{"id":9193,"date":"2017-05-02T16:35:12","date_gmt":"2017-05-02T16:35:12","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=9193"},"modified":"2020-09-14T21:37:37","modified_gmt":"2020-09-14T21:37:37","slug":"notation-and-modeling-subtraction-of-whole-numbers","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/chapter\/notation-and-modeling-subtraction-of-whole-numbers\/","title":{"raw":"Notation and Modeling Subtraction of Whole Numbers","rendered":"Notation and Modeling Subtraction of Whole Numbers"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Use symbols and words to represent subtraction<\/li>\r\n \t<li>Translate subtractions from math notation to words<\/li>\r\n \t<li>Use base-10 blocks to model subtraction<\/li>\r\n<\/ul>\r\n<\/div>\r\n&nbsp;\r\n<h2 data-type=\"title\">Use Subtraction Notation<\/h2>\r\nSuppose there are seven bananas in a bowl. Elana uses three of them to make a smoothie. How many bananas are left in the bowl? To answer the question, we subtract three from seven. When we subtract, we take one number away from another to find the difference. The notation we use to subtract [latex]3[\/latex] from [latex]7[\/latex] is\r\n<p style=\"text-align: center;\">[latex]7 - 3[\/latex]<\/p>\r\nWe read [latex]7 - 3[\/latex] as <em data-effect=\"italics\">seven minus three<\/em> and the result is <em data-effect=\"italics\">the difference of seven and three<\/em>.\r\n<div class=\"textbox shaded\">\r\n<h3>Subtraction Notation<\/h3>\r\nTo describe subtraction, we can use symbols and words.\r\n<table id=\"fs-id2434601\" class=\"unnumbered\" style=\"width: 80%;\" summary=\"This is a table with two rows and five columns. The top row is a header row. Each column is labeled from left to right operation, notation, expression, read as, and result. Under operation it says subtraction; under notation is the minus sign; under expression is seven minus three, under read as are the words seven minus three, under result are the words the difference of 7 and 3.\" data-label=\"\">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th data-align=\"left\">Operation<\/th>\r\n<th data-align=\"left\">Notation<\/th>\r\n<th data-align=\"left\">Expression<\/th>\r\n<th data-align=\"left\">Read as<\/th>\r\n<th data-align=\"left\">Result<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td data-align=\"left\">Subtraction<\/td>\r\n<td data-align=\"left\">[latex]-[\/latex]<\/td>\r\n<td data-align=\"left\">[latex]7 - 3[\/latex]<\/td>\r\n<td data-align=\"left\">seven minus three<\/td>\r\n<td data-align=\"left\">the difference of [latex]7[\/latex] and [latex]3[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nTranslate from math notation to words:\r\n\r\n1. [latex]8 - 1[\/latex]\r\n2. [latex]26 - 14[\/latex] .\r\n\r\nSolution\r\n<ol id=\"eip-id1168289601814\" data-labeled-item=\"true\">\r\n \t<li>We read this as <em data-effect=\"italics\">eight minus one<\/em>. The result is <em data-effect=\"italics\">the difference of eight and one<\/em>.<\/li>\r\n \t<li>We read this as <em data-effect=\"italics\">twenty-six minus fourteen<\/em>. The result is <em data-effect=\"italics\">the difference of twenty-six and fourteen<\/em>.<\/li>\r\n<\/ol>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n<iframe id=\"mom1\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=143245&amp;theme=oea&amp;iframe_resize_id=mom1\" width=\"100%\" height=\"280\"><\/iframe>\r\n\r\n<\/div>\r\n&nbsp;\r\n\r\nThe video below provides more examples of how to translate subtraction word phrases.\r\n\r\nhttps:\/\/youtu.be\/vtnAdQHCt5s\r\n<h2 data-type=\"title\">Model Subtraction of Whole Numbers<\/h2>\r\nA model can help us visualize the process of subtraction much as it did with addition. Again, we will use [latex]\\text{base - 10}[\/latex] blocks. Remember a block represents 1 and a rod represents 10. Let\u2019s start by modeling the subtraction expression we just considered, [latex]7 - 3[\/latex].\r\n<table id=\"eip-696\" class=\"unnumbered unstyled\" style=\"width: 90%;\" summary=\".\" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td>We start by modeling the first number, [latex]7[\/latex].