{"id":16092,"date":"2019-10-01T17:20:25","date_gmt":"2019-10-01T17:20:25","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/chapter\/rules-for-adding-real-numbers\/"},"modified":"2020-09-11T00:34:12","modified_gmt":"2020-09-11T00:34:12","slug":"rules-for-adding-real-numbers","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/chapter\/rules-for-adding-real-numbers\/","title":{"raw":"5.1.b - Adding and Subtracting Real Numbers","rendered":"5.1.b &#8211; Adding and Subtracting Real Numbers"},"content":{"raw":"<div class=\"bcc-box bcc-highlight\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Add and subtract real numbers\r\n<ul>\r\n \t<li>Add\u00a0real numbers with the same and different signs<\/li>\r\n \t<li>Subtract real numbers with the same and different signs<\/li>\r\n \t<li>Simplify combinations that require both addition and subtraction of real numbers.<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<\/div>\r\nSome important terminology to remember before we begin is as follows:\r\n<ul>\r\n \t<li><strong>integers:\u00a0<\/strong>counting numbers like \u00a0[latex]1, 2, 3[\/latex], etc., including negatives and zero<\/li>\r\n \t<li><strong>real number:\u00a0<\/strong>fractions, negative numbers, decimals, integers, and zero are all real numbers<\/li>\r\n \t<li><strong>absolute value:<\/strong> a number's distance from zero; it's always positive. [latex]|-7| = 7[\/latex]<\/li>\r\n \t<li><strong>sign:\u00a0<\/strong>this refers to whether a number is positive or negative, we use [latex]+[\/latex] for positive (to the right of zero on the number line) and [latex]-[\/latex] for negative (to the left of zero on the number line)<\/li>\r\n \t<li><strong>difference:\u00a0<\/strong>the result of subtraction<\/li>\r\n \t<li><strong>sum:\u00a0<\/strong>the result of addition<\/li>\r\n<\/ul>\r\nThe ability to work comfortably with negative numbers is essential to success in algebra. For this reason we will do a quick review of adding, subtracting, multiplying and dividing integers. Integers are all the positive whole numbers, zero, and their opposites (negatives). As this is intended to be a review of integers, the descriptions and examples will not be as detailed as a normal lesson.\r\n\r\nWhen adding integers we have two cases to consider. The first case is whether\u00a0the signs match (both positive or both negative). If the signs match, we will add the numbers together and keep the sign.\r\n\r\nIf the signs don\u2019t match (one positive and one negative number) we will subtract the numbers (as if they were all positive) and then use the sign from the larger number. This means if the larger number is positive, the answer is positive. If the larger number is negative, the answer is negative.\r\n<div class=\"textbox shaded\">\r\n<h3>To add two numbers with the same sign (both positive or both negative)<\/h3>\r\n<ul>\r\n \t<li><i>Add<\/i> their absolute values (without the [latex]+[\/latex] or [latex]-[\/latex] sign)<\/li>\r\n \t<li>Give the sum the same sign.<\/li>\r\n<\/ul>\r\n<h3>To add two numbers with different signs (one positive and one negative)<\/h3>\r\n<ul>\r\n \t<li>Find the<i> difference <\/i>of<i> <\/i>their absolute values. (Note that when you find the difference of the absolute values, you always subtract the lesser absolute value from the greater one.)<\/li>\r\n \t<li>Give the sum the same sign as the number with the greater absolute value.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nFind\u00a0[latex]23\u201373[\/latex].\r\n\r\n[reveal-answer q=\"951238\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"951238\"]You can't use your usual method of subtraction because [latex]73[\/latex] is greater than [latex]23[\/latex].\u00a0Rewrite the subtraction as adding the opposite.\r\n<p style=\"text-align: center\">[latex]23+\\left(\u221273\\right)[\/latex]<\/p>\r\nThe addends have different signs, so find the difference of their absolute values.