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438 lines
13 KiB
HTML
438 lines
13 KiB
HTML
<!DOCTYPE html>
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<html lang="en"><!-- #BeginTemplate "/Templates/Main.dwt" --><!-- DW6 -->
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<!-- Mirrored from www.mathsisfun.com/fractions_division.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:36:09 GMT -->
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<title>Dividing Fractions</title>
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<meta name="description" content="Turn the second fraction upside down, then multiply, Ther are 3 simple steps:">
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<div id="adTop"></div>
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<div id="hdr"></div>
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<div id="cookOK"></div>
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</header>
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<div class="mid">
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<nav>
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<div id="menuWide" class="menu"></div>
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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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<span class="video">6i9DOPwHZWw</span>
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<h1 id="title" align="center">Dividing Fractions</h1>
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<p class="center"><i>Turn the second fraction upside down, then multiply.</i></p>
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<h2>There are 3 Simple Steps to Divide Fractions:</h2>
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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>
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<p>Step 1. Turn the second fraction <i>(the one you want to divide by)</i> upside down<br>
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(this is now a <a href="reciprocal-fraction.html">reciprocal</a>).</p>
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<p>Step 2. <a href="fractions_multiplication.html">Multiply</a> the first fraction by that reciprocal<br>
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<br>
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Step 3. <a href="simplifying-fractions.html">Simplify</a> the fraction (if needed)</p></td>
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</tr>
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</tbody></table>
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</div>
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<div class="example">
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<h3>Example:</h3>
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<table align="center">
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<tbody>
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<tr>
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<td><iframe src="https://www.youtube.com/embed/IVVB_zxAOws?rel=0&showinfo=0" allowfullscreen="" height="203" frameborder="0" width="360"></iframe><br>
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</td>
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</tr>
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</tbody></table>
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</div>
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<div class="example">
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<h3>Example:
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<p class="center large"><span class="intbl">
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<em>1</em>
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<strong>2</strong>
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</span> ÷ <span class="intbl">
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<em>1</em>
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<strong>6</strong>
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</span></p></h3>
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<p><br>
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Step 1. Turn the second fraction upside down (it becomes a <b>reciprocal</b>):</p>
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<p class="center large"><span class="intbl">
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<em>1</em>
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<strong>6</strong>
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</span> becomes <span class="intbl">
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<em>6</em>
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<strong>1</strong>
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</span></p>
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<p><br>
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Step 2. Multiply the first fraction by that <b>reciprocal</b>:</p>
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<p class="center"><i>(multiply tops ...)</i></p>
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<p class="center large"><span class="intbl">
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<em>1</em>
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<strong>2</strong>
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</span> × <span class="intbl">
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<em>6</em>
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<strong>1</strong>
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</span> = <span class="intbl">
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<em>1 × 6</em>
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<strong>2 × 1</strong>
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</span> = <span class="intbl">
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<em>6</em>
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<strong>2</strong>
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</span></p>
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<p class="center"><i>(... multiply bottoms)</i></p>
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<p> </p>
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<p>Step 3. Simplify the fraction:</p>
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<p class="center large"><span class="intbl">
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<em>6</em>
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<strong>2</strong>
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</span> = 3</p>
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</div>
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<h3>With Pen and Paper</h3>
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<p>And here is how to do it with a pen and paper (press the play button):</p>
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<script>playerMain("numbers/images/fractions-div-a.txt",640,140,'');</script>
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<p>To help you remember:</p>
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<p class="center larger"><i><span class="times">♫</span> "Dividing fractions, as easy as pie,<br>
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Flip the second fraction, then multiply.<br>
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And don't forget to simplify,<br>
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Before it's time to say goodbye"</i> <i><span class="times">♫</span></i></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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<p>Another way to remember is:</p>
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<p><b>"leave me, change me, turn me over"</b></p></td>
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<td> </td>
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<td><img src="numbers/images/fraction-divide-leave.svg" alt="leave change turn"></td>
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</tr>
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</tbody></table>
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<p> </p>
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<div class="center80">
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<h3>How Many?</h3>
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<p><b>20 divided by 5</b> is asking <b>"how many 5s in 20?"</b> (=4) and so:</p>
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<p> </p>
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<p class="center large"><span class="intbl">
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<em>1</em>
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<strong>2</strong>
