{"id":4597,"date":"2020-04-21T00:19:05","date_gmt":"2020-04-21T00:19:05","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/chapter\/subtracting-whole-numbers\/"},"modified":"2025-09-02T22:20:18","modified_gmt":"2025-09-02T22:20:18","slug":"subtracting-whole-numbers","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/chapter\/subtracting-whole-numbers\/","title":{"raw":"Subtracting Whole Numbers: Notation and Modeling","rendered":"Subtracting Whole Numbers: Notation and Modeling"},"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>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>seven minus three<\/em> and the result is <em>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.\">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th>Operation<\/th>\r\n<th>Notation<\/th>\r\n<th>Expression<\/th>\r\n<th>Read as<\/th>\r\n<th>Result<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td>Subtraction<\/td>\r\n<td>[latex]-[\/latex]<\/td>\r\n<td>[latex]7 - 3[\/latex]<\/td>\r\n<td>seven minus three<\/td>\r\n<td>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\">\r\n \t<li>We read this as <em>eight minus one<\/em>. The result is <em>the difference of eight and one<\/em>.<\/li>\r\n \t<li>We read this as <em>twenty-six minus fourteen<\/em>. The result is <em>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[ohm_question hide_question_numbers=1]143245[\/ohm_question]\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>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\u00a0[latex]1[\/latex] and a rod represents\u00a0[latex]10[\/latex]. 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=\".\">\r\n<tbody>\r\n<tr>\r\n<td>We start by modeling the first number, [latex]7[\/latex].<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215416\/CNX_BMath_Figure_01_03_018_img-02.png\" alt=\"CNX_BMath_Figure_01_03_018_img-02.png\" \/><\/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 src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215417\/CNX_BMath_Figure_01_03_018_img-03.png\" alt=\"CNX_BMath_Figure_01_03_018_img-03.png\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Count the number of blocks remaining.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215418\/CNX_BMath_Figure_01_03_018_img-04.png\" alt=\"CNX_BMath_Figure_01_03_018_img-04.png\" \/><\/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 \">\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><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215419\/CNX_BMath_Figure_01_03_019_img-02.png\" alt=\"CNX_BMath_Figure_01_03_019_img-02.png\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Take away the second number, [latex]2[\/latex].<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215420\/CNX_BMath_Figure_01_03_019_img-03.png\" alt=\"CNX_BMath_Figure_01_03_019_img-03.png\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Count the number of blocks remaining.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215421\/CNX_BMath_Figure_01_03_019_img-04.png\" alt=\"CNX_BMath_Figure_01_03_019_img-04.png\" \/><\/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 src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215422\/CNX_BMath_Figure_01_03_006.png\" alt=\"No Alt Text\" \/>\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 src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215423\/CNX_BMath_Figure_01_03_007.png\" alt=\"No Alt Text\" \/>\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%;\" summary=\"This image has two columns. The left column contains annotations and the right column contains base ten blocks. The left column states \">\r\n<tbody>\r\n<tr>\r\n<td>Model the first number, [latex]13[\/latex]. We use [latex]1[\/latex] ten and [latex]3[\/latex] ones.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215424\/CNX_BMath_Figure_01_03_020_img-02.png\" alt=\"CNX_BMath_Figure_01_03_020_img-02.png\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>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><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215426\/CNX_BMath_Figure_01_03_020_img-03.png\" alt=\"CNX_BMath_Figure_01_03_020_img-03.png\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Now we can take away [latex]8[\/latex] ones.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215427\/CNX_BMath_Figure_01_03_020_img-04.png\" alt=\"CNX_BMath_Figure_01_03_020_img-04.png\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Count the blocks remaining.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215429\/CNX_BMath_Figure_01_03_020_img-05.png\" alt=\"CNX_BMath_Figure_01_03_020_img-05.png\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>There are five ones left.<\/td>\r\n<td>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 src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215431\/CNX_BMath_Figure_01_03_011_img.png\" alt=\"No Alt Text\" \/>\r\n\r\n[\/hidden-answer]\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 src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215432\/CNX_BMath_Figure_01_03_012_img.png\" alt=\"No Alt Text\" \/>\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 src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215433\/CNX_BMath_Figure_01_03_013_img.png\" alt=\"An image containing two items. The first item is 4 horizontal rods containing 10 blocks each. The second item is 3 individual blocks.\" \/>\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 src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215435\/CNX_BMath_Figure_01_03_014_img.png\" alt=\"This figure contains two groups. The first group on the left includes 3 rows of blue base 10 blocks and 1 red row of 10 blocks. This is labeled 4 tens. Alongside the first row of ten blocks are 3 individual blocks. This is labeled 3 ones. An arrow points to the right to the second group in which there are three rows of 10 base blocks labeled 3 tens. Next to this is a row of 3 blue individual blocks and two rows each with five individual blocks in red. This is labeled 13 ones.\" \/>\r\nNow we can take away [latex]2[\/latex] tens and [latex]6[\/latex] ones.\r\n\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215437\/CNX_BMath_Figure_01_03_015_img.png\" alt=\"This image includes one row of base ten blocks at the top of the image; Next to it are seven individual blocks. Below this, is a group of two rows of base ten blocks, and two rows of 3 individual blocks with a circle around all. The arrow points to the right and shows one row of ten blocks and seven individual blocks underneath.