<\/td>\r\n<td><img class=\"alignleft wp-image-16113 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/05\/14205810\/IMG_01_01_066.png\" alt=\"Seven blocks\" width=\"556\" height=\"144\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Now take away the second number, [latex]3[\/latex]. We'll circle [latex]3[\/latex] blocks to show that we are taking them away.<\/td>\r\n<td><img class=\"wp-image-16115 size-full alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/05\/14205831\/IMG_01_01_067.png\" alt=\"Seven blocks minus three blocks\" width=\"591\" height=\"121\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Count the number of blocks remaining.<\/td>\r\n<td><img class=\"alignleft wp-image-16117 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/05\/14210027\/IMG_01_01_068.png\" alt=\"Four blocks\" width=\"620\" height=\"122\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>There are [latex]4[\/latex] ones blocks left.<\/td>\r\n<td>We have shown that [latex]7 - 3=4[\/latex] .<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nModel the subtraction: [latex]8 - 2[\/latex]\r\n[reveal-answer q=\"250813\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"250813\"]\r\n\r\nSolution\r\n<table id=\"eip-35\" class=\"unnumbered unstyled\" style=\"width: 90%;\" summary=\"This image has two columns. The left column contains annotations and the right column contains base ten blocks. The left column states \" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td>[latex]8 - 2[\/latex] means the difference of [latex]8[\/latex] and [latex]2[\/latex].<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Model the first, [latex]8[\/latex].<\/td>\r\n<td data-align=\"right\"><img class=\"wp-image-16118 size-full alignleft\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/05\/14210114\/IMG_01_01_069.png\" alt=\"Eight blocks\" width=\"667\" height=\"139\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Take away the second number, [latex]2[\/latex].<\/td>\r\n<td data-align=\"right\"><img class=\"alignleft wp-image-16119 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/05\/14210133\/IMG_01_01_070.png\" alt=\"Eight blocks minus two blocks\" width=\"635\" height=\"121\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Count the number of blocks remaining.<\/td>\r\n<td data-align=\"right\"><img class=\"alignleft wp-image-16120\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/05\/14210158\/IMG_01_01_071.png\" alt=\"Six blocks\" width=\"430\" height=\"113\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>There are [latex]6[\/latex] ones blocks left.<\/td>\r\n<td>We have shown that [latex]8 - 2=6[\/latex] .<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\nModel: [latex]9 - 6[\/latex]\r\n[reveal-answer q=\"788582\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"788582\"]\r\n\r\n<img class=\"alignleft wp-image-16121 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/05\/14210416\/IMG_01_01_072.png\" alt=\"Nine minus six equals three\" width=\"726\" height=\"141\" \/>\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\nModel: [latex]6 - 1[\/latex]\r\n[reveal-answer q=\"527873\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"527873\"]\r\n\r\n<img class=\"alignleft wp-image-16122\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/05\/14210429\/IMG_01_01_073.png\" alt=\"Six minus one equals five\" width=\"375\" height=\"104\" \/>\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\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\nModel the subtraction: [latex]13 - 8[\/latex].\r\n[reveal-answer q=\"254544\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"254544\"]\r\n\r\nSolution\r\n<table id=\"eip-811\" class=\"unnumbered unstyled\" style=\"width: 90%; height: 250px;\" summary=\"This image has two columns. The left column contains annotations and the right column contains base ten blocks. The left column states \" data-label=\"\">\r\n<tbody>\r\n<tr style=\"height: 65px;\">\r\n<td style=\"height: 65px;\">Model the first number, [latex]13[\/latex]. We use [latex]1[\/latex] ten and [latex]3[\/latex] ones.<\/td>\r\n<td style=\"height: 65px;\"><img class=\"alignleft wp-image-16123\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/05\/14210956\/IMG_01_01_074.png\" alt=\"One rod and three blocks\" width=\"450\" height=\"59\" \/><\/td>\r\n<\/tr>\r\n<tr style=\"height: 69px;\">\r\n<td style=\"height: 69px;\">Take away the second number, [latex]8[\/latex]. However, there are not [latex]8[\/latex] ones, so we will exchange the [latex]1[\/latex] ten for [latex]10[\/latex] ones.