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</span> ÷ <span class="intbl">
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<em>1</em>
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<strong>6</strong>
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</span> is really asking:</p>
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<p class="center large">how many <span class="intbl">
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<em>1</em>
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<strong>6</strong>
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</span>s in <span class="intbl">
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<em>1</em>
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<strong>2</strong>
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</span> ?</p>
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<p> </p>
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<p>Now look at the pizzas below ... how many "1/6th slices" fit into a "1/2 slice"?</p>
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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 class="large">How many</td>
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<td><img src="images/fractions/pizza-1-6.svg" alt="1/6" height="111" width="112"></td>
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<td class="large" width="30">in</td>
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<td><img src="images/fractions/pizza-3-6.svg" alt="3/6" height="111" width="112"></td>
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<td class="large">?</td>
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<td width="20"> </td>
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<td class="large"><b> Answer: 3</b></td>
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</tr>
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</tbody></table>
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<p> </p>
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<p class="center large">So now you can see why <span class="intbl">
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<em>1</em>
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<strong>2</strong>
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</span> ÷ <span class="intbl">
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<em>1</em>
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<strong>6</strong>
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</span> = 3</p>
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<p> </p>
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<p>In other words "I have half a pizza, if I divide it into one-sixth slices, how many slices is that?"</p>
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<p> </p>
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</div>
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<p><br></p>
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<div class="example">
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<h3>Another Example:
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<p class="center large"><span class="intbl">
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<em>1</em>
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<strong>8</strong>
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</span> ÷ <span class="intbl">
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<em>1</em>
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<strong>4</strong>
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</span></p></h3>
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<p><br>
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Step 1. Turn the second fraction upside down (the <b>reciprocal</b>):</p>
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<p class="center large"><span class="intbl">
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<em>1</em>
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<strong>4</strong>
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</span> becomes <span class="intbl">
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<em>4</em>
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<strong>1</strong>
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</span></p>
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<p><br>
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Step 2. Multiply the first fraction by that <b>reciprocal</b>:</p>
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<p class="center large"><span class="intbl">
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<em>1</em>
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<strong>8</strong>
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</span> × <span class="intbl">
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<em>4</em>
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<strong>1</strong>
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</span> = <span class="intbl">
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<em>1 × 4</em>
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<strong>8 × 1</strong>
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</span> = <span class="intbl">
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<em>4</em>
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<strong>8</strong>
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</span></p>
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<p><br>
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Step 3. Simplify the fraction:</p>
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<p class="center large"><span class="intbl">
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<em>4</em>
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<strong>8</strong>
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</span> = <span class="intbl">
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<em>1</em>
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<strong>2</strong>
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</span></p>
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</div>
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<h2>Fractions and Whole Numbers</h2>
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<p>What about division with fractions <b>and</b> whole numbers?</p>
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<p><b>Make the whole number a fraction, by putting it over 1.</b></p>
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<div class="center80">
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<p class="center large">Example: 5 is also <span class="intbl">
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<em>5</em>
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<strong>1</strong>
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</span></p>
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</div>
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<p>Then continue as before.</p>
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<div class="example">
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<h3>Example:
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<p class="center large"><span class="intbl">
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<em>2</em>
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<strong>3</strong>
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</span> ÷ 5</p></h3>
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<p>Make 5 into <span class="intbl">
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<em>5</em>
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<strong>1</strong>
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</span> :</p>
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<p class="center large"><span class="intbl">
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<em>2</em>
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<strong>3</strong>
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</span> ÷ <span class="intbl">
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<em>5</em>
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<strong>1</strong>
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</span></p>
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<p>Then continue as before.</p>
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<p>Step 1. Turn the second fraction upside down (the <b>reciprocal</b>):</p>
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<p class="center large"><span class="intbl">
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<em>5</em>
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<strong>1</strong>
