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369 lines
13 KiB
HTML
369 lines
13 KiB
HTML
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<article id="content" role="main">
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<!-- #BeginEditable "Body" -->
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<h1 class="center">Comparing Fractions</h1>
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<div style="background: url(numbers/images/hdr-two-apples.jpg) no-repeat; width: 100%; height: 100px; background-position: center center;"></div>
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<p>Sometimes we need to compare two fractions to discover which is larger or smaller.</p>
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<p>There are two main ways to compare fractions: using <b>decimals</b>, or using the<b> same denominator</b>.</p>
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<h2>The Decimal Method of Comparing Fractions</h2>
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<p>Convert each fraction to decimals, and then compare the decimals.</p>
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<div class="example">
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<h3>Example: which is bigger: <span class="intbl">
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<em>3</em>
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<strong>8</strong>
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</span> or <span class="intbl">
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<em>5</em>
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<strong>12 </strong>
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</span>?</h3>
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<p>Convert each fraction to a decimal.</p>
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<p>We can use a calculator (3÷8 and 5÷12), or the method on <a href="converting-fractions-decimals.html">Converting Fractions to Decimals</a>.</p>
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<p>Anyway, these are the answers I get:</p>
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<p class="center"><span class="intbl">
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<em>3</em>
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<strong>8</strong>
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</span> = 0.375, and <span class="intbl">
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<em>5</em>
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<strong>12 </strong>
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</span> = 0.4166...</p>
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<p class="center">So <b> <span class="intbl">
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<em>5</em>
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<strong>12 </strong>
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</span></b> is bigger.</p>
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</div>
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<h2>The Same Denominator Method</h2>
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<p style="float:right; margin: 0 0 5px 10px;"><img src="numbers/images/fraction.svg" alt="fraction" /></p>
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<p><i>The <b>denominator</b> is the bottom number in a fraction.</i></p>
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<p><i>It shows how many equal parts the item is divided into</i></p>
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<div style="clear:both"></div>
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<p>When two fractions have the <b>same denominator</b> they are easy to compare:</p>
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<div class="example">
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<h3>Example: <span class="intbl">
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<em>4</em>
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<strong>9</strong>
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</span> is less than <span class="intbl">
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<em>5</em>
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<strong>9</strong>
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</span> (because
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4 is less than 5)</h3>
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<table style="border: 0; margin:auto;">
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<tr>
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<td><img src="numbers/images/frac4-9.gif" width="145" height="145" alt="frac 4/9" /></td>
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<td> is less than </td>
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<td><img src="numbers/images/frac5-9.gif" width="145" height="145" alt="frac 5/9" /></td>
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</tr>
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<tr>
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<td style="text-align:center;"><span class="intbl">
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<em>4</em>
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<strong>9</strong>
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</span></td>
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<td style="text-align:center;"> </td>
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<td style="text-align:center;"><span class="intbl">
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<em>5</em>
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<strong>9</strong>
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</span></td>
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</tr>
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</table>
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</div>
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<p>But when the denominators are not the same we need to <b>make them the same</b> (using <a href="equivalent_fractions.html">Equivalent Fractions</a>).</p>
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<div class="example">
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<h3>Example: Which is larger: <span class="intbl">
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<em>3</em>
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<strong>8</strong>
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</span> or <span class="intbl">
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<em>5</em>
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<strong>12 </strong>
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</span>?</h3>
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<p>Look at this:</p>
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<ul>
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<li>When we multiply 8 <b>× </b>3 we get 24,</li>
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<li>and when we multiply 12 <b>× </b>2
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we <b>also</b> get 24,</li>
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</ul>
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<p>so let's try that (<i>important: what we do to the bottom we must also do to the top</i>):</p>
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<table style="border: 0; margin:auto;">
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<tr>
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<td><table align="center" border="0" cellspacing="3" cellpadding="0">
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<tr align="center">
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<td> </td>
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<td><b>× 3</b></td>
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<td> </td>
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</tr>
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<tr align="center">
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<td colspan="3"><div class="center"><img src="images/style/right-over-arrow.gif" width="75" height="25" alt="right over arrow" /></div></td>
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</tr>
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<tr align="center">
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<td>3</td>
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<td rowspan="2"> = </td>
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<td>9</td>
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</tr>
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<tr align="center">
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<td style="border-top: 1px solid black;">8</td>
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<td style="border-top: 1px solid black;">24</td>
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</tr>
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<tr align="center">
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<td colspan="3"><div class="center"><img src="images/style/right-under-arrow.gif" width="75" height="25" alt="right under arrow" /></div></td>
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</tr>
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<tr align="center">
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<td> </td>
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<td><b>× 3</b></td>
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<td> </td>
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</tr>
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</table></td>
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<td width="100" align="center">and</td>
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<td><table align="center" border="0" cellspacing="3" cellpadding="0">
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<tr align="center">
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<td> </td>
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<td><b>× 2</b></td>
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<td> </td>
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</tr>
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<tr align="center">
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<td colspan="3"><div class="center"><img src="images/style/right-over-arrow.gif" width="75" height="25" alt="right over arrow" /></div></td>
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</tr>
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<tr align="center">
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<td>5</td>
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<td rowspan="2"> = </td>
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<td>10</td>
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</tr>
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<tr align="center">
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<td style="border-top: 1px solid black;">12</td>
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<td style="border-top: 1px solid black;">24</td>
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</tr>
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<tr align="center">
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<td colspan="3"><div class="center"><img src="images/style/right-under-arrow.gif" width="75" height="25" alt="right under arrow" /></div></td>
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</tr>
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<tr align="center">
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<td> </td>
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<td><b>× 2</b></td>
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<td> </td>
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</tr>
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</table></td>
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</tr>
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</table>
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<p>We can now see that <span class="intbl">
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<em>9</em>
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<strong>24</strong>
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</span> is smaller than <span class="intbl">
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<em>10</em>
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<strong>24</strong>
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</span> (because 9 is smaller than 10).</p>
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<div class="so"> so <span class="intbl">
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<em>5</em>
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<strong>12</strong>
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</span> is the larger
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fraction.</div>
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<table style="border: 0; margin:auto;">
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<tr>
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<td><img src="numbers/images/frac-3-8.gif" width="142" height="145" alt="frac 3/8" /></td>
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<td> is less than </td>
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<td><img src="numbers/images/frac5-12.gif" width="145" height="145" alt="frac 5/12" /></td>
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</tr>
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<tr>
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<td style="text-align:center;"><span class="intbl">
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<em>3</em>
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<strong>8</strong>
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</span></td>
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<td style="text-align:center;"> </td>
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<td style="text-align:center