{"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":"2024-04-29T18:31:52","modified_gmt":"2024-04-29T18:31:52","slug":"notation-and-modeling-subtraction-of-whole-numbers","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/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 of single and double digit numbers<\/li>\r\n \t<li>Translate subtraction from math notation to words<\/li>\r\n \t<li>Model subtraction of whole numbers<\/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[embed]https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=143245&amp;theme=oea&amp;iframe_resize_id=mom1[\/embed]\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 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=\".\">\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=\"alignnone\" 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=\"An image of 7 blocks, labeled with the number 7. \" width=\"199\" height=\"49\" \/><\/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=\"alignnone\" 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=\"An image with two groups of blocks, 7 blocks total. On the left there are 3 blocks, with a circle around them and an arrow pointing away from the group, signaling their removal. On the right there are 4 blocks. \" width=\"199\" height=\"69\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Count the number of blocks remaining.<\/td>\r\n<td><img class=\"alignnone\" 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=\"An image of 4 blocks. \" width=\"199\" height=\"27\" \/><\/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 class=\"alignnone\" 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=\"An image of 8 blocks, labeled with the number 8. \" width=\"199\" height=\"44\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Take away the second number, [latex]2[\/latex].<\/td>\r\n<td><img class=\"alignnone\" 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=\"An image with two groups of blocks, 8 blocks total. On the left there are 2 blocks, with a circle around them and an arrow pointing away from the group, signaling their removal. On the right there are 6 blocks. \" width=\"199\" height=\"54\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Count the number of blocks remaining.<\/td>\r\n<td><img class=\"alignnone\" 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=\"An image of 6 blocks. \" width=\"199\" height=\"24\" \/><\/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=\"alignnone\" 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=\"An image with two groups of blocks, 9 blocks total. On the left there are 6 blocks, with a circle around them and an arrow pointing away from the group, signaling their removal. On the right there are 3 blocks. Below, the image is labeled with the equation &quot;9 - 6 = 3&quot;. \" width=\"163\" height=\"85\" \/>\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=\"alignnone\" 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=\"An image with two groups of blocks, 6 blocks total. On the left there is 1 block, with a circle around it and an arrow pointing away from the group, signaling its removal. On the right there are 5 blocks. Below, the image is labeled with the equation &quot;6 - 1 = 5&quot;. \" width=\"119\" height=\"63\" \/>\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 class=\"alignnone\" 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=\"An image containing two items. The first item is 1 horizontal rod containing 10 blocks. The second item is 3 individual blocks.\" width=\"327\" height=\"27\" \/><\/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 class=\"alignnone\" 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=\"An image with two groups of items. The first is a group of 10 individual blocks, labeled with the number 10. The second is 3 individual blocks, labeled with the number 3. \" width=\"327\" height=\"58\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Now we can take away [latex]8[\/latex] ones.<\/td>\r\n<td><img class=\"alignnone\" 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=\"An image showing two groups of items. The first is a group of 8 blocks, circled with an arrow indicating their removal. The second is a group of five blocks. \" width=\"327\" height=\"100\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Count the blocks remaining.<\/td>\r\n<td><img class=\"alignnone\" 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=\"An image of 5 blocks. \" width=\"327\" height=\"27\" \/><\/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 class=\"alignnone\" 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=\"An image with two groups of blocks, 12 blocks total. On the left there are 7 blocks, with a circle around them and an arrow pointing away from the group, signaling their removal. On the right there are 5 blocks. Below, the image is labeled with the equation &quot;12 - 7 = 5&quot;. \" width=\"216\" height=\"86\" \/>\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 class=\"alignnone\" 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=\"An image with two groups of blocks, 14 blocks total. On the left there are 8 blocks, with a circle around them and an arrow pointing away from the group, signaling their removal. On the right there are 6 blocks. Below, the image is labeled with the equation &quot;14 - 8 = 6&quot;. \" width=\"249\" height=\"87\" \/>\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 class=\"alignnone\" 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=\"An image including 3 horizontal rods containing 10 blocks each, and 12 individual blocks. Two of the rods and 7 of the individual blocks are circled with an arrow indicating their removal. Below, the image is labeled with the equation &quot;42 - 27 = 15&quot;. \" width=\"243\" height=\"166\" \/>\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 class=\"alignnone\" 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=\"An image including 3 horizontal rods containing 10 blocks each, and 15 individual blocks. Two of the rods and 9 of the individual blocks are circled with an arrow indicating their removal. Below, the image is labeled with the equation &quot;45 - 29 = 16&quot;. \" width=\"197\" height=\"149\" \/>\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 of single and double digit numbers<\/li>\n<li>Translate subtraction from math notation to words<\/li>\n<li>Model subtraction of whole numbers<\/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&#38;theme=oea&#38;iframe_resize_id=ohm143245&#38;show_question_numbers\" 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 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=\".