{"id":4596,"date":"2020-04-21T00:19:05","date_gmt":"2020-04-21T00:19:05","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/chapter\/adding-whole-numbers-in-applications-2\/"},"modified":"2024-06-26T17:17:26","modified_gmt":"2024-06-26T17:17:26","slug":"adding-whole-numbers-in-applications-2","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/chapter\/adding-whole-numbers-in-applications-2\/","title":{"raw":"Adding Whole Numbers in Applications","rendered":"Adding Whole Numbers in Applications"},"content":{"raw":"\n<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n \t<li>Translate word phrases into mathematical notation representing addition<\/li>\n \t<li>Solve application problems by translating word phrases into mathematical expressions<\/li>\n<\/ul>\n<\/div>\n&nbsp;\n<h2>Translate Word Phrases to Math Notation<\/h2>\nWe've seen a few problems where we translate math notation into words. Now we\u2019ll reverse the process. We\u2019ll translate word phrases into math notation. Some of the word phrases that indicate addition are listed in the table below.\n<table id=\"fs-id1826990\" summary=\"This is a table with two rows and four columns. The top row is a header row. The column names from left to right are operation, words, example, and expression. In the row beneath, the content reads from left to right under each column, addition as the operation, \">\n<thead>\n<tr valign=\"top\">\n<th>Operation<\/th>\n<th>Words<\/th>\n<th>Example<\/th>\n<th>Expression<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td>Addition<\/td>\n<td>plus\n\nsum\n\nincreased by\n\nmore than\n\ntotal of\n\nadded to<\/td>\n<td>[latex]1[\/latex] plus [latex]2[\/latex]\n\nthe sum of [latex]3[\/latex] and [latex]4[\/latex]\n\n[latex]5[\/latex] increased by [latex]6[\/latex]\n\n[latex]8[\/latex] more than [latex]7[\/latex]\n\nthe total of [latex]9[\/latex] and [latex]5[\/latex]\n\n[latex]6[\/latex] added to [latex]4[\/latex]<\/td>\n<td>[latex]1+2[\/latex]\n\n[latex]3+4[\/latex]\n\n[latex]5+6[\/latex]\n\n[latex]7+8[\/latex]\n\n[latex]9+5[\/latex]\n\n[latex]4+6[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n&nbsp;\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\nTranslate and simplify: the sum of [latex]19[\/latex] and [latex]23[\/latex].\n\nSolution\nThe word <em>sum<\/em> tells us to add. The words <em>of<\/em> [latex]19[\/latex] <em>and<\/em> [latex]23[\/latex] tell us the addends.\n<table id=\"eip-id1168288294973\" class=\"unnumbered unstyled\" summary=\"a\">\n<tbody>\n<tr>\n<td><\/td>\n<td>The sum of [latex]19[\/latex] and [latex]23[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Translate.<\/td>\n<td>[latex]19+23[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td>[latex]42[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>The sum of [latex]19[\/latex] and [latex]23[\/latex] is [latex]42[\/latex].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n&nbsp;\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=143207&amp;theme=oea&amp;iframe_resize_id=mom1[\/embed]\n\n<\/div>\n&nbsp;\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\nTranslate and simplify: [latex]28[\/latex] increased by [latex]31[\/latex].\n[reveal-answer q=\"852875\"]Show Solution[\/reveal-answer]\n[hidden-answer a=\"852875\"]\n\nSolution\nThe words <em>increased by<\/em> tell us to add. The numbers given are the addends.\n<table id=\"eip-id1168288520954\" class=\"unnumbered unstyled\" summary=\"a\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]28[\/latex] increased by [latex]31[\/latex].<\/td>\n<\/tr>\n<tr>\n<td>Translate.<\/td>\n<td>[latex]28+31[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td>[latex]59[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>So [latex]28[\/latex] increased by [latex]31[\/latex] is [latex]59[\/latex].<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n[\/hidden-answer]\n\n<\/div>\n&nbsp;\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\nTranslate and simplify: [latex]29[\/latex] increased by [latex]76[\/latex].\n[reveal-answer q=\"297255\"]Show Solution[\/reveal-answer]\n[hidden-answer a=\"297255\"]Translate: [latex]29+76[\/latex]; Simplify [latex]105[\/latex][\/hidden-answer]\n\n&nbsp;\n\nTranslate and simplify: [latex]37[\/latex] increased by [latex]69[\/latex].\n[reveal-answer q=\"555812\"]Show Solution[\/reveal-answer]\n[hidden-answer a=\"555812\"]Translate: [latex]37+69[\/latex]; Simplify [latex]106[\/latex][\/hidden-answer]\n\n<\/div>\n&nbsp;\n\nIn the video below we present more examples of how to translate from words to expressions.