<\/td>\r\n<td style=\"height: 69px;\"><img class=\"alignleft wp-image-16124 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/05\/14211033\/IMG_01_01_075.png\" alt=\"Ten blocks and three blocks\" width=\"1006\" height=\"143\" \/><\/td>\r\n<\/tr>\r\n<tr style=\"height: 50px;\">\r\n<td style=\"height: 50px;\">Now we can take away [latex]8[\/latex] ones.<\/td>\r\n<td style=\"height: 50px;\"><img class=\"alignleft wp-image-16126 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/05\/14211658\/IMG_01_01_076.png\" alt=\"Thirteen blocks minus eight blocks\" width=\"1006\" height=\"96\" \/><\/td>\r\n<\/tr>\r\n<tr style=\"height: 55px;\">\r\n<td style=\"height: 55px;\">Count the blocks remaining.<\/td>\r\n<td style=\"height: 55px;\"><img class=\"alignleft wp-image-16127\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/05\/14211732\/IMG_01_01_0771.png\" alt=\"Five blocks\" width=\"175\" height=\"45\" \/><\/td>\r\n<\/tr>\r\n<tr style=\"height: 11px;\">\r\n<td style=\"height: 11px;\">There are five ones left.<\/td>\r\n<td style=\"height: 11px;\">We have shown that [latex]13 - 8=5[\/latex] .<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n\r\nAs we did with addition, we can describe the models as ones blocks and tens rods, or we can simply say ones and tens.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\nModel the subtraction: [latex]12 - 7[\/latex]\r\n[reveal-answer q=\"493917\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"493917\"]\r\n\r\n<img class=\"alignleft wp-image-16129 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/05\/14212226\/IMG_01_01_078.png\" alt=\"Twelve minus seven equals five\" width=\"896\" height=\"131\" \/>\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\nModel the subtraction: [latex]14 - 8[\/latex]\r\n[reveal-answer q=\"445440\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"445440\"]\r\n\r\n<img class=\"alignleft wp-image-16130 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/05\/14212242\/IMG_01_01_079.png\" alt=\"Fourteen minus eight equals six\" width=\"1029\" height=\"131\" \/>\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\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\nModel the subtraction: [latex]43 - 26[\/latex]\r\n[reveal-answer q=\"746173\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"746173\"]\r\n\r\nSolution\r\nBecause [latex]43 - 26[\/latex] means [latex]43[\/latex] take away [latex]26[\/latex], we begin by modeling the [latex]43[\/latex].\r\n\r\n<img class=\"wp-image-16131 size-full alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/05\/14212445\/IMG_01_01_080.png\" alt=\"Four rods and three blocks\" width=\"757\" height=\"309\" \/>\r\n\r\nNow, we need to take away [latex]26[\/latex], which is [latex]2[\/latex] tens and [latex]6[\/latex] ones. We cannot take away [latex]6[\/latex] ones from [latex]3[\/latex] ones. So, we exchange [latex]1[\/latex] ten for [latex]10[\/latex] ones.\r\n\r\n<img class=\"wp-image-16132 size-full aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/05\/14212517\/IMG_01_01_081.png\" alt=\"Four rods and three ones broken down into three rods and thirteen blocks.\" width=\"1744\" height=\"356\" \/>\r\n\r\nNow we can take away [latex]2[\/latex] tens and [latex]6[\/latex] ones.\r\n\r\n<img class=\"wp-image-16133 size-full aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/05\/14212602\/IMG_01_01_082.png\" alt=\"Three rods and thirteen blocks minus two rods and six blocks equals one rod and seven blocks\" width=\"1583\" height=\"316\" \/>\r\n\r\nCount the number of blocks remaining. There is [latex]1[\/latex] ten and [latex]7[\/latex] ones, which is [latex]17[\/latex].\r\n[latex]43 - 26=17[\/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\nModel the subtraction: [latex]42 - 27[\/latex]\r\n[reveal-answer q=\"564148\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"564148\"]\r\n\r\n<img class=\"alignleft wp-image-16134 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/05\/14212700\/IMG_01_01_083.png\" alt=\"Forty-two minus twenty-seven equals fifteen, or three rods and twelve blocks minus two rods and seven blocks equals one rod and five blocks.