\">\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=\"alignnone\" 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=\"An image of 7 blocks, labeled with the number 7.\" width=\"199\" height=\"49\" \/><\/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=\"alignnone\" 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=\"An image with two groups of blocks, 7 blocks total. On the left there are 3 blocks, with a circle around them and an arrow pointing away from the group, signaling their removal. On the right there are 4 blocks.\" width=\"199\" height=\"69\" \/><\/td>\n<\/tr>\n<tr>\n<td>Count the number of blocks remaining.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" 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=\"An image of 4 blocks.\" width=\"199\" height=\"27\" \/><\/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 loading=\"lazy\" decoding=\"async\" class=\"alignnone\" 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=\"An image of 8 blocks, labeled with the number 8.\" width=\"199\" height=\"44\" \/><\/td>\n<\/tr>\n<tr>\n<td>Take away the second number, [latex]2[\/latex].<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" 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=\"An image with two groups of blocks, 8 blocks total. On the left there are 2 blocks, with a circle around them and an arrow pointing away from the group, signaling their removal. On the right there are 6 blocks.\" width=\"199\" height=\"54\" \/><\/td>\n<\/tr>\n<tr>\n<td>Count the number of blocks remaining.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" 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=\"An image of 6 blocks.\" width=\"199\" height=\"24\" \/><\/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=\"alignnone\" 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=\"An image with two groups of blocks, 9 blocks total. On the left there are 6 blocks, with a circle around them and an arrow pointing away from the group, signaling their removal. On the right there are 3 blocks. Below, the image is labeled with the equation &quot;9 - 6 = 3&quot;.\" width=\"163\" height=\"85\" \/><\/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=\"alignnone\" 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=\"An image with two groups of blocks, 6 blocks total. On the left there is 1 block, with a circle around it and an arrow pointing away from the group, signaling its removal. On the right there are 5 blocks. Below, the image is labeled with the equation &quot;6 - 1 = 5&quot;.\" width=\"119\" height=\"63\" \/><\/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 loading=\"lazy\" decoding=\"async\" class=\"alignnone\" 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=\"An image containing two items. The first item is 1 horizontal rod containing 10 blocks. The second item is 3 individual blocks.\" width=\"327\" height=\"27\" \/><\/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 loading=\"lazy\" decoding=\"async\" class=\"alignnone\" 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=\"An image with two groups of items. The first is a group of 10 individual blocks, labeled with the number 10. The second is 3 individual blocks, labeled with the number 3.\" width=\"327\" height=\"58\" \/><\/td>\n<\/tr>\n<tr>\n<td>Now we can take away [latex]8[\/latex] ones.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" 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=\"An image showing two groups of items. The first is a group of 8 blocks, circled with an arrow indicating their removal. The second is a group of five blocks.\" width=\"327\" height=\"100\" \/><\/td>\n<\/tr>\n<tr>\n<td>Count the blocks remaining.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" 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=\"An image of 5 blocks.\" width=\"327\" height=\"27\" \/><\/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 loading=\"lazy\" decoding=\"async\" class=\"alignnone\" 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=\"An image with two groups of blocks, 12 blocks total. On the left there are 7 blocks, with a circle around them and an arrow pointing away from the group, signaling their removal. On the right there are 5 blocks. Below, the image is labeled with the equation &quot;12 - 7 = 5&quot;.\" width=\"216\" height=\"86\" \/><\/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 loading=\"lazy\" decoding=\"async\" class=\"alignnone\" 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=\"An image with two groups of blocks, 14 blocks total. On the left there are 8 blocks, with a circle around them and an arrow pointing away from the group, signaling their removal. On the right there are 6 blocks. Below, the image is labeled with the equation &quot;14 - 8 = 6&quot;.\" width=\"249\" height=\"87\" \/><\/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 loading=\"lazy\" decoding=\"async\" class=\"alignnone\" 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=\"An image including 3 horizontal rods containing 10 blocks each, and 12 individual blocks. Two of the rods and 7 of the individual blocks are circled with an arrow indicating their removal. Below, the image is labeled with the equation &quot;42 - 27 = 15&quot;.\" width=\"243\" height=\"166\" \/><\/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 loading=\"lazy\" decoding=\"async\" class=\"alignnone\" 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=\"An image including 3 horizontal rods containing 10 blocks each, and 15 individual blocks. Two of the rods and 9 of the individual blocks are circled with an arrow indicating their removal. Below, the image is labeled with the equation &quot;45 - 29 = 16&quot;.\" width=\"197\" height=\"149\" \/><\/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 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