\n\nhttps:\/\/youtu.be\/sFbNgjxdf1A\n<h2>Add Whole Numbers in Applications<\/h2>\nNow that we have practiced adding whole numbers, let\u2019s use what we\u2019ve learned to solve real-world problems. We\u2019ll start by outlining a plan. First, we need to read the problem to determine what we are looking for. Then we write a word phrase that gives the information to find it. Next we translate the word phrase into math notation and then simplify. Finally, we write a sentence to answer the question.\n\n&nbsp;\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\nHao earned grades of [latex]87,93,68,95,\\text{and }89[\/latex] on the five tests of the semester. What is the total number of points he earned on the five tests?\n[reveal-answer q=\"430478\"]Show Solution[\/reveal-answer]\n[hidden-answer a=\"430478\"]\n\nSolution\nWe are asked to find the total number of points on the tests.\n<table id=\"eip-id1168288617772\" class=\"unnumbered unstyled\" summary=\"a\">\n<tbody>\n<tr>\n<td>Write a phrase.<\/td>\n<td>the sum of points on the tests<\/td>\n<\/tr>\n<tr>\n<td>Translate to math notation.<\/td>\n<td>[latex]87+93+68+95+89[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Then we simplify by adding.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Since there are several numbers, we will write them vertically.<\/td>\n<td>[latex]\\begin{array}{}\\\\ \\\\ \\\\ \\stackrel{3}{8}7\\hfill \\\\ 93\\hfill \\\\ 68\\hfill \\\\ 95\\hfill \\\\ \\underset{\\text{+____}}{89}\\hfill \\\\ 432\\hfill \\end{array}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write a sentence to answer the question.<\/td>\n<td>Hao earned a total of 432 points.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\nNotice that we added <em>points<\/em>, so the sum is [latex]432[\/latex] <em>points<\/em>. It is important to include the appropriate units in all answers to applications problems.\n\n[\/hidden-answer]\n\n<\/div>\n&nbsp;\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n[ohm_question]143227[\/ohm_question]\n\n<\/div>\n&nbsp;\n\nSome application problems involve shapes. For example, a person might need to know the distance around a garden to put up a fence or around a picture to frame it. The perimeter is the distance around a geometric figure. The perimeter of a figure is the sum of the lengths of its sides.\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\nFind the perimeter of the patio shown.\n\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215342\/CNX_BMath_Figure_01_02_002.png\" alt=\"This is an image of a perimeter of a patio. There are six sides. The far left side is labeled 4 feet, the top side is labeled 9 feet, the right side is short and labeled 2 feet, then extends across to the left and is labeled 3 feet. From here, the side extends down and is labeled 2 feet. Finally, the base is labeled 6 feet.\">\n[reveal-answer q=\"126824\"]Show Solution[\/reveal-answer]\n[hidden-answer a=\"126824\"]\n\nSolution\n<table id=\"eip-id1168289453960\" class=\"unnumbered unstyled\" summary=\"a\">\n<tbody>\n<tr>\n<td>We are asked to find the perimeter.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Write a phrase.<\/td>\n<td>the sum of the sides<\/td>\n<\/tr>\n<tr>\n<td>Translate to math notation.<\/td>\n<td>[latex]4+6+2+3+2+9[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify by adding.<\/td>\n<td>[latex]26[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write a sentence to answer the question.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>We added feet, so the sum is [latex]26[\/latex] feet.<\/td>\n<td>The perimeter of the patio is [latex]26[\/latex] feet.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n[\/hidden-answer]\n\n<\/div>\n&nbsp;\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=7964&amp;theme=oea&amp;iframe_resize_id=mom3[\/embed]\n\n<\/div>\n&nbsp;\n\nThe video below helps with finding the perimeter of an L-shaped Polygon involving hole numbers.\nhttps:\/\/youtu.be\/0HfnFXm7zHI\n","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Translate word phrases into mathematical notation representing addition<\/li>\n<li>Solve application problems by translating word phrases into mathematical expressions<\/li>\n<\/ul>\n<\/div>\n<p>&nbsp;<\/p>\n<h2>Translate Word Phrases to Math Notation<\/h2>\n<p>We&#8217;ve seen a few problems where we translate math notation into words. Now we\u2019ll reverse the process. We\u2019ll translate word phrases into math notation. Some of the word phrases that indicate addition are listed in the table below.