\" width=\"900\" height=\"422\" \/>\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\nModel the subtraction: [latex]45 - 29[\/latex]\r\n[reveal-answer q=\"980973\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"980973\"]\r\n\r\n<img class=\"alignleft wp-image-16135 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/05\/14212805\/IMG_01_01_084.png\" alt=\"Forty-five minus twenty-nine equals sixteen, or three rods and fifteen blocks minus two rods and nine blocks equals one rod and six blocks\" width=\"900\" height=\"422\" \/>\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n\r\nWatch the video below to see more examples of using base 10 blocks to model subtraction.\r\n\r\nhttps:\/\/youtu.be\/FQI0IgA-7fI","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Use symbols and words to represent subtraction<\/li>\n<li>Translate subtractions from math notation to words<\/li>\n<li>Use base-10 blocks to model subtraction<\/li>\n<\/ul>\n<\/div>\n<p>&nbsp;<\/p>\n<h2 data-type=\"title\">Use Subtraction Notation<\/h2>\n<p>Suppose there are seven bananas in a bowl. Elana uses three of them to make a smoothie. How many bananas are left in the bowl? To answer the question, we subtract three from seven. When we subtract, we take one number away from another to find the difference. The notation we use to subtract [latex]3[\/latex] from [latex]7[\/latex] is<\/p>\n<p style=\"text-align: center;\">[latex]7 - 3[\/latex]<\/p>\n<p>We read [latex]7 - 3[\/latex] as <em data-effect=\"italics\">seven minus three<\/em> and the result is <em data-effect=\"italics\">the difference of seven and three<\/em>.<\/p>\n<div class=\"textbox shaded\">\n<h3>Subtraction Notation<\/h3>\n<p>To describe subtraction, we can use symbols and words.<\/p>\n<table id=\"fs-id2434601\" class=\"unnumbered\" style=\"width: 80%;\" summary=\"This is a table with two rows and five columns. The top row is a header row. Each column is labeled from left to right operation, notation, expression, read as, and result. Under operation it says subtraction; under notation is the minus sign; under expression is seven minus three, under read as are the words seven minus three, under result are the words the difference of 7 and 3.\" data-label=\"\">\n<thead>\n<tr valign=\"top\">\n<th data-align=\"left\">Operation<\/th>\n<th data-align=\"left\">Notation<\/th>\n<th data-align=\"left\">Expression<\/th>\n<th data-align=\"left\">Read as<\/th>\n<th data-align=\"left\">Result<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td data-align=\"left\">Subtraction<\/td>\n<td data-align=\"left\">[latex]-[\/latex]<\/td>\n<td data-align=\"left\">[latex]7 - 3[\/latex]<\/td>\n<td data-align=\"left\">seven minus three<\/td>\n<td data-align=\"left\">the difference of [latex]7[\/latex] and [latex]3[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Translate from math notation to words:<\/p>\n<p>1. [latex]8 - 1[\/latex]<br \/>\n2. [latex]26 - 14[\/latex] .<\/p>\n<p>Solution<\/p>\n<ol id=\"eip-id1168289601814\" data-labeled-item=\"true\">\n<li>We read this as <em data-effect=\"italics\">eight minus one<\/em>. The result is <em data-effect=\"italics\">the difference of eight and one<\/em>.<\/li>\n<li>We read this as <em data-effect=\"italics\">twenty-six minus fourteen<\/em>. The result is <em data-effect=\"italics\">the difference of twenty-six and fourteen<\/em>.<\/li>\n<\/ol>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"mom1\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=143245&amp;theme=oea&amp;iframe_resize_id=mom1\" width=\"100%\" height=\"280\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<p>The video below provides more examples of how to translate subtraction word phrases.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"The Language of Subtraction\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/vtnAdQHCt5s?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h2 data-type=\"title\">Model Subtraction of Whole Numbers<\/h2>\n<p>A model can help us visualize the process of subtraction much as it did with addition. Again, we will use [latex]\\text{base - 10}[\/latex] blocks. Remember a block represents 1 and a rod represents 10. Let\u2019s start by modeling the subtraction expression we just considered, [latex]7 - 3[\/latex].