex]{\\Large\\frac{3}{4}}[\/latex].\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220810\/CNX_BMath_Figure_04_01_048_img.png\" alt=\"A number line is shown. It shows 0, 1 fourth, 2 fourths, 3 fourths, and 1. There is a red dot at 3 fourths.\" \/>\r\nNext, locate the mixed number [latex]4{\\Large\\frac{1}{5}}[\/latex]. It is between [latex]4[\/latex] and [latex]5[\/latex] on the number line. Divide the number line between [latex]4[\/latex] and [latex]5[\/latex] into five equal parts, and then plot [latex]4{\\Large\\frac{1}{5}}[\/latex] one-fifth of the way between [latex]4[\/latex] and [latex]5[\/latex] .\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220811\/CNX_BMath_Figure_04_01_049_img.png\" alt=\"A number line is shown. It shows 4, 4 and 1 fifth, 4 and 2 fifths, 4 and 3 fifths, 4 and 4 fifths, and 5. There is a red dot at 4 and 1 fifth.\" \/>\r\nNow locate the improper fractions [latex]{\\Large\\frac{4}{3}}[\/latex] and [latex]{\\Large\\frac{5}{3}}[\/latex]. It is easier to plot them if we convert them to mixed numbers first.\r\n\r\n[latex]{\\Large\\frac{4}{3}}=1{\\Large\\frac{1}{3}},{\\Large\\frac{5}{3}}=1{\\Large\\frac{2}{3}}[\/latex]\r\nDivide the distance between [latex]1[\/latex] and [latex]2[\/latex] into thirds.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220813\/CNX_BMath_Figure_04_01_050_img.png\" alt=\"A number line is shown. It shows 1, 1 and 1 third, 1 and 2 thirds, and 2. Below 1 it says 3 thirds. Below 1 and 1 third it says 4 thirds. Below 1 and 2 thirds it says 5 thirds. Below 2 it says 6 thirds. There are red dots at 1 and 1 third and 1 and 2 thirds.\" \/>\r\nNext let us plot [latex]{\\Large\\frac{7}{2}}[\/latex]. We write it as a mixed number, [latex]{\\Large\\frac{7}{2}}=3{\\Large\\frac{1}{2}}[\/latex] . Plot it between [latex]3[\/latex] and [latex]4[\/latex].\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220815\/CNX_BMath_Figure_04_01_051_img.png\" alt=\"A number line is shown. It shows 3, 3 and 1 half, and 4. Below 3 it says 6 halves. Below 3 and 1 half it says 7 halves. Below 4 it says 8 halves. There is a red dot at 3 and 1 half.\" \/>\r\nThe number line shows all the numbers located on the number line.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24220817\/CNX_BMath_Figure_04_01_052.png\" alt=\"A number line is shown. It shows the whole numbers 0 through 5. Between any 2 numbers are 10 tick marks. Between 0 and 1, between the 7th and 8th tick mark, 3 fourths is labeled and shown with a red dot. Between 1 and 2, 4 thirds and 5 thirds are labeled and shown with red dots. Between 3 and 4, 7 halves is labeled and shown with a red dot. Between 4 and 5, 4 and 1 fifth is labeled and shown with a red dot.\" \/>\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\"]146007[\/ohm_question]\r\n\r\n[ohm_question height=\"270\"]146008[\/ohm_question]\r\n\r\n<\/div>\r\nWatch the following video to see more examples of how to locate fractions on a number line.\r\n\r\nhttps:\/\/youtu.be\/EIdmdTRQWTE","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Locate and label improper and proper fractions on a number line<\/li>\n<li>Order fractions and mixed numbers on a number line<\/li>\n<li>Use inequality symbols to compare fractions and mixed numbers<\/li>\n<\/ul>\n<\/div>\n<p>Now we are ready to plot fractions on a number line. This will help us visualize fractions and understand their values.<\/p>\n<p>Let us locate [latex]{\\Large\\frac{1}{5},\\frac{4}{5}},3,3{\\Large\\frac{1}{3},\\frac{7}{4},\\frac{9}{2}},5[\/latex], and [latex]{\\Large\\frac{8}{3}}[\/latex] on the number line.<\/p>\n<p>We will start with the whole numbers [latex]3[\/latex] and [latex]5[\/latex] because they are the easiest to plot.<\/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\/24220803\/CNX_BMath_Figure_04_01_044_img.png\" alt=\"A number line is shown with the numbers 3, 4, and 5. There are red dots at 3 and at 5.