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388 lines
9.7 KiB
HTML
388 lines
9.7 KiB
HTML
<!DOCTYPE html>
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<title>Adding Decimals</title>
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<meta name="description" content="Adding decimals is easy when you keep your work neat">
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<div id="logo"><a href="index.html"><img src="images/style/logo.svg" alt="Math is Fun"></a></div>
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<article id="content" role="main">
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<!-- #BeginEditable "Body" -->
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<h1 class="center">Adding and Subtracting Decimals</h1>
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<div style="background: url(numbers/images/hdr-decimal-led.jpg) no-repeat; width: 100%; height: 80px; background-position: center center;"></div>
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<p class="center"><i>Adding decimals is easy when you keep your work <b>neat</b></i></p>
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<p>To add decimals, follow these steps:</p>
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<ul>
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<li>Write down the numbers, one under the other, with the <b>decimal points lined up</b></li>
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<li><b>Put in zeros</b> so the numbers have the same length (<a href="#zero">see below</a> for why that is OK)</li>
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<li><b>Then add</b>, using <a href="numbers/addition-column.html">column addition</a>, remembering to put the decimal point in the answer</li>
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</ul>
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<div class="example">
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<h3>Example: Add 1.452 to 1.3</h3>
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<div class="clear">
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<table style="border: 0; margin:auto;">
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<tbody>
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<tr>
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<td>Line up the decimal points:</td>
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<td> </td>
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<td> </td>
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<td>1<span class="hilite">.</span>452</td>
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</tr>
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<tr>
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<td> </td>
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<td> </td>
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<td>+</td>
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<td>1<span class="hilite">.</span>3</td>
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</tr>
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<tr>
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<td> </td>
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<td> </td>
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<td> </td>
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<td> </td>
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</tr>
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<tr>
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<td>"Pad" with zeros:</td>
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<td> </td>
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<td> </td>
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<td>1.452</td>
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</tr>
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<tr>
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<td> </td>
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<td> </td>
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<td>+</td>
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<td>1.3<span class="hilite">00</span></td>
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</tr>
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<tr>
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<td> </td>
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<td> </td>
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<td> </td>
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<td> </td>
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</tr>
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<tr>
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<td>Add:</td>
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<td> </td>
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<td> </td>
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<td>1.452</td>
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</tr>
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<tr>
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<td> </td>
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<td> </td>
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<td>+</td>
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<td>1.300</td>
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</tr>
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<tr>
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<td> </td>
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<td> </td>
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<td> </td>
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<td class="hilite" style="border-top: 1px solid black;">2.752</td>
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</tr>
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</tbody></table>
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</div>
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</div>
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<div class="example">
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<h3>Example: Add 3.25, 0.075 and 5</h3>
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<table style="border: 0; margin:auto;">
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<tbody>
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<tr>
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<td>Line up the decimal points:</td>
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<td> </td>
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<td> </td>
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<td>3<span class="hilite">.</span>25</td>
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</tr>
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<tr>
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<td> </td>
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<td> </td>
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<td> </td>
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<td>0<span class="hilite">.</span>075</td>
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</tr>
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<tr>
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<td> </td>
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<td> </td>
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<td>+</td>
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<td>5<span class="hilite">.</span></td>
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</tr>
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<tr>
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<td> </td>
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<td> </td>
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<td> </td>
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<td> </td>
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</tr>
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<tr>
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<td>"Pad" with zeros:</td>
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<td> </td>
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<td> </td>
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<td>3.25<span class="hilite">0</span></td>
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</tr>
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<tr>
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<td> </td>
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<td> </td>
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<td> </td>
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<td>0.075</td>
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</tr>
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<tr>
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<td> </td>
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<td> </td>
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<td>+</td>
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<td>5.<span class="hilite">000</span></td>
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</tr>
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<tr>
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<td> </td>
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<td> </td>
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<td> </td>
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<td> </td>
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</tr>
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<tr>
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<td>Add:</td>
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<td> </td>
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<td> </td>
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<td>3.250</td>
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</tr>
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<tr>
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<td> </td>
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<td> </td>
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<td> </td>
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<td>0.075</td>
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</tr>
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<tr>
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<td> </td>
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<td> </td>
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<td>+</td>
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<td>5.000</td>
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</tr>
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<tr>
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<td> </td>
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<td> </td>
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<td> </td>
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<td class="hilite" style="border-top: 1px solid black;">8.325</td>
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</tr>
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</tbody></table>
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</div>
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<p>That's all there is to it: line up the decimal points, pad with zeros, then add normally.</p>