<\/p>\n<table id=\"eip-696\" class=\"unnumbered unstyled\" style=\"width: 90%;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>We start by modeling the first number, [latex]7[\/latex].<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"alignleft wp-image-16113 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/05\/14205810\/IMG_01_01_066.png\" alt=\"Seven blocks\" width=\"556\" height=\"144\" \/><\/td>\n<\/tr>\n<tr>\n<td>Now take away the second number, [latex]3[\/latex]. We&#8217;ll circle [latex]3[\/latex] blocks to show that we are taking them away.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-16115 size-full alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/05\/14205831\/IMG_01_01_067.png\" alt=\"Seven blocks minus three blocks\" width=\"591\" height=\"121\" \/><\/td>\n<\/tr>\n<tr>\n<td>Count the number of blocks remaining.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"alignleft wp-image-16117 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/05\/14210027\/IMG_01_01_068.png\" alt=\"Four blocks\" width=\"620\" height=\"122\" \/><\/td>\n<\/tr>\n<tr>\n<td>There are [latex]4[\/latex] ones blocks left.<\/td>\n<td>We have shown that [latex]7 - 3=4[\/latex] .<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Model the subtraction: [latex]8 - 2[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q250813\">Show Solution<\/span><\/p>\n<div id=\"q250813\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-35\" class=\"unnumbered unstyled\" style=\"width: 90%;\" summary=\"This image has two columns. The left column contains annotations and the right column contains base ten blocks. The left column states\" data-label=\"\">\n<tbody>\n<tr>\n<td>[latex]8 - 2[\/latex] means the difference of [latex]8[\/latex] and [latex]2[\/latex].<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Model the first, [latex]8[\/latex].<\/td>\n<td data-align=\"right\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-16118 size-full alignleft\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/05\/14210114\/IMG_01_01_069.png\" alt=\"Eight blocks\" width=\"667\" height=\"139\" \/><\/td>\n<\/tr>\n<tr>\n<td>Take away the second number, [latex]2[\/latex].<\/td>\n<td data-align=\"right\"><img loading=\"lazy\" decoding=\"async\" class=\"alignleft wp-image-16119 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/05\/14210133\/IMG_01_01_070.png\" alt=\"Eight blocks minus two blocks\" width=\"635\" height=\"121\" \/><\/td>\n<\/tr>\n<tr>\n<td>Count the number of blocks remaining.<\/td>\n<td data-align=\"right\"><img loading=\"lazy\" decoding=\"async\" class=\"alignleft wp-image-16120\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/05\/14210158\/IMG_01_01_071.png\" alt=\"Six blocks\" width=\"430\" height=\"113\" \/><\/td>\n<\/tr>\n<tr>\n<td>There are [latex]6[\/latex] ones blocks left.<\/td>\n<td>We have shown that [latex]8 - 2=6[\/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>Model: [latex]9 - 6[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q788582\">Show Solution<\/span><\/p>\n<div id=\"q788582\" class=\"hidden-answer\" style=\"display: none\">\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft wp-image-16121 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/05\/14210416\/IMG_01_01_072.png\" alt=\"Nine minus six equals three\" width=\"726\" height=\"141\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>Model: [latex]6 - 1[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q527873\">Show Solution<\/span><\/p>\n<div id=\"q527873\" class=\"hidden-answer\" style=\"display: none\">\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft wp-image-16122\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/05\/14210429\/IMG_01_01_073.png\" alt=\"Six minus one equals five\" width=\"375\" height=\"104\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Model the subtraction: [latex]13 - 8[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q254544\">Show Solution<\/span><\/p>\n<div id=\"q254544\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-811\" class=\"unnumbered unstyled\" style=\"width: 90%; height: 250px;\" summary=\"This image has two columns. The left column contains annotations and the right column contains base ten blocks. The left column states\" data-label=\"\">\n<tbody>\n<tr style=\"height: 65px;\">\n<td style=\"height: 65px;\">Model the first number, [latex]13[\/latex]. We use [latex]1[\/latex] ten and [latex]3[\/latex] ones.