\r\n<p style=\"text-align: center\">[latex]\\begin{array}{c}\\left|23\\right|=23\\,\\,\\,\\text{and}\\,\\,\\,\\left|\u221273\\right|=73\\\\73-23=50\\end{array}[\/latex]<\/p>\r\nSince [latex]\\left|\u221273\\right|&gt;\\left|23\\right|[\/latex], the final answer is negative.\r\n<h4>Answer<\/h4>\r\n[latex]23\u201373=\u221250[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n\r\nAnother way to think about subtracting is to think about the distance between the two numbers on the number line. In the example below, [latex]382[\/latex] is to the <i>right<\/i> of 0 by [latex]382[\/latex] units, and [latex]\u221293[\/latex] is to the <i>left<\/i> of 0 by 93 units. The distance between them is the sum of their distances to 0: [latex]382+93[\/latex].\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1468\/2016\/03\/17170754\/image050.gif\" alt=\"A number line from negative 93 to 382. Negative 93 is 93 units from 0 and 382 is 382 units from 0. The total distance from negative 93 to 382 can be found by adding them together. 382+93=475 units.\" width=\"575\" height=\"147\" \/>\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nFind\u00a0[latex]382\u2013\\left(\u221293\\right)[\/latex].\r\n\r\n[reveal-answer q=\"342295\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"342295\"]You are subtracting a negative, so think of this as taking the negative sign away. This becomes an addition problem. [latex]-93[\/latex] becomes [latex]+93[\/latex]\r\n<p style=\"text-align: center\">[latex]382+93=475[\/latex]<\/p>\r\n\r\n<h4>Answer<\/h4>\r\n[latex]382\u2013(\u221293)=475[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nThe following video explains how to subtract two signed integers.\r\nhttps:\/\/youtu.be\/ciuIKFCtWWU\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try it<\/h3>\r\n[ohm_question]8033[\/ohm_question]\r\n\r\n<\/div>\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nFind [latex]-\\frac{3}{7}-\\frac{6}{7}+\\frac{2}{7}[\/latex]\r\n\r\n[reveal-answer q=\"11416\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"11416\"]Add the first two and give the result a negative sign:\r\n\r\nSince the signs of the first two are the same, find the sum of the absolute values of the fractions\r\n\r\nSince both numbers are negative, the sum is negative. If you owe money, then borrow more, the amount you owe becomes larger.\r\n<p style=\"text-align: center\">[latex]\\left| -\\frac{3}{7} \\right|=\\frac{3}{7}[\/latex] and [latex]\\left| -\\frac{6}{7} \\right|=\\frac{6}{7}[\/latex]<\/p>\r\n<p style=\"text-align: center\">[latex]\\begin{array}{c}\\frac{3}{7}+\\frac{6}{7}=\\frac{9}{7}\\\\\\\\-\\frac{3}{7}-\\frac{6}{7} =-\\frac{9}{7}\\end{array}[\/latex]<\/p>\r\nNow add the third number. The signs are different, so find the <em>difference<\/em> of their absolute values.\r\n<p style=\"text-align: center\">[latex] \\left| -\\frac{9}{7} \\right|=\\frac{9}{7}[\/latex] and [latex] \\left| \\frac{2}{7} \\right|=\\frac{2}{7}[\/latex]<\/p>\r\n<p style=\"text-align: center\">[latex] \\frac{9}{7}-\\frac{2}{7}=\\frac{7}{7}[\/latex]<\/p>\r\nSince [latex]\\left|\\frac{-9}{7}\\right|&gt;\\left|\\frac{2}{7}\\right|[\/latex], the sign of the final sum is the same as the sign of [latex]-\\frac{9}{7}[\/latex].<i>\r\n<\/i>\r\n<p style=\"text-align: center\">[latex] -\\frac{9}{7}+\\frac{2}{7}=-\\frac{7}{7}=-1[\/latex]<\/p>\r\n\r\n<h4>Answer<\/h4>\r\n[latex]-\\frac{3}{7}+\\left(-\\frac{6}{7}\\right)+\\frac{2}{7}=-\\frac{7}{7}=-1[\/latex]\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]593[\/ohm_question]\r\n\r\n<\/div>\r\nIn the following video you will see an example of how to add three fractions with a common denominator that have different signs.\r\n\r\nhttps:\/\/youtu.be\/P972VVbR98k\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nEvaluate [latex]27.832+(\u22123.06)[\/latex]. When you add decimals, remember to line up the decimal points so you are adding tenths to tenths, hundredths to hundredths, and so on.