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<h2>Subtracting</h2>
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<p>To subtract, follow the same method: line up the decimal points, then <a href="numbers/subtraction-regrouping.html">subtract</a>.</p>
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<div class="example">
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<h3>Example: What is 7.368 − 1.15 ?</h3>
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<table style="border: 0; margin:auto;">
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<tbody>
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<tr>
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<td>Line up the decimal points:</td>
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<td> </td>
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<td> </td>
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<td>7<span class="hilite">.</span>368</td>
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</tr>
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<tr>
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<td> </td>
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<td> </td>
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<td>−</td>
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<td>1<span class="hilite">.</span>15</td>
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</tr>
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<tr>
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<td> </td>
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<td> </td>
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<td> </td>
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<td> </td>
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</tr>
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<tr>
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<td>"Pad" with zeros:</td>
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<td> </td>
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<td> </td>
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<td>7.368</td>
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</tr>
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<tr>
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<td> </td>
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<td> </td>
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<td>−</td>
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<td>1.15<span class="hilite">0</span></td>
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</tr>
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<tr>
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<td> </td>
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<td> </td>
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<td> </td>
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<td> </td>
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</tr>
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<tr>
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<td>Subtract:</td>
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<td> </td>
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<td> </td>
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<td>7.368</td>
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</tr>
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<tr>
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<td> </td>
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<td> </td>
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<td>−</td>
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<td>1.150</td>
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</tr>
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<tr>
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<td> </td>
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<td> </td>
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<td> </td>
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<td class="hilite" style="border-top: 1px solid black;">6.218</td>
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</tr>
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</tbody></table>
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</div>
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<p><b>To check</b> we can add the answer to the number subtracted:</p>
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<div class="example">
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<h3>Example: Check that 7.368 minus 1.15 equals 6.218</h3>
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<p>Let us try adding 6.218 to 1.15</p>
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<table style="border: 0; margin:auto;">
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<tbody>
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<tr>
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<td>Line up the decimal points:</td>
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<td> </td>
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<td> </td>
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<td>6<span class="hilite">.</span>218</td>
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</tr>
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<tr>
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<td> </td>
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<td> </td>
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<td>+</td>
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<td>1<span class="hilite">.</span>15</td>
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</tr>
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<tr>
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<td> </td>
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<td> </td>
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<td> </td>
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<td> </td>
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</tr>
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<tr>
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<td>"Pad" with zeros:</td>
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<td> </td>
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<td> </td>
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<td>6.218</td>
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</tr>
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<tr>
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<td> </td>
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<td> </td>
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<td>+</td>
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<td>1.15<span class="hilite">0</span></td>
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</tr>
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<tr>
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<td> </td>
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<td> </td>
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<td> </td>
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<td> </td>
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</tr>
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<tr>
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<td>Add:</td>
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<td> </td>
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<td> </td>
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<td>6.218</td>
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</tr>
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<tr>
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<td> </td>
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<td> </td>
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<td>+</td>
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<td>1.150</td>
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</tr>
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<tr>
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<td> </td>
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<td> </td>
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<td> </td>
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<td class="hilite" style="border-top: 1px solid black;">7.368</td>
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</tr>
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</tbody></table>
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<p>It matches the number we started with, so it checks out.</p>
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</div>
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<p> </p>
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<div class="fun">
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<h3><a id="zero"></a>Putting In Zeros</h3>
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<p>Why can we put in extra zeros?</p>
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<p>A zero is really saying "there is no value at this decimal place".</p>
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<ul>
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<li>In a number like 10, the zero is saying "no ones"</li>
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<li>In a number like 2.50 the zero is saying "no hundredths"</li>
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</ul>
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<p>So it is safe to take a number like 2.5 and make it 2.50 or 2.500 etc</p>
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<p>But DON'T take 2.5 and make it 20.5, that is plain wrong.</p>
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</div>
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<p> </p>
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<div class="questions">
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<script>getQ(958, 959, 1336, 1337, 3455, 3456, 3457, 3458);</script> </div>
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<div class="related">
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<a href="decimals.html">Decimals</a>
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<a href="decimals-menu.html">Decimals Index</a>
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<a href="worksheets/decimals.html">Decimal Worksheets</a>
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<a href="subtracting-decimals.html">Subtracting Decimals</a>
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<a href="multiplying-decimals.html">Multiplying Decimals</a>
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<a href="dividing-decimals.html">Dividing Decimals</a>
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</div>
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<!-- #EndEditable -->
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</article>
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<script>document.write(getFooter());</script>
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</footer>
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Copyright © 2020 MathsIsFun.com
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