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132 lines
4.9 KiB
HTML
132 lines
4.9 KiB
HTML
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<title>Division and Remainders</title>
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<meta name="description" content="Sometimes when dividing there is something left over: it is called the remainder.">
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<!-- #BeginEditable "Body" -->
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<h1 class="center">Division and Remainders</h1>
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<p class="center">Sometimes when dividing there is something left over. It is called the <b>remainder</b>.</p>
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<h3><span class="larger"><b>Example:</b> There are <b>7</b> bones to share with <b>2</b> pups.</span></h3>
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<p class="center">But 7 cannot be divided exactly into 2 groups,<br>
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so each pup gets 3 bones,<br>
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and there is <b>1 left over</b>:</p>
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<p class="center larger"><img src="images/remainder-7-2-pups.svg" alt="7 / 2 = 3 R 1 (remainder 1)" height="230" width="472"></p>
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<p>We say:</p>
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<p class="center larger"><i> "7 divided by 2 equals <b>3</b> with a <b>remainder of 1</b>"</i></p>
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<p>And we write:</p>
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<p class="center larger">7 ÷ 2 = 3 R 1</p>
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<h3>As a Fraction</h3>
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<p>It is also possible to <b>cut the remaining bone in half</b>, so each pup gets <b>3 ½</b> bones:</p>
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<p class="center large">7 ÷ 2 = 3 R 1 = 3 ½</p>
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<p class="center">"<b>7 divided by 2</b> equals <b>3 remainder 1</b> equals <b>3 and a half</b>"</p>
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<h2>Play with the Idea</h2>
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<p>Try changing the values here ... sometimes there will be a remainder:</p>
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<div class="script" style="height: 530px;">
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images/divide-marbles.js
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</div>
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<h2>Check by Multiplying</h2>
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<p>If we look at it "the other way around" we can check our answer:</p>
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<p class="center large">2 × 3 + 1 = 7</p>
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<p class="center">"2 groups of 3, plus 1 extra, equals 7"</p>
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<h2>Another Example</h2>
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<div class="center"></div>
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<div class="example">
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<p class="center"><span class="large"><img src="images/remainder.svg" alt="remainder 19 5" height="91" width="302"></span></p>
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<p>19 cannot be divided exactly by 5. The closest we can get (<i>without going over</i>) is:</p>
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<p class="center"><span class="large">3 x 5 = 15</span></p>
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<p class="center">which is 4 less than 19.</p>
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<p>So the answer of 19 ÷ 5 is:</p>
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<p class="center"><span class="large">19 ÷ 5 = 3 R 4</span></p>
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<p>Check it by multiplying: <b>5 × 3 + 4 = 19</b></p>
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</div>
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<h3>As a Fraction</h3>
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<p>We can also make a fraction with:</p>
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<ul>
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<li>the <b>remainder on top</b>, and</li>
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<li>the number you are <b>dividing by on the bottom</b>,</li>
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</ul>
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<p>so we also have:</p>
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<p class="center"><span class="large">19 ÷ 5 = 3 R 4 = 3 <span class="frac"><sup>4</sup>/<sub>5</sub></span></span></p>
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<p> </p>
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<div class="questions">1635, 1636, 1637, 1638, 3431, 3432, 3433, 3434, 3435, 3436</div>
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<div class="related">
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<a href="division.html">Division</a>
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<a href="index.html">Numbers Index</a>
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