\" \/><br \/>\nThe proper fractions listed are [latex]{\\Large\\frac{1}{5}}[\/latex] and [latex]{\\Large\\frac{4}{5}}[\/latex]. We know proper fractions have values less than one, so [latex]{\\Large\\frac{1}{5}}[\/latex] and [latex]{\\Large\\frac{4}{5}}[\/latex] are located between the whole numbers [latex]0[\/latex] and [latex]1[\/latex]. The denominators are both [latex]5[\/latex], so we need to divide the segment of the number line between [latex]0[\/latex] and [latex]1[\/latex] into five equal parts. We can do this by drawing four equally spaced marks on the number line, which we can then label as [latex]{\\Large\\frac{1}{5},\\frac{2}{5},\\frac{3}{5}}[\/latex], and [latex]{\\Large\\frac{4}{5}}[\/latex].<\/p>\n<p>Now plot points at [latex]{\\Large\\frac{1}{5}}[\/latex] and [latex]{\\Large\\frac{4}{5}}[\/latex].<\/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\/24220805\/CNX_BMath_Figure_04_01_045_img.png\" alt=\"A number line is shown. It shows 0, 1 fifth, 2 fifths, 3 fifths, 4 fifths, and 1. There are red dots at 1 fifth and at 4 fifths.\" \/><br \/>\nThe only mixed number to plot is [latex]3{\\Large\\frac{1}{3}}[\/latex]. Between what two whole numbers is [latex]3{\\Large\\frac{1}{3}}[\/latex]? Remember that a mixed number is a whole number plus a proper fraction, so [latex]3{\\Large\\frac{1}{3}}>3[\/latex]. Since it is greater than [latex]3[\/latex], but not a whole unit greater, [latex]3{\\Large\\frac{1}{3}}[\/latex] is between [latex]3[\/latex] and [latex]4[\/latex]. We need to divide the portion of the number line between [latex]3[\/latex] and [latex]4[\/latex] into three equal pieces (thirds) and plot [latex]3{\\Large\\frac{1}{3}}[\/latex] at the first mark.<\/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\/24220806\/CNX_BMath_Figure_04_01_046_img.png\" alt=\"A number line is shown with whole number 0 through 5. Between 3 and 4, 3 and 1 third and 3 and 2 thirds are labeled. There is a red dot at 3 and 1 third.\" \/><br \/>\nFinally, look at the improper fractions [latex]{\\Large\\frac{7}{4},\\frac{9}{2}}[\/latex], and [latex]{\\Large\\frac{8}{3}}[\/latex]. Locating these points will be easier if you change each of them to a mixed number.<\/p>\n<p style=\"text-align: center\">[latex]{\\Large\\frac{7}{4}}=1{\\Large\\frac{3}{4}},{\\Large\\frac{9}{2}}=4{\\Large\\frac{1}{2}},{\\Large\\frac{8}{3}}=2{\\Large\\frac{2}{3}}[\/latex]<\/p>\n<p>Here is the number line with all the points plotted.<\/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\/24220808\/CNX_BMath_Figure_04_01_047_img.png\" alt=\"A number line is shown with whole numbers 0 through 6. Between 0 and 1, 1 fifth and 4 fifths are labeled and shown with red dots. Between 1 and 2, 7 fourths is labeled and shown with a red dot. Between 2 and 3, 8 thirds is labeled and shown with a red dot. Between 3 and 4, 3 and 1 third is labeled and shown with a red dot. Between 4 and 5, 9 halves is labeled and shown with a red dot.\" \/><\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Locate and label the following on a number line: [latex]{\\Large\\frac{3}{4},\\frac{4}{3},\\frac{5}{3}},4{\\Large\\frac{1}{5}}[\/latex], and [latex]{\\Large\\frac{7}{2}}[\/latex].<\/p>\n<p>Solution:<br \/>\nStart by locating the proper fraction [latex]{\\Large\\frac{3}{4}}[\/latex]. It is between [latex]0[\/latex] and [latex]1[\/latex]. To do this, divide the distance between [latex]0[\/latex] and [latex]1[\/latex] into four equal parts. Then plot [latex]{\\Large\\frac{3}{4}}[\/latex].<\/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\/24220810\/CNX_BMath_Figure_04_01_048_img.png\" alt=\"A number line is shown. It shows 0, 1 fourth, 2 fourths, 3 fourths, and 1. There is a red dot at 3 fourths.\" \/><br \/>\nNext, locate the mixed number [latex]4{\\Large\\frac{1}{5}}[\/latex]. It is between [latex]4[\/latex] and [latex]5[\/latex] on the number line. Divide the number line between [latex]4[\/latex] and [latex]5[\/latex] into five equal parts, and then plot [latex]4{\\Large\\frac{1}{5}}[\/latex] one-fifth of the way between [latex]4[\/latex] and [latex]5[\/latex] .