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</span> becomes <span class="intbl">
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<em>1</em>
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<strong>5</strong>
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</span></p>
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<p><br>
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Step 2. Multiply the first fraction by that <b>reciprocal</b>:</p>
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<p class="center large"><span class="intbl">
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<em>2</em>
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<strong>3</strong>
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</span> × <span class="intbl">
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<em>1</em>
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<strong>5</strong>
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</span> = <span class="intbl">
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<em>2 × 1</em>
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<strong>3 × 5</strong>
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</span> = <span class="intbl">
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<em>2</em>
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<strong>15</strong>
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</span></p>
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<p><br>
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Step 3. Simplify the fraction:</p>
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<p>The fraction is already as simple as it can be.</p>
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<p class="center large">Answer = <span class="intbl">
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<em>2</em>
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<strong>15</strong>
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</span></p>
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</div>
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<div class="example">
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<h3>Example:
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<p class="center large">3 ÷ <span class="intbl">
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<em>1</em>
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<strong>4</strong>
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</span></p></h3>
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<p>Make 3 into <span class="intbl">
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<em>3</em>
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<strong>1</strong>
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</span> :</p>
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<p class="center large"><span class="intbl">
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<em>3</em>
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<strong>1</strong>
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</span> ÷ <span class="intbl">
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<em>1</em>
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<strong>4</strong>
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</span></p>
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<p><br>
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Then continue as before.</p>
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<p>Step 1. Turn the second fraction upside down (the <b>reciprocal</b>):</p>
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<p class="center large"><span class="intbl">
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<em>1</em>
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<strong>4</strong>
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</span> becomes <span class="intbl">
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<em>4</em>
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<strong>1</strong>
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</span></p>
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<p><br>
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Step 2. Multiply the first fraction by that <b>reciprocal</b>:</p>
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<p class="center large"><span class="intbl">
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<em>3</em>
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<strong>1</strong>
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</span> × <span class="intbl">
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<em>4</em>
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<strong>1</strong>
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</span> = <span class="intbl">
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<em>3 × 4</em>
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<strong>1 × 1</strong>
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</span> = <span class="intbl">
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<em>12</em>
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<strong>1</strong>
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</span></p>
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<p><br>
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Step 3. Simplify the fraction:</p>
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<p class="center large"><span class="intbl">
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<em>12</em>
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<strong>1</strong>
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</span> = 12</p>
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<div class="center80">
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<h3>And Remember ...</h3>
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<p>You can rewrite a question like "20 divided by 5" into <b>"how many 5s in 20"</b></p>
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<p>So you can also rewrite "3 divided by ¼" into <b>"how many ¼s in 3"</b> (=12)</p>
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</div>
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</div>
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<p> </p>
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<div class="def">
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<h3>Why Turn the Fraction Upside Down?</h3>
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<p class="large">Because dividing is the opposite of multiplying!</p>
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<h3> </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> A fraction says to:</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>
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<ul>
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<li>multiply by the top number</li>
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<li>divide by the bottom number</li>
|
||
</ul></td>
|
||
<td> </td>
|
||
<td><img src="numbers/images/fraction-multiply-divide.svg" alt="fraction multiply divide" height="" width=""></td>
|
||
</tr>
|
||
</tbody></table>
|
||
<p>But for <b>DIVISION</b> we:</p>
|
||
<ul>
|
||
<li><b>divide</b> by the top number</li>
|
||
<li><b>multiply</b> by the bottom number</li>
|
||
</ul>
|
||
<div class="example">
|
||
<h3>Example: dividing by <b><sup>5</sup>/<sub>2</sub></b> is the same as multiplying by <b><sup>2</sup>/<sub>5</sub></b></h3>
|
||
<p class="center"><img src="numbers/images/fraction-multiply-divide-2.svg" alt="fraction multiply divide" height="" width=""></p>
|
||
</div>
|
||
<p>So instead of dividing by a fraction, it is easier to turn that fraction upside down, then do a multiply.</p>
|
||
</div>
|
||
<p> </p>
|
||
<div class="questions">937,938,939, 1411, 1412, 1413, 3575, 3576, 3577, 3578</div>
|
||
|
||
<div class="related">
|
||
<a href="fractions.html">Introduction to Fractions</a>
|
||
<a href="numbers/fractions-division-whole-numbers.html">Dividing Fractions by Whole Numbers</a>
|
||
<a href="fractions_multiplication.html">Multiplying Fractions</a>
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||
<a href="simplifying-fractions.html">Simplifying Fractions</a>
|
||
<a href="equivalent_fractions.html">Equivalent Fractions</a>
|
||
<a href="fractions_addition.html">Adding Fractions</a>
|
||
<a href="fractions_subtraction.html">Subtracting Fractions</a>
|
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<a href="divisibility-rules.html">Divisibility Rules</a>
|
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<a href="fractions-menu.html">Fractions Index</a>
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