<\/td>\n<td style=\"height: 65px;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignleft wp-image-16123\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/05\/14210956\/IMG_01_01_074.png\" alt=\"One rod and three blocks\" width=\"450\" height=\"59\" \/><\/td>\n<\/tr>\n<tr style=\"height: 69px;\">\n<td style=\"height: 69px;\">Take away the second number, [latex]8[\/latex]. However, there are not [latex]8[\/latex] ones, so we will exchange the [latex]1[\/latex] ten for [latex]10[\/latex] ones.<\/td>\n<td style=\"height: 69px;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignleft wp-image-16124 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/05\/14211033\/IMG_01_01_075.png\" alt=\"Ten blocks and three blocks\" width=\"1006\" height=\"143\" \/><\/td>\n<\/tr>\n<tr style=\"height: 50px;\">\n<td style=\"height: 50px;\">Now we can take away [latex]8[\/latex] ones.<\/td>\n<td style=\"height: 50px;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignleft wp-image-16126 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/05\/14211658\/IMG_01_01_076.png\" alt=\"Thirteen blocks minus eight blocks\" width=\"1006\" height=\"96\" \/><\/td>\n<\/tr>\n<tr style=\"height: 55px;\">\n<td style=\"height: 55px;\">Count the blocks remaining.<\/td>\n<td style=\"height: 55px;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignleft wp-image-16127\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/05\/14211732\/IMG_01_01_0771.png\" alt=\"Five blocks\" width=\"175\" height=\"45\" \/><\/td>\n<\/tr>\n<tr style=\"height: 11px;\">\n<td style=\"height: 11px;\">There are five ones left.<\/td>\n<td style=\"height: 11px;\">We have shown that [latex]13 - 8=5[\/latex] .<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>As we did with addition, we can describe the models as ones blocks and tens rods, or we can simply say ones and tens.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p>Model the subtraction: [latex]12 - 7[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q493917\">Show Solution<\/span><\/p>\n<div id=\"q493917\" class=\"hidden-answer\" style=\"display: none\">\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft wp-image-16129 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/05\/14212226\/IMG_01_01_078.png\" alt=\"Twelve minus seven equals five\" width=\"896\" height=\"131\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>Model the subtraction: [latex]14 - 8[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q445440\">Show Solution<\/span><\/p>\n<div id=\"q445440\" class=\"hidden-answer\" style=\"display: none\">\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft wp-image-16130 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/05\/14212242\/IMG_01_01_079.png\" alt=\"Fourteen minus eight equals six\" width=\"1029\" height=\"131\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Model the subtraction: [latex]43 - 26[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q746173\">Show Solution<\/span><\/p>\n<div id=\"q746173\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<br \/>\nBecause [latex]43 - 26[\/latex] means [latex]43[\/latex] take away [latex]26[\/latex], we begin by modeling the [latex]43[\/latex].<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-16131 size-full alignnone\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/05\/14212445\/IMG_01_01_080.png\" alt=\"Four rods and three blocks\" width=\"757\" height=\"309\" \/><\/p>\n<p>Now, we need to take away [latex]26[\/latex], which is [latex]2[\/latex] tens and [latex]6[\/latex] ones. We cannot take away [latex]6[\/latex] ones from [latex]3[\/latex] ones. So, we exchange [latex]1[\/latex] ten for [latex]10[\/latex] ones.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-16132 size-full aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/05\/14212517\/IMG_01_01_081.png\" alt=\"Four rods and three ones broken down into three rods and thirteen blocks.