<\/p>\n<table id=\"fs-id1826990\" summary=\"This is a table with two rows and four columns. The top row is a header row. The column names from left to right are operation, words, example, and expression. In the row beneath, the content reads from left to right under each column, addition as the operation,\">\n<thead>\n<tr valign=\"top\">\n<th>Operation<\/th>\n<th>Words<\/th>\n<th>Example<\/th>\n<th>Expression<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td>Addition<\/td>\n<td>plus<\/p>\n<p>sum<\/p>\n<p>increased by<\/p>\n<p>more than<\/p>\n<p>total of<\/p>\n<p>added to<\/td>\n<td>[latex]1[\/latex] plus [latex]2[\/latex]<\/p>\n<p>the sum of [latex]3[\/latex] and [latex]4[\/latex]<\/p>\n<p>[latex]5[\/latex] increased by [latex]6[\/latex]<\/p>\n<p>[latex]8[\/latex] more than [latex]7[\/latex]<\/p>\n<p>the total of [latex]9[\/latex] and [latex]5[\/latex]<\/p>\n<p>[latex]6[\/latex] added to [latex]4[\/latex]<\/td>\n<td>[latex]1+2[\/latex]<\/p>\n<p>[latex]3+4[\/latex]<\/p>\n<p>[latex]5+6[\/latex]<\/p>\n<p>[latex]7+8[\/latex]<\/p>\n<p>[latex]9+5[\/latex]<\/p>\n<p>[latex]4+6[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Translate and simplify: the sum of [latex]19[\/latex] and [latex]23[\/latex].<\/p>\n<p>Solution<br \/>\nThe word <em>sum<\/em> tells us to add. The words <em>of<\/em> [latex]19[\/latex] <em>and<\/em> [latex]23[\/latex] tell us the addends.<\/p>\n<table id=\"eip-id1168288294973\" class=\"unnumbered unstyled\" summary=\"a\">\n<tbody>\n<tr>\n<td><\/td>\n<td>The sum of [latex]19[\/latex] and [latex]23[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Translate.<\/td>\n<td>[latex]19+23[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td>[latex]42[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>The sum of [latex]19[\/latex] and [latex]23[\/latex] is [latex]42[\/latex].<\/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><iframe loading=\"lazy\" id=\"ohm143207\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=143207&#38;theme=oea&#38;iframe_resize_id=ohm143207&#38;show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Translate and simplify: [latex]28[\/latex] increased by [latex]31[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q852875\">Show Solution<\/span><\/p>\n<div id=\"q852875\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<br \/>\nThe words <em>increased by<\/em> tell us to add. The numbers given are the addends.<\/p>\n<table id=\"eip-id1168288520954\" class=\"unnumbered unstyled\" summary=\"a\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]28[\/latex] increased by [latex]31[\/latex].<\/td>\n<\/tr>\n<tr>\n<td>Translate.<\/td>\n<td>[latex]28+31[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td>[latex]59[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>So [latex]28[\/latex] increased by [latex]31[\/latex] is [latex]59[\/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>Translate and simplify: [latex]29[\/latex] increased by [latex]76[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q297255\">Show Solution<\/span><\/p>\n<div id=\"q297255\" class=\"hidden-answer\" style=\"display: none\">Translate: [latex]29+76[\/latex]; Simplify [latex]105[\/latex]<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>Translate and simplify: [latex]37[\/latex] increased by [latex]69[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q555812\">Show Solution<\/span><\/p>\n<div id=\"q555812\" class=\"hidden-answer\" style=\"display: none\">Translate: [latex]37+69[\/latex]; Simplify [latex]106[\/latex]<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>In the video below we present more examples of how to translate from words to expressions.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"The Language of Addition\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/sFbNgjxdf1A?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h2>Add Whole Numbers in Applications<\/h2>\n<p>Now that we have practiced adding whole numbers, let\u2019s use what we\u2019ve learned to solve real-world problems. We\u2019ll start by outlining a plan. First, we need to read the problem to determine what we are looking for. Then we write a word phrase that gives the information to find it. Next we translate the word phrase into math notation and then simplify. Finally, we write a sentence to answer the question.<\/p>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Hao earned grades of [latex]87,93,68,95,\\text{and }89[\/latex] on the five tests of the semester. What is the total number of points he earned on the five tests?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q430478\">Show Solution<\/span><\/p>\n<div id=\"q430478\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<br \/>\nWe are asked to find the total number of points on the tests.<\/p>\n<table id=\"eip-id1168288617772\" class=\"unnumbered unstyled\" summary=\"a\">\n<tbody>\n<tr>\n<td>Write a phrase.