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171 lines
7.5 KiB
HTML
171 lines
7.5 KiB
HTML
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<h1 align="center">Long Division Index</h1>
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<p align="center">Long Division is easy, <b>once you get the idea</b>. <br />
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Hopefully some of these pages will "click" with you, and you will be a master! </p>
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<h2>Why Long Division</h2>
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<p>The simplest way to do division is by <b>repeated subtraction</b>:</p>
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<div class="example">
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<h3>Example: What is 48 / 12?</h3>
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<ul>
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<li>Start with 48, subtract 12, we get 36</li>
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<li>Repeat: 36-12 = 24</li>
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<li>Repeat: 24-12 = 12</li>
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<li>Repeat: 12-12 = 0</li>
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</ul>
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<p>We did 4 subtractions, so 48 / 12 = 4</p>
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</div>
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<p>But this could take a long time for something like 3768 / 12</p>
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<div class="example">
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<h3>Example: What is 3768 / 12?</h3>
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<ul>
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<li>Start with 3768, subtract 12, we get 3756</li>
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<li>Repeat: 3756-12 = 3744</li>
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<li>Repeat: 3744-12 = 3732</li>
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<li>Repeat: 3732-12 = 3720</li>
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<li> ... oh No! This will take a long long time!</li>
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</ul>
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<p>Maybe we could do 100 subtracts in one go</p>
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<ul>
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<li>Start with 3768, subtract <b>100 lots of 12</b>, we get 3768-1200 = 2568</li>
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<li>Repeat: 2568-1200 = 1368</li>
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<li>Repeat: 1368-1200 = 168</li>
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</ul>
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<p>Now lets move to 10 subtracts in one go</p>
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<ul>
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<li>168, subtract <b>10 lots of 12</b>, we get 168-120 = 48</li>
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</ul>
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<p>Now lets move to singles:</p>
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<ul>
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<li>48, subtract 12, we get 36</li>
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<li>Repeat: 36-12 = 24</li>
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<li>Repeat: 24-12 = 12</li>
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<li>Repeat: 12-12 = 0</li>
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</ul>
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<p>So we did <b>3 lots of 100</b>, <b>1 lot of 10</b> and <b>4 single</b> subtracts of 12, which is a total of <b>314 subtracts of 12 </b></p>
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<p class="center large">So 3768 / 12 = 314</p>
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<p>That is the <b>Idea behind Long Division</b></p>
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<p>Long division looks like this: </p>
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<div class="mono">
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<span style="border-bottom: 1px solid black;"> 0314</span><br>
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12 )3768<br> <span style="border-bottom: 1px solid black;">0</span><br>
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37<br>
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<span style="border-bottom: 1px solid black;">36</span><br>
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16<br>
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<span style="border-bottom: 1px solid black;">12</span><br>
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48<br>
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<span style="border-bottom: 1px solid black;">48</span><br>
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0
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</div>
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<p>It may look a little strange at first, but can you see the "3768" near the top?</p>
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<p>And then the "12" at its left, and the actual answer of "314" at the top.</p>
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<p>That shows us we worked out <b>3768 / 12 = 314</b></p>
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<ul>
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<li>Now look down for the "36": That is where we tackled the <b>100s</b> (3 × 12 = 36)</li>
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<li>And a bit below that is the "12", which is where we did the <b>10s</b> (1 × 12 = 12)</li>
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<li>And at the bottom is the "48" (4 × 12 = 48) </li>
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</ul>
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<p>So we tackled the 100s, then the 10s, then the units, just like above.</p>
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<p>And the "0" at the bottom means that after all the subtracts there is nothing left over.</p>
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<p>Continue on and learn how to do this yourself! </p>
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</div>
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<h2>Understanding Long Division</h2>
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<div class="vlist">
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<p><a href="long-division-introduction.html">Long Division - Introduction</a></p>
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<p><a href="long-division-how-works.html">Long Division - How It Works</a></p>
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<p><a href="long-division-animation.html">Long Division Animation</a> </p>
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<!-- <p><a href="../long-division-organised.html">Long Division - Organized Guessing</a></p>
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--> </div>
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<h2>Long Division</h2>
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<div class="vlist">
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<p><a href="../long_division.html">Long Division</a></p>
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<p><a href="../long_division2.html">Long Division with Remainders</a></p>
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<p><a href="../long_division3.html">Long Division to Decimal Places</a></p>
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</div>
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<h2>Practice</h2>
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<div class="vlist">
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<p><a href="../worksheets/long-division.html">Long Division Worksheets</a>
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</p>
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</div>
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<h2>Advanced</h2>
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<div class="vlist">
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<p><a href="../algebra/polynomials-division-long.html">Polynomial Long Division</a></p>
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</div><p> </p>
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<div class="related"><a href="long-division-introduction.html">Long Division Introduction</a> <a href="index.html">Numbers Index</a></div>
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