\r\n\r\n[reveal-answer q=\"545871\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"545871\"]Since the addends have different signs, subtract their absolute values.\r\n<p style=\"text-align: center\">[latex] \\begin{array}{r}\\underline{\\begin{array}{r}27.832\\\\-\\text{ }3.06\\,\\,\\,\\end{array}}\\\\24.772\\end{array}[\/latex]<\/p>\r\n<p style=\"text-align: center\">[latex]\\left|-3.06\\right|=3.06[\/latex]<\/p>\r\nThe sum has the same sign as [latex]27.832[\/latex] whose absolute value is greater.\r\n<h4>Answer<\/h4>\r\n[latex]27.832+\\left(-3.06\\right)=24.772[\/latex]\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]783[\/ohm_question]\r\n\r\n<\/div>\r\nIn the following video are\u00a0examples of adding and subtracting decimals with different signs.\r\n\r\nhttps:\/\/youtu.be\/3FHZQ5iKcpI","rendered":"<div class=\"bcc-box bcc-highlight\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Add and subtract real numbers\n<ul>\n<li>Add\u00a0real numbers with the same and different signs<\/li>\n<li>Subtract real numbers with the same and different signs<\/li>\n<li>Simplify combinations that require both addition and subtraction of real numbers.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/div>\n<p>Some important terminology to remember before we begin is as follows:<\/p>\n<ul>\n<li><strong>integers:\u00a0<\/strong>counting numbers like \u00a0[latex]1, 2, 3[\/latex], etc., including negatives and zero<\/li>\n<li><strong>real number:\u00a0<\/strong>fractions, negative numbers, decimals, integers, and zero are all real numbers<\/li>\n<li><strong>absolute value:<\/strong> a number&#8217;s distance from zero; it&#8217;s always positive. [latex]|-7| = 7[\/latex]<\/li>\n<li><strong>sign:\u00a0<\/strong>this refers to whether a number is positive or negative, we use [latex]+[\/latex] for positive (to the right of zero on the number line) and [latex]-[\/latex] for negative (to the left of zero on the number line)<\/li>\n<li><strong>difference:\u00a0<\/strong>the result of subtraction<\/li>\n<li><strong>sum:\u00a0<\/strong>the result of addition<\/li>\n<\/ul>\n<p>The ability to work comfortably with negative numbers is essential to success in algebra. For this reason we will do a quick review of adding, subtracting, multiplying and dividing integers. Integers are all the positive whole numbers, zero, and their opposites (negatives). As this is intended to be a review of integers, the descriptions and examples will not be as detailed as a normal lesson.<\/p>\n<p>When adding integers we have two cases to consider. The first case is whether\u00a0the signs match (both positive or both negative). If the signs match, we will add the numbers together and keep the sign.<\/p>\n<p>If the signs don\u2019t match (one positive and one negative number) we will subtract the numbers (as if they were all positive) and then use the sign from the larger number. This means if the larger number is positive, the answer is positive. If the larger number is negative, the answer is negative.<\/p>\n<div class=\"textbox shaded\">\n<h3>To add two numbers with the same sign (both positive or both negative)<\/h3>\n<ul>\n<li><i>Add<\/i> their absolute values (without the [latex]+[\/latex] or [latex]-[\/latex] sign)<\/li>\n<li>Give the sum the same sign.<\/li>\n<\/ul>\n<h3>To add two numbers with different signs (one positive and one negative)<\/h3>\n<ul>\n<li>Find the<i> difference <\/i>of<i> <\/i>their absolute values. (Note that when you find the difference of the absolute values, you always subtract the lesser absolute value from the greater one.)<\/li>\n<li>Give the sum the same sign as the number with the greater absolute value.<\/li>\n<\/ul>\n<\/div>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>Find\u00a0[latex]23\u201373[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q951238\">Show Solution<\/span><\/p>\n<div id=\"q951238\" class=\"hidden-answer\" style=\"display: none\">You can&#8217;t use your usual method of subtraction because [latex]73[\/latex] is greater than [latex]23[\/latex].