<h2>Model Subtraction of Whole Numbers</h2>
<p><a href="https://data.ulearngo.com/assets/173166e5-56e6-42f1-a4ae-7dc5d785a1cb"><img alt="model-subtraction" class="size-full wp-image-101881 alignnone" height="538" src="https://data.ulearngo.com/assets/173166e5-56e6-42f1-a4ae-7dc5d785a1cb" width="800"/></a></p>
<p>A model can help us visualize the process of subtraction much as it did with addition. Again, we will use \(\text{base-10}\) blocks. Remember a block represents 1 and a rod represents 10. Let’s start by modeling the subtraction expression we just considered, \(7-3.\)</p>
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<td>We start by modeling the first number, 7.</td>
<td><img alt="CNX_BMath_Figure_01_03_018_img-02.png" src="https://data.ulearngo.com/assets/dccefd18-6a1a-4493-8bf4-3c334e6194f1"/></td>
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<td>Now take away the second number, 3. We'll circle 3 blocks to show that we are taking them away.</td>
<td><img alt="CNX_BMath_Figure_01_03_018_img-03.png" src="https://data.ulearngo.com/assets/79bbd513-1593-4f99-ac93-0f83093cc47f"/></td>
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<td>Count the number of blocks remaining.</td>
<td><img alt="CNX_BMath_Figure_01_03_018_img-04.png" src="https://data.ulearngo.com/assets/438ff6d8-5c93-4a06-8e97-38b70d3439b6"/></td>
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<td>There are 4 ones blocks left.</td>
<td>We have shown that \(7-3=4\).</td>
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<h3>Example</h3>
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<p>Model the subtraction: \(8-2.\)</p>
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<h4>Solution</h4>
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<table data-label="" summary="This image has two columns. The left column contains annotations and the right column contains base ten blocks.  The left column states “8 minus 2 means the difference between 8 and 2. Model the first number 8, which is followed by 8 individual blocks labeled 8 underneath. The next line says “take away the second number, 2.  This is followed by the same 8 individual blocks, with a circle around the first 2. The next line reads “count the number of blocks remaining” followed by six individual blocks. The last line says “there are six ones blocks left” followed by “we have shown that 8 minus 2 equals 6.">
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<td>\(8-2\) means the difference of 8 and 2.</td>
<td> </td>
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<td>Model the first, 8.</td>
<td><img alt="CNX_BMath_Figure_01_03_019_img-02.png" src="https://data.ulearngo.com/assets/54936951-1151-4d5e-ab39-51ffb401ad24"/></td>
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<td>Take away the second number, 2.</td>
<td><img alt="CNX_BMath_Figure_01_03_019_img-03.png" src="https://data.ulearngo.com/assets/bc381811-4a89-44cd-b2aa-9c030b92729c"/></td>
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<td>Count the number of blocks remaining.</td>
<td><img alt="CNX_BMath_Figure_01_03_019_img-04.png" src="https://data.ulearngo.com/assets/5bd44f02-2f63-49ca-bc11-7460fe42e221"/></td>
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<td>There are 6 ones blocks left.</td>
<td>We have shown that \(8-2=6\).</td>
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<h3>Extra:</h3>
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<p>Model: \(9-6.\)</p>
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<section><img alt="No Alt Text" src="https://data.ulearngo.com/assets/65b2170a-931a-461d-92a2-eeee8e591825"/></section>
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<h3>Extra:</h3>
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<p>Model: \(6-1.\)</p>
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<section><img alt="No Alt Text" src="https://data.ulearngo.com/assets/913a7a3e-18cc-4d1d-a782-bec48f6a8351"/></section>
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<h3>Example</h3>
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<p>Model the subtraction: \(13-8.\)</p>
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<h4>Solution</h4>
<table data-label="" summary="This image has two columns. The left column contains annotations and the right column contains base ten blocks. The left column states “Model the first number 13. We use 1 ten and 3 ones,” which is followed by one row of 10 blocks and 3 individual blocks. The next line says “take away the second number, 8. However, there are not eight ones, so we will exchange the 1 ten for 10 ones. This is followed by the same 10 individual blocks, and three individual blocks. The next line reads “now we can take away 8 ones” which is followed by 10 individual blocks then two individual blocks, then three individual blocks, with a circle around the 10 individual blocks. The next line states “count the number of blocks remaining” followed by 2 individual blocks, then three individual blocks. The last line says “there are five ones blocks left” followed by “we have shown that 13 minus 8 equals 5.">
