<h2>Subtraction of Whole Numbers</h2>
<p>Addition and subtraction are inverse operations. Addition undoes subtraction, and subtraction undoes addition.</p>
<p>We know \(7-3=4\) because \(4+3=7.\) Knowing all the addition number facts will help with subtraction. Then we can check subtraction by adding. In the examples above, our subtractions can be checked by addition.</p>
<p>\(\begin{array}{ccccccc}\phantom{\rule{1em}{0ex}}7-3=4\hfill &amp; &amp; &amp; \text{because}\hfill &amp; &amp; &amp; \phantom{\rule{1em}{0ex}}4+3=7\hfill \\ \phantom{\rule{0.5em}{0ex}}13-8=5\hfill &amp; &amp; &amp; \text{because}\hfill &amp; &amp; &amp; \phantom{\rule{1em}{0ex}}5+8=13\hfill \\ 43-26=17\hfill &amp; &amp; &amp; \text{because}\hfill &amp; &amp; &amp; 17+26=43\hfill \end{array}\)</p>
<div class="ns-school-emp">
<h3>Example</h3>
<div class="ns-school-defn">
<p>Subtract and then check by adding:</p>
<ol style="list-style-type: lower-alpha;" type="1">
<li>\(9-7\)</li>
<li>\(8-3.\)</li>
</ol>
<h4>Solution</h4>
<table>
<tbody>
<tr>
<td>(a)</td>
<td> </td>
</tr>
<tr>
<td> </td>
<td>\(9-7\)</td>
</tr>
<tr>
<td>Subtract 7 from 9.</td>
<td>\(2\)</td>
</tr>
<tr>
<td>Check with addition.<br/>
 \(2+7=9✓\)</td>
<td> </td>
</tr>
</tbody>
</table>
<table>
<tbody>
<tr>
<td>(b)</td>
<td> </td>
</tr>
<tr>
<td> </td>
<td>\(8-3\)</td>
</tr>
<tr>
<td>Subtract 3 from 8.</td>
<td>\(5\)</td>
</tr>
<tr>
<td>Check with addition.<br/>
 \(5+3=8✓\)</td>
<td> </td>
</tr>
</tbody>
</table>
</div>
</div>
<div class="ns-tutorial">
<div class="ns-school-defn2">
<h3>Extra:</h3>
<p>Subtract and then check by adding:</p>
<p>\(7-0\)</p>
<h4>Solution:</h4>
<p>7 − 0 = 7; 7 + 0 = 7</p>
</div>
</div>
<div class="ns-tutorial">
<div class="ns-school-defn2">
<h3>Extra:</h3>
<div data-type="note">
<div>
<div>
<p>Subtract and then check by adding:</p>
<p>\(6-2\)</p>
</div>
<div>
<h4>Solution</h4>
<p>6 − 2 = 4; 2 + 4 = 6</p>
</div>
</div>
</div>
</div>
</div>
<p>To subtract numbers with more than one digit, it is usually easier to write the numbers vertically in columns just as we did for addition. Align the digits by place value, and then subtract each column starting with the ones and then working to the left.</p>
<div class="ns-school-emp">
<h3>Example</h3>
<div class="ns-school-defn">
<p>Subtract and then check by adding: \(89-61.\)</p>
<h4>Solution</h4>
<table>
<tbody>
<tr>
<td>Write the numbers so the ones and tens digits line up vertically.</td>
<td>\(\begin{array}{r}<br/>
 89 \\<br/>
 \underline{-\;61} \\<br/>
 \end{array}\)</td>
</tr>
<tr>
<td>Subtract the digits in each place value.<br/>
 Subtract the ones: \(9-1=8\)<br/>
 Subtract the tens: \(8-6=2\)</td>
<td>\(\begin{array}{r}<br/>
 89 \\<br/>
 -\;61 \\<br/>
 \hline<br/>
 28 \\<br/>
 \end{array}\)</td>
</tr>
<tr>
<td>
<p>Check using addition.<br/>
 \(\begin{array}{r}<br/>
 28 \\<br/>
 +\;61 \\<br/>
 \hline<br/>
 89 \\<br/>
 \end{array}\)</p>
</td>
<td> </td>
</tr>
</tbody>
</table>
<p>Our answer is correct.</p>
</div>
</div>
<div class="ns-tutorial">
<div class="ns-school-defn2">
<h3>Extra:</h3>
<p>Subtract and then check by adding: \(86-54.\)</p>
<h4>Solution</h4>
<p>86 − 54 = 32 because 54 + 32 = 86</p>
</div>
</div>
<div class="ns-tutorial">
<div class="ns-school-defn2">
<h3>Extra:</h3>
<p>Subtract and then check by adding: \(99-74.\)</p>
<h4>Solution </h4>
<p>99 − 74 = 25 because 74 + 25 = 99</p>
</div>
</div>
<p>When we modeled subtracting \(26\) from \(43,\) we exchanged \(1\) ten for \(10\) ones. When we do this without the model, we say we borrow \(1\) from the tens place and add \(10\) to the ones place.</p>

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Properties of Subtraction

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Mathematics

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Properties of Subtraction

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