<\/td>\n<td>the sum of points on the tests<\/td>\n<\/tr>\n<tr>\n<td>Translate to math notation.<\/td>\n<td>[latex]87+93+68+95+89[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Then we simplify by adding.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Since there are several numbers, we will write them vertically.<\/td>\n<td>[latex]\\begin{array}{}\\\\ \\\\ \\\\ \\stackrel{3}{8}7\\hfill \\\\ 93\\hfill \\\\ 68\\hfill \\\\ 95\\hfill \\\\ \\underset{\\text{+____}}{89}\\hfill \\\\ 432\\hfill \\end{array}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write a sentence to answer the question.<\/td>\n<td>Hao earned a total of 432 points.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Notice that we added <em>points<\/em>, so the sum is [latex]432[\/latex] <em>points<\/em>. It is important to include the appropriate units in all answers to applications problems.<\/p>\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=\"ohm143227\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=143227&theme=oea&iframe_resize_id=ohm143227&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<p>Some application problems involve shapes. For example, a person might need to know the distance around a garden to put up a fence or around a picture to frame it. The perimeter is the distance around a geometric figure. The perimeter of a figure is the sum of the lengths of its sides.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Find the perimeter of the patio shown.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215342\/CNX_BMath_Figure_01_02_002.png\" alt=\"This is an image of a perimeter of a patio. There are six sides. The far left side is labeled 4 feet, the top side is labeled 9 feet, the right side is short and labeled 2 feet, then extends across to the left and is labeled 3 feet. From here, the side extends down and is labeled 2 feet. Finally, the base is labeled 6 feet.\" \/><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q126824\">Show Solution<\/span><\/p>\n<div id=\"q126824\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168289453960\" class=\"unnumbered unstyled\" summary=\"a\">\n<tbody>\n<tr>\n<td>We are asked to find the perimeter.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Write a phrase.<\/td>\n<td>the sum of the sides<\/td>\n<\/tr>\n<tr>\n<td>Translate to math notation.<\/td>\n<td>[latex]4+6+2+3+2+9[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify by adding.<\/td>\n<td>[latex]26[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write a sentence to answer the question.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>We added feet, so the sum is [latex]26[\/latex] feet.<\/td>\n<td>The perimeter of the patio is [latex]26[\/latex] feet.<\/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=\"ohm7964\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=7964&#38;theme=oea&#38;iframe_resize_id=ohm7964&#38;show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<p>The video below helps with finding the perimeter of an L-shaped Polygon involving hole numbers.<br \/>\n<iframe loading=\"lazy\" id=\"oembed-2\" title=\"Ex: Find the Perimeter of an L-shaped Polygon Involving Whole Numbers\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/0HfnFXm7zHI?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-4596\">\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>Ex: Find the Perimeter of an L-shaped Polygon Involving Whole Numbers. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/0HfnFXm7zHI\">https:\/\/youtu.be\/0HfnFXm7zHI<\/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>The Language of Addition. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/sFbNgjxdf1A\">https:\/\/youtu.be\/sFbNgjxdf1A<\/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>Question ID: 143207, 143227. <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><li>Question ID: 7964. <strong>Authored by<\/strong>: James Sousa. <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, Specific attribution<\/div><ul class=\"citation-list\"><li>Prealgebra. <strong>Provided by<\/strong>: OpenStax. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":17533,"menu_order":8,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Ex: Find the Perimeter of an L-shaped Polygon Involving Whole Numbers\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/0HfnFXm7zHI\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"The Language of Addition\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/sFbNgjxdf1A\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at 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