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334 lines
12 KiB
HTML
334 lines
12 KiB
HTML
<!DOCTYPE html>
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<html lang="en"><!-- #BeginTemplate "/Templates/Main.dwt" --><!-- DW6 -->
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<title>Long Division - Organized Guessing</title>
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<article id="content" role="main">
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<!-- #BeginEditable "Body" -->
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<h1 class="center">Long Division - Organized Guessing</h1>
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<p>So, how does Long Division work?</p>
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<p>It works by breaking up the big number
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and solving it a section at a time.</p>
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<h2>Thousands, Hundreds, ...</h2>
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<p>To illustrate, let us try guessing the answer to <b>7,698 ÷ 6</b>,
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but following a special method.</p>
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<p>We will start at the thousands, then move to the hundreds, then tens,
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then ones.</p>
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<p> </p>
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<p>OK, starting at the <font color="blue">thousands:</font> How many <font color="blue">6
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lots of a thousand</font> can we fit into <b>7,698</b> ? Well, just one, really.
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Two is too much:</p>
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<div class="simple">
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<table align="center" cellpadding="6" border="0">
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<tbody>
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<tr>
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<td><b>1</b>,000 x 6 = 6,000</td>
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<td>too small</td>
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</tr>
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<tr>
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<td><b>2</b>,000 x 6 = 12,000</td>
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<td>too big</td>
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</tr>
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</tbody></table> </div>
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<p>We have made progress of sorts. We can guess that the answer is between
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1,000 and 2,000.</p>
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<p>Now let's move onto the hundreds. Let's add a hundred at a time:</p>
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<div class="simple">
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<table align="center" cellpadding="6" border="0">
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<tbody>
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<tr>
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<td>1,<b>1</b>00 x 6 = 6,600</td>
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<td>too small</td>
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</tr>
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<tr>
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<td>1,<b>2</b>00 x 6 = 7,200</td>
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<td>too small</td>
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</tr>
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<tr>
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<td>1,<b>3</b>00 x 6 = 7,800</td>
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<td>too big</td>
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</tr>
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</tbody></table></div>
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<p>So, somewhere between 1,200 and 1,300.</p>
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<p>Let's move on to the tens:</p>
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<div class="simple">
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<table align="center" cellpadding="6" border="0">
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<tbody>
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<tr>
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<td>1,2<b>1</b>0 x 6 = 7,260</td>
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<td>too small</td>
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</tr>
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<tr>
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<td>1,2<b>2</b>0 x 6 = 7,320</td>
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<td>too small</td>
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</tr>
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<tr>
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<td>
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1,2<b>3</b>0 x 6 = ...</td>
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<td> </td>
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</tr>
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</tbody></table></div>
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<p class="large">Stop! All this multiplying is <b>taking too long</b> ...</p>
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<div class="indent50px">
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<p class="large">...there should be an easier way</p></div>
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<p>At the start, when we worked on the thousands, why not chop off what we know already?</p>
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<p>We could chop off 1,000 x 6 = 6,000 and get:</p>
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<div class="beach">
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<table align="center" cellpadding="6" border="0">
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<tbody>
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<tr>
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<td>Answer so far</td>
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<td>Number left</td>
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</tr>
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<tr>
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<td>1,000 x 6 = 6,000</td>
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<td><b>7,698 − 6,000 = 1,698</b></td>
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</tr>
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</tbody></table></div>
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<p>Now (remembering we have chopped off 1,000 x 6) we can continue, but we work on <b>1,698</b> now.</p>
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<div class="beach">
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<table align="center" cellpadding="6" border="0">
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<tbody>
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<tr>
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<td>Guesses</td>
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<td>Compared to <b>1,698</b></td>
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</tr>
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<tr>
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<td><b>1</b>00 x 6 = 600</td>
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<td>too small</td>
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</tr>
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<tr>
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<td><b>2</b>00 x 6 = 1,200</td>
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<td>too small</td>
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</tr>
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<tr>
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<td><b>3</b>00 x 6 = 1,800</td>
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<td>too big</td>
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</tr>
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</tbody></table></div>
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<p>Now we can take <b>2</b>00 x 6 = 1,200 from 1,698: 1,698 − 1200 = 498</p>
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<p>And now we are only working on 498 ...</p>
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<p>We can continue like this, following this idea:</p>
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<p class="center"><b> <font class="large" size="+1">Don't work on the entire number every time,<br>
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just work
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on whatever is left.</font></b></p>
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<h2>Let's try the whole thing from the start, working neatly:</h2>
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<p class="center">Start with <b>7,698</b></p>
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<div class="simple">
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<table align="center" cellpadding="6" border="0">
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<tbody>
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<tr>
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<td>Thousands</td>