<\/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\/24220811\/CNX_BMath_Figure_04_01_049_img.png\" alt=\"A number line is shown. It shows 4, 4 and 1 fifth, 4 and 2 fifths, 4 and 3 fifths, 4 and 4 fifths, and 5. There is a red dot at 4 and 1 fifth.\" \/><br \/>\nNow locate the improper fractions [latex]{\\Large\\frac{4}{3}}[\/latex] and [latex]{\\Large\\frac{5}{3}}[\/latex]. It is easier to plot them if we convert them to mixed numbers first.<\/p>\n<p>[latex]{\\Large\\frac{4}{3}}=1{\\Large\\frac{1}{3}},{\\Large\\frac{5}{3}}=1{\\Large\\frac{2}{3}}[\/latex]<br \/>\nDivide the distance between [latex]1[\/latex] and [latex]2[\/latex] into thirds.<\/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\/24220813\/CNX_BMath_Figure_04_01_050_img.png\" alt=\"A number line is shown. It shows 1, 1 and 1 third, 1 and 2 thirds, and 2. Below 1 it says 3 thirds. Below 1 and 1 third it says 4 thirds. Below 1 and 2 thirds it says 5 thirds. Below 2 it says 6 thirds. There are red dots at 1 and 1 third and 1 and 2 thirds.\" \/><br \/>\nNext let us plot [latex]{\\Large\\frac{7}{2}}[\/latex]. We write it as a mixed number, [latex]{\\Large\\frac{7}{2}}=3{\\Large\\frac{1}{2}}[\/latex] . Plot it between [latex]3[\/latex] and [latex]4[\/latex].<\/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\/24220815\/CNX_BMath_Figure_04_01_051_img.png\" alt=\"A number line is shown. It shows 3, 3 and 1 half, and 4. Below 3 it says 6 halves. Below 3 and 1 half it says 7 halves. Below 4 it says 8 halves. There is a red dot at 3 and 1 half.\" \/><br \/>\nThe number line shows all the numbers located on the number line.<\/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\/24220817\/CNX_BMath_Figure_04_01_052.png\" alt=\"A number line is shown. It shows the whole numbers 0 through 5. Between any 2 numbers are 10 tick marks. Between 0 and 1, between the 7th and 8th tick mark, 3 fourths is labeled and shown with a red dot. Between 1 and 2, 4 thirds and 5 thirds are labeled and shown with red dots. Between 3 and 4, 7 halves is labeled and shown with a red dot. Between 4 and 5, 4 and 1 fifth is labeled and shown with a red dot.\" \/><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146007\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146007&theme=oea&iframe_resize_id=ohm146007&show_question_numbers\" width=\"100%\" height=\"270\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146008\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146008&theme=oea&iframe_resize_id=ohm146008&show_question_numbers\" width=\"100%\" height=\"270\"><\/iframe><\/p>\n<\/div>\n<p>Watch the following video to see more examples of how to locate fractions on a number line.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Ex:  Identify a Fraction on a Number Line\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/EIdmdTRQWTE?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-3515\">\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: 146007, 146008. <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: Identify a Fraction on a Number Line. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/EIdmdTRQWTE\">https:\/\/youtu.be\/EIdmdTRQWTE<\/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>Compare Integers, Fractions, and Mixed Numbers (Number Line and Common Denom). <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/Phsf_fJgerc\">https:\/\/youtu.be\/Phsf_fJgerc<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>Prealgebra. <strong>Provided by<\/strong>: OpenStax. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":25777,"menu_order":4,"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: Identify a Fraction on a Number Line\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/EIdmdTRQWTE\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Question ID: 146007, 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