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256 lines
9.6 KiB
HTML
256 lines
9.6 KiB
HTML
<!DOCTYPE html>
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<title>Dividing Decimals</title>
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<div id="hdr"></div>
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<div id="tran"></div>
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<div id="cookOK"></div>
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<div id="menuWide" class="menu"></div>
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<article id="content" role="main">
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<!-- #BeginEditable "Body" -->
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<h1 class="center">Dividing Decimals</h1>
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<p>How do we divide when there are decimal points involved?</p>
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<p>Well, it is easier to divide by a <b>whole number</b> ... so multiply by 10 until it is!</p>But we must do the <b>same thing</b> to both numbers in the division.
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<div class="example">
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<h3>Example: 15 divided by 0.2</h3>
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<p>When we multiply the 0.2 by 10 we get a whole number:</p>
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<p class="so">0.2 × 10 = 2</p>
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<p>But we must <b>also</b> do it to the 15:</p>
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<p class="so">15 × 10 = 150</p>
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<p>So 15 ÷ 0.2 has become 150 ÷ 2 (<b>both</b> numbers are 10 times larger):</p>
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<p class="center larger">150 ÷ 2 = 75</p>
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<p>And so the answer is:</p>
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<p class="center larger"><b>15 ÷ 0.2 = 75</b></p>
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</div>
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<p class="center"><img src="numbers/images/decimals-divide-a.svg" height="57" width="333"><br>
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The number we divide by is called the divisor.</p>
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<p><span class="center larger">To divide decimal numbers:</span></p>
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<div class="def">
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<p class="center large">Multiply the divisor by as many 10's as we need, until it is a whole number.<br>
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Remember to multiply the dividend by the same number of 10's.</p>
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</div>
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<p>Multiplying by 10 is easy, we just shift one space over like this:</p>
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<div class="example">
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<h3>Example: Divide 6.4 by 0.4</h3>
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<p>Let us move one space <b>for both</b>:</p>
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<div class="simple">
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<table style="border: 0; margin:auto;">
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<tbody>
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<tr style="text-align:center;">
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<td colspan="3">move 1</td>
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</tr>
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<tr style="text-align:center;">
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<td><b>6.4</b></td>
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<td><img src="images/arrow.gif" alt="right arrow" height="30" width="30"></td>
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<td><b>64</b></td>
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</tr>
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<tr style="text-align:center;">
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<td><b>0.4</b></td>
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<td><img src="images/arrow.gif" alt="right arrow" height="30" width="30"></td>
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<td><b>4</b></td>
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</tr>
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<tr style="text-align:center;">
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<td colspan="3">move 1</td>
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</tr>
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</tbody></table>
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</div>
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<p class="center"><b><span class="intbl"><em>6.4</em><strong>0.4</strong></span> is exactly the same as <span class="intbl"><em>64</em><strong>4</strong></span></b><br>
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as we did the move for <b>both numbers</b>.</p>
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<p>Now we can calculate:</p>
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<p class="center larger"><span class="intbl"><em>64</em><strong>4</strong></span> = 16</p>
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<p>So the answer is:</p>
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<p class="center larger"><span class="intbl"><em>6.4</em><strong>0.4</strong></span> = 16</p>
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<p> </p>
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<p>Are there really 16 lots of <b>0.4</b> in <b>6.4</b>? Let's see:</p>
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<p class="center"><img src="numbers/images/decimals-divide-64-4.svg" alt="decimals divide 64 04" height="" width=""></p>
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</div>
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<p>For harder questions we may need to use <a href="long_division.html">Long Division</a>:</p>
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<div class="example">
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<h3>Example: Divide 0.539 by 0.11</h3>
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<p>First we need to make the move twice to make 0.11 into a whole number:</p>
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<div class="simple">
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<table style="border: 0; margin:auto;">
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<tbody>
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<tr style="text-align:center;">
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<td colspan="5">move 2 spaces</td>
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</tr>
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<tr style="text-align:center;">
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<td><b>0.539</b></td>
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<td><img src="images/arrow.gif" alt="right arrow" height="30" width="30"></td>
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<td><b>5.39</b></td>
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<td><img src="images/arrow.gif" alt="right arrow" height="30" width="30"></td>
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<td><b>53.9</b></td>
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</tr>
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<tr style="text-align:center;">
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<td><b>0.11</b></td>
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<td><img src="images/arrow.gif" alt="right arrow" height="30" width="30"></td>
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<td><b>1.1</b></td>
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<td><img src="images/arrow.gif" alt="right arrow" height="30" width="30"></td>
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<td><b>11</b></td>
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</tr>
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<tr style="text-align:center;">
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<td colspan="5">move 2 spaces</td>
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</tr>
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</tbody></table>
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</div>
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<p class="center"><b><span class="intbl"><em>0.539</em><strong>0.11</strong></span> is exactly the same as <span class="intbl"><em>53.9</em><strong>11</strong></span></b></p>
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<p></p>
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<p>But what about 53.9? It still has a decimal point.</p>
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<p>Well, we can ignore the decimal point in the dividend so long as we remember to <b>put it back later</b>.</p>
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<p>First we do the calculation without the decimal point:</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>
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<div class="mono"> <u> 049</u><br>
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11)539<br>
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<u>0</u><br>
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53<br>
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<u>44</u><br>
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99<br>
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<u>99</u><br>
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0</div></td>
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</tr>
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</tbody></table>
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<p>Now put the decimal point in the answer directly above the decimal point in the dividend:</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>
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<div class="mono"> <u> 04.9</u><br>
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11)53.9</div></td>
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</tr>
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</tbody></table>
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<p><br>
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The answer is <span class="large">4.9</span></p>
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</div>
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<p>Another example:</p>
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<div class="example">
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<h3>Example: Divide 9.1 by 7</h3>
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<p>The divisor (7) is already a whole number, so no need for any moves.</p>
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<p>Now, ignore the decimal point in the dividend and use Long Division:</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 style="text-align:left;">
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<div class="mono"> <u> 13</u><br>
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7)91<br>
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<u>7</u><br>
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21<br>
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<u>21</u><br>
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0</div></td>
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</tr>
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</tbody></table>
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<p><br>
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Put the decimal point in the answer directly above the decimal point in the dividend:</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>
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<div class="mono"> <u> 1.3</u><br>
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7)9.1 </div></td>
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</tr>
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</tbody></table>
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<p>The answer is <span class="large">1.3</span></p>
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</div>
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<h2>Animations</h2>
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<p>Have a look at these <a href="numbers/decimals-dividing-animation.html">Decimal Division Animations</a> for further help.</p>
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<h2><br>
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Lastly ...</h2>
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<p>As a final check we can put our "common sense" hat on and think "is that the right size?", because we don't want to pay ten times too much for anything, nor do we want to get only one-tenth of what we need!</p>
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<p> </p>
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<div class="questions">965, 1351,966, 1352,967, 1353, 3467, 3468, 3469, 3470</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="long_division.html">Long Division</a>
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<a href="divisibility-rules.html">Divisibility Rules</a>
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<a href="worksheets/decimals.html">Decimal Worksheets</a>
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<a href="adding-decimals.html">Adding Decimals</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="index-notation-powers.html">Powers of 10</a>
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</div>
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