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<td>1,000 x 6 = 6,000</td>
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<td>too small</td>
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</tr>
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<tr>
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<td> </td>
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<td>2,000 x 6 = 12,000</td>
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<td>too big</td>
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</tr>
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</tbody></table></div>
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<p class="center">So the answer for thousands is <b>1,000 x 6</b>.</p>
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<hr align="center" width="50">
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<p class="center"><b>7,698</b> − 1,000 x 6 = <b>1,698</b> left to figure
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out:</p>
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<div class="simple">
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<table align="center" cellpadding="6" border="0">
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<tbody>
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<tr>
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<td>Hundreds</td>
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<td>100 x 6 = 600</td>
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<td>too small</td>
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</tr>
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<tr>
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<td> </td>
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<td>200 x 6 = 1,200</td>
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<td>too small</td>
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</tr>
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<tr>
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<td> </td>
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<td>300 x 6 = 1,800</td>
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<td>too big</td>
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</tr>
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</tbody></table></div>
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<p class="center">So the answer for hundreds is <b>200 x 6</b>.</p>
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<hr align="center" width="50">
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<p class="center"><b>1,698</b> − 200 x 6 = 1,698 - 1,200 = <b>498</b> left
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to figure out</p>
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<div class="simple">
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<table align="center" cellpadding="6" border="0">
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<tbody>
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<tr>
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<td>Tens</td>
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<td>80 x 6 = 480</td>
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<td>too small</td>
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</tr>
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<tr>
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<td> </td>
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<td>90 x 6 = 540</td>
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<td>too big</td>
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</tr>
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</tbody></table></div>
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<p class="center">So the answer for tens is <b>80 x 6</b></p>
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<hr align="center" width="50">
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<p class="center">498 - 80 x 6 = 498 − 480<b> = 18</b> left to figure out</p>
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<div class="simple">
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<table align="center" cellpadding="6" border="0">
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<tbody>
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<tr>
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<td>Ones</td>
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<td>3 x 6 = 18</td>
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<td>perfect!</td>
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</tr>
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</tbody></table></div>
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<p class="center">So the answer for ones is <b>3 x 6</b></p>
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<hr align="center" width="50">
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<p class="center">Our Answer: <b>1,000</b> x 6 + <b>200</b> x 6 + <b>80</b>
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x 6 + <b>3</b> x 6 = 7,698</p>
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<p class="center">Which is: <span class="larger">1,283</span> x 6 = 7,698 </p>
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<hr align="center" width="50">
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<p> </p>
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<p>But instead of using all those words,
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we write it down like this:</p>
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<div class="simple">
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<table align="center" border="0">
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<tbody>
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<tr>
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<th>
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What We Did
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</th>
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<td style="width: 80px;"><br></td>
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<th>
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Best Written
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</th>
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</tr>
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<tr>
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<td>
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<div class="mono">
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<span style="border-bottom: 1px solid;"> 1,283</span><br>
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6 )7,698<br>
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<span style="border-bottom: 1px solid;">-6,000</span><br>
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1,698<br>
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<span style="border-bottom: 1px solid;">-1,200</span><br>
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498<br>
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<span style="border-bottom: 1px solid;">-480</span><br>
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18<br>
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<span style="border-bottom: 1px solid;">-18</span><br>
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0
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</div></td>
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<td class="center"><img src="images/style/right-arrow.gif" alt="arrow"></td>
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<td>
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<div class="mono">
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<span style="border-bottom: 1px solid;"> 1283</span><br>
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6 )7698<br>
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<span style="border-bottom: 1px solid;">6</span><br>
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16<br>
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<span style="border-bottom: 1px solid;">12</span><br>
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49<br>
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<span style="border-bottom: 1px solid;">48</span><br>
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18<br>
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<span style="border-bottom: 1px solid;">18</span><br>
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0
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</div>
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</td>
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</tr>
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</tbody></table></div>
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<p>And that is how you do Long Division.</p>
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<p>Now look at this <a href="long_division.html">Long Division</a> page.</p>
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<p> </p>
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<div class="related">
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<a href="long_division.html">Long Division</a>
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<a href="worksheets/long-division.html">Long Division Worksheets</a>
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<a href="numbers/long-division-index.html">Long Division Index</a>
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<a href="numbers/index.html">Numbers Index</a>
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</div>
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