\" \/>\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 src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215439\/CNX_BMath_Figure_01_03_016_img.png\" alt=\"No Alt Text\" \/>\r\n\r\n[\/hidden-answer]\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 src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215440\/CNX_BMath_Figure_01_03_017_img.png\" alt=\"No Alt Text\" \/>\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>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>seven minus three<\/em> and the result is <em>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.\">\n<thead>\n<tr valign=\"top\">\n<th>Operation<\/th>\n<th>Notation<\/th>\n<th>Expression<\/th>\n<th>Read as<\/th>\n<th>Result<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td>Subtraction<\/td>\n<td>[latex]-[\/latex]<\/td>\n<td>[latex]7 - 3[\/latex]<\/td>\n<td>seven minus three<\/td>\n<td>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\">\n<li>We read this as <em>eight minus one<\/em>. The result is <em>the difference of eight and one<\/em>.<\/li>\n<li>We read this as <em>twenty-six minus fourteen<\/em>. The result is <em>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=\"ohm143245\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=143245&theme=oea&iframe_resize_id=ohm143245\" width=\"100%\" height=\"150\"><\/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>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\u00a0[latex]1[\/latex] and a rod represents\u00a0[latex]10[\/latex]. 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=\".\">\n<tbody>\n<tr>\n<td>We start by modeling the first number, [latex]7[\/latex].<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215416\/CNX_BMath_Figure_01_03_018_img-02.png\" alt=\"CNX_BMath_Figure_01_03_018_img-02.png\" \/><\/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 decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215417\/CNX_BMath_Figure_01_03_018_img-03.png\" alt=\"CNX_BMath_Figure_01_03_018_img-03.png\" \/><\/td>\n<\/tr>\n<tr>\n<td>Count the number of blocks remaining.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215418\/CNX_BMath_Figure_01_03_018_img-04.png\" alt=\"CNX_BMath_Figure_01_03_018_img-04.png\" \/><\/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\">\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><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215419\/CNX_BMath_Figure_01_03_019_img-02.png\" alt=\"CNX_BMath_Figure_01_03_019_img-02.png\" \/><\/td>\n<\/tr>\n<tr>\n<td>Take away the second number, [latex]2[\/latex].<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215420\/CNX_BMath_Figure_01_03_019_img-03.png\" alt=\"CNX_BMath_Figure_01_03_019_img-03.png\" \/><\/td>\n<\/tr>\n<tr>\n<td>Count the number of blocks remaining.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215421\/CNX_BMath_Figure_01_03_019_img-04.png\" alt=\"CNX_BMath_Figure_01_03_019_img-04.png\" \/><\/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 decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215422\/CNX_BMath_Figure_01_03_006.png\" alt=\"No Alt Text\" \/><\/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 decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215423\/CNX_BMath_Figure_01_03_007.png\" alt=\"No Alt Text\" \/><\/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%;\" summary=\"This image has two columns. The left column contains annotations and the right column contains base ten blocks. The left column states\">\n<tbody>\n<tr>\n<td>Model the first number, [latex]13[\/latex]. We use [latex]1[\/latex] ten and [latex]3[\/latex] ones.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215424\/CNX_BMath_Figure_01_03_020_img-02.png\" alt=\"CNX_BMath_Figure_01_03_020_img-02.png\" \/><\/td>\n<\/tr>\n<tr>\n<td>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><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215426\/CNX_BMath_Figure_01_03_020_img-03.png\" alt=\"CNX_BMath_Figure_01_03_020_img-03.png\" \/><\/td>\n<\/tr>\n<tr>\n<td>Now we can take away [latex]8[\/latex] ones.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215427\/CNX_BMath_Figure_01_03_020_img-04.png\" alt=\"CNX_BMath_Figure_01_03_020_img-04.png\" \/><\/td>\n<\/tr>\n<tr>\n<td>Count the blocks remaining.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215429\/CNX_BMath_Figure_01_03_020_img-05.png\" alt=\"CNX_BMath_Figure_01_03_020_img-05.png\" \/><\/td>\n<\/tr>\n<tr>\n<td>There are five ones left.<\/td>\n<td>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 decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215431\/CNX_BMath_Figure_01_03_011_img.png\" alt=\"No Alt Text\" \/><\/p>\n<\/div>\n<\/div>\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 decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215432\/CNX_BMath_Figure_01_03_012_img.png\" alt=\"No Alt Text\" \/><\/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 decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215433\/CNX_BMath_Figure_01_03_013_img.png\" alt=\"An image containing two items. The first item is 4 horizontal rods containing 10 blocks each. The second item is 3 individual blocks.\" \/><br \/>\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.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215435\/CNX_BMath_Figure_01_03_014_img.png\" alt=\"This figure contains two groups. The first group on the left includes 3 rows of blue base 10 blocks and 1 red row of 10 blocks. This is labeled 4 tens. Alongside the first row of ten blocks are 3 individual blocks. This is labeled 3 ones. An arrow points to the right to the second group in which there are three rows of 10 base blocks labeled 3 tens. Next to this is a row of 3 blue individual blocks and two rows each with five individual blocks in red. This is labeled 13 ones.\" \/><br \/>\nNow we can take away [latex]2[\/latex] tens and [latex]6[\/latex] ones.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215437\/CNX_BMath_Figure_01_03_015_img.png\" alt=\"This image includes one row of base ten blocks at the top of the image; Next to it are seven individual blocks. Below this, is a group of two rows of base ten blocks, and two rows of 3 individual blocks with a circle around all. The arrow points to the right and shows one row of ten blocks and seven individual blocks underneath.\" \/><br \/>\nCount 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 decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215439\/CNX_BMath_Figure_01_03_016_img.png\" alt=\"No Alt Text\" \/><\/p>\n<\/div>\n<\/div>\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 decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24215440\/CNX_BMath_Figure_01_03_017_img.png\" alt=\"No Alt Text\" \/><\/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-4597\">\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":9,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Model Subtraction of Two Digit Whole Numbers Using Base Ten Blocks\",\"author\":\"James Sousa 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