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<td>Model the first number, 13. We use 1 ten and 3 ones.</td>
<td><img alt="CNX_BMath_Figure_01_03_020_img-02.png" src="https://data.ulearngo.com/assets/50b41892-20ee-444b-b72f-2efa95429c43"/></td>
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<td>Take away the second number, 8. However, there are not 8 ones, so we will exchange the 1 ten for 10 ones.</td>
<td><img alt="CNX_BMath_Figure_01_03_020_img-03.png" src="https://data.ulearngo.com/assets/eac4685d-fa13-4a94-979d-12e8e22ec6a2"/></td>
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<td>Now we can take away 8 ones.</td>
<td><img alt="CNX_BMath_Figure_01_03_020_img-04.png" src="https://data.ulearngo.com/assets/78a78c50-5018-4e49-86f9-0674f6f44b83"/></td>
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<td>Count the blocks remaining.</td>
<td><img alt="CNX_BMath_Figure_01_03_020_img-05.png" src="https://data.ulearngo.com/assets/2a2d400b-d8a9-4cd6-894d-4cfab1bdf9ca"/></td>
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<td>There are five ones left.</td>
<td>We have shown that \(13-8=5\).</td>
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<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>
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<h3>Extra:</h3>
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<p>Model the subtraction: \(12-7.\)</p>
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<section><img alt="No Alt Text" src="https://data.ulearngo.com/assets/3810c931-e0dd-42b7-9323-22bef97727f5"/></section>
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<h3>Extra:</h3>
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<p>Model the subtraction: \(14-8.\)</p>
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<section><img alt="No Alt Text" src="https://data.ulearngo.com/assets/55359825-7244-4c75-b98c-1640d61834ef"/></section>
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<h3>Example</h3>
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<p>Model the subtraction: \(43-26.\)</p>
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<h4>Solution</h4>
<p>Because \(43-26\) means \(43\) take away \(26,\) we begin by modeling the \(43.\) </p>
<img alt="An image containing two items. The first item is 4 horizontal rods containing 10 blocks each. The second item is 3 individual blocks." src="https://data.ulearngo.com/assets/01c3c764-873e-4e14-9d05-bcac7d25ab1c"/>
<p>Now, we need to take away \(26,\) which is \(2\) tens and \(6\) ones. We cannot take away \(6\) ones from \(3\) ones. So, we exchange \(1\) ten for \(10\) ones.</p>
<img 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." src="https://data.ulearngo.com/assets/ff2bf651-0ba8-4ac5-bedd-159125fc232e"/>
<p>Now we can take away \(2\) tens and \(6\) ones.</p>
<img 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." src="https://data.ulearngo.com/assets/8e7acd3a-d2d7-4570-a7f7-0a5ed2b4615c"/>
<p>Count the number of blocks remaining. There is \(1\) ten and \(7\) ones, which is \(17.\)</p>
<p>\(43-26=17\)</p>
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<h3>Extra:</h3>
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<p>Model the subtraction: \(42-27.\) </p>
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<section><img alt="No Alt Text" src="https://data.ulearngo.com/assets/d4cacfab-863c-4aa8-abe6-794a646afea5"/></section>
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<h3>Extra:</h3>
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<p>Model the subtraction: \(45-29.\)</p>
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<section><img alt="No Alt Text" src="https://data.ulearngo.com/assets/d8534074-8058-484b-b77d-cf6820594b3d"/></section>
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<section></section>
<h2>Optional Video: Model Subtraction of Three Digit Whole Numbers Using Base Ten Blocks</h2>
<p>This video below by <a href="http://www.mathispower4u.com/">Mathispower4u</a> explains subtraction of three digit whole numbers by using base ten blocks.</p>
<p><iframe allowfullscreen="allowfullscreen" frameborder="0" height="360" src="https://www.youtube.com/embed/znEkj0vlooI?rel=0&amp;modestbranding=1&amp;cc_lang_pref=en&amp;cc_load_policy=1" width="640"></iframe></p>

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Model Subtraction

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Model Subtraction

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