\" width=\"1744\" height=\"356\" \/><\/p>\n<p>Now we can take away [latex]2[\/latex] tens and [latex]6[\/latex] ones.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-16133 size-full aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/05\/14212602\/IMG_01_01_082.png\" alt=\"Three rods and thirteen blocks minus two rods and six blocks equals one rod and seven blocks\" width=\"1583\" height=\"316\" \/><\/p>\n<p>Count the number of blocks remaining. There is [latex]1[\/latex] ten and [latex]7[\/latex] ones, which is [latex]17[\/latex].<br \/>\n[latex]43 - 26=17[\/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>Model the subtraction: [latex]42 - 27[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q564148\">Show Solution<\/span><\/p>\n<div id=\"q564148\" class=\"hidden-answer\" style=\"display: none\">\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft wp-image-16134 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/05\/14212700\/IMG_01_01_083.png\" alt=\"Forty-two minus twenty-seven equals fifteen, or three rods and twelve blocks minus two rods and seven blocks equals one rod and five blocks.\" width=\"900\" height=\"422\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>Model the subtraction: [latex]45 - 29[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q980973\">Show Solution<\/span><\/p>\n<div id=\"q980973\" class=\"hidden-answer\" style=\"display: none\">\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft wp-image-16135 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2302\/2017\/05\/14212805\/IMG_01_01_084.png\" alt=\"Forty-five minus twenty-nine equals sixteen, or three rods and fifteen blocks minus two rods and nine blocks equals one rod and six blocks\" width=\"900\" height=\"422\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>Watch the video below to see more examples of using base 10 blocks to model subtraction.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Model Subtraction of Two Digit Whole Numbers Using Base Ten Blocks\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/FQI0IgA-7fI?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-9193\">\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>Model Subtraction of Two Digit Whole Numbers Using Base Ten Blocks. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/FQI0IgA-7fI\">https:\/\/youtu.be\/FQI0IgA-7fI<\/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 Subtraction. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/vtnAdQHCt5s\">https:\/\/youtu.be\/vtnAdQHCt5s<\/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: 143245. <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, 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":13,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Model Subtraction of Two Digit Whole Numbers Using Base Ten Blocks\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/FQI0IgA-7fI\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"The Language of Subtraction\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/vtnAdQHCt5s\",\"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 http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757\"},{\"type\":\"cc\",\"description\":\"Question ID: 143245\",\"author\":\"Alyson Day\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"IMathAS Community License CC-BY + GPL\"}]","CANDELA_OUTCOMES_GUID":"bb21dc14-63fd-4f1e-8dc3-d0d61791509f","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-9193","chapter","type-chapter","status-publish","hentry"],"part":5884,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/9193","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":19,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/9193\/revisions"}],"predecessor-version":[{"id":16136,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/9193\/revisions\/16136"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/parts\/5884"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/9193\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/wp\/v2\/media?parent=9193"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=9193"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/wp\/v2\/contributor?post=9193"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/wp\/v2\/license?post=9193"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}