\u00a0Rewrite the subtraction as adding the opposite.<\/p>\n<p style=\"text-align: center\">[latex]23+\\left(\u221273\\right)[\/latex]<\/p>\n<p>The addends have different signs, so find the difference of their absolute values.<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{c}\\left|23\\right|=23\\,\\,\\,\\text{and}\\,\\,\\,\\left|\u221273\\right|=73\\\\73-23=50\\end{array}[\/latex]<\/p>\n<p>Since [latex]\\left|\u221273\\right|>\\left|23\\right|[\/latex], the final answer is negative.<\/p>\n<h4>Answer<\/h4>\n<p>[latex]23\u201373=\u221250[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>Another way to think about subtracting is to think about the distance between the two numbers on the number line. In the example below, [latex]382[\/latex] is to the <i>right<\/i> of 0 by [latex]382[\/latex] units, and [latex]\u221293[\/latex] is to the <i>left<\/i> of 0 by 93 units. The distance between them is the sum of their distances to 0: [latex]382+93[\/latex].<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1468\/2016\/03\/17170754\/image050.gif\" alt=\"A number line from negative 93 to 382. Negative 93 is 93 units from 0 and 382 is 382 units from 0. The total distance from negative 93 to 382 can be found by adding them together. 382+93=475 units.\" width=\"575\" height=\"147\" \/><\/p>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>Find\u00a0[latex]382\u2013\\left(\u221293\\right)[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q342295\">Show Solution<\/span><\/p>\n<div id=\"q342295\" class=\"hidden-answer\" style=\"display: none\">You are subtracting a negative, so think of this as taking the negative sign away. This becomes an addition problem. [latex]-93[\/latex] becomes [latex]+93[\/latex]<\/p>\n<p style=\"text-align: center\">[latex]382+93=475[\/latex]<\/p>\n<h4>Answer<\/h4>\n<p>[latex]382\u2013(\u221293)=475[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>The following video explains how to subtract two signed integers.<br \/>\n<iframe loading=\"lazy\" id=\"oembed-1\" title=\"Ex 2:  Subtracting Integers (Two Digit Integers)\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/ciuIKFCtWWU?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm8033\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=8033&theme=oea&iframe_resize_id=ohm8033&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>Find [latex]-\\frac{3}{7}-\\frac{6}{7}+\\frac{2}{7}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q11416\">Show Solution<\/span><\/p>\n<div id=\"q11416\" class=\"hidden-answer\" style=\"display: none\">Add the first two and give the result a negative sign:<\/p>\n<p>Since the signs of the first two are the same, find the sum of the absolute values of the fractions<\/p>\n<p>Since both numbers are negative, the sum is negative. If you owe money, then borrow more, the amount you owe becomes larger.<\/p>\n<p style=\"text-align: center\">[latex]\\left| -\\frac{3}{7} \\right|=\\frac{3}{7}[\/latex] and [latex]\\left| -\\frac{6}{7} \\right|=\\frac{6}{7}[\/latex]<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{c}\\frac{3}{7}+\\frac{6}{7}=\\frac{9}{7}\\\\\\\\-\\frac{3}{7}-\\frac{6}{7} =-\\frac{9}{7}\\end{array}[\/latex]<\/p>\n<p>Now add the third number. The signs are different, so find the <em>difference<\/em> of their absolute values.<\/p>\n<p style=\"text-align: center\">[latex]\\left| -\\frac{9}{7} \\right|=\\frac{9}{7}[\/latex] and [latex]\\left| \\frac{2}{7} \\right|=\\frac{2}{7}[\/latex]<\/p>\n<p style=\"text-align: center\">[latex]\\frac{9}{7}-\\frac{2}{7}=\\frac{7}{7}[\/latex]<\/p>\n<p>Since [latex]\\left|\\frac{-9}{7}\\right|>\\left|\\frac{2}{7}\\right|[\/latex], the sign of the final sum is the same as the sign of [latex]-\\frac{9}{7}[\/latex].<i><br \/>\n<\/i><\/p>\n<p style=\"text-align: center\">[latex]-\\frac{9}{7}+\\frac{2}{7}=-\\frac{7}{7}=-1[\/latex]<\/p>\n<h4>Answer<\/h4>\n<p>[latex]-\\frac{3}{7}+\\left(-\\frac{6}{7}\\right)+\\frac{2}{7}=-\\frac{7}{7}=-1[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm593\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=593&theme=oea&iframe_resize_id=ohm593&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the following video you will see an example of how to add three fractions with a common denominator that have different signs.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Find the Sum and Difference of Three Signed Fractions (Common Denom)\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/P972VVbR98k?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>Evaluate [latex]27.832+(\u22123.06)[\/latex]. When you add decimals, remember to line up the decimal points so you are adding tenths to tenths, hundredths to hundredths, and so on.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q545871\">Show Solution<\/span><\/p>\n<div id=\"q545871\" class=\"hidden-answer\" style=\"display: none\">Since the addends have different signs, subtract their absolute values.<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{r}\\underline{\\begin{array}{r}27.832\\\\-\\text{ }3.06\\,\\,\\,\\end{array}}\\\\24.772\\end{array}[\/latex]<\/p>\n<p style=\"text-align: center\">[latex]\\left|-3.06\\right|=3.06[\/latex]<\/p>\n<p>The sum has the same sign as [latex]27.832[\/latex] whose absolute value is greater.<\/p>\n<h4>Answer<\/h4>\n<p>[latex]27.832+\\left(-3.06\\right)=24.772[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm783\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=783&theme=oea&iframe_resize_id=ohm783&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the following video are\u00a0examples of adding and subtracting decimals with different signs.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-3\" title=\"Ex:  Adding Signed Decimals\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/3FHZQ5iKcpI?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-16092\">\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>Ex 2: Subtracting Integers (Two Digit Integers). <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/ciuIKFCtWWU\">https:\/\/youtu.be\/ciuIKFCtWWU<\/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>Find the Sum and Difference of Three Signed Fractions (Common Denom). <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/P972VVbR98k\">https:\/\/youtu.be\/P972VVbR98k<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Ex: Adding Signed Decimals. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/3FHZQ5iKcpI\">https:\/\/youtu.be\/3FHZQ5iKcpI<\/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>Unit 9: Real Numbers, from Developmental Math: An Open Program. <strong>Provided by<\/strong>: Monterey Institute of Technology and Education. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/nrocnetwork.org\/resources\/downloads\/nroc-math-open-textbook-units-1-12-pdf-and-word-formats\/\">http:\/\/nrocnetwork.org\/resources\/downloads\/nroc-math-open-textbook-units-1-12-pdf-and-word-formats\/<\/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>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":169554,"menu_order":4,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Ex 2: Subtracting Integers (Two Digit Integers)\",\"author\":\"James Sousa (Mathispower4u.com) for Lumen Learning\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/ciuIKFCtWWU\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Find the Sum and Difference of Three Signed Fractions (Common Denom)\",\"author\":\"James Sousa (Mathispower4u.com) for Lumen Learning\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/P972VVbR98k\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Ex: Adding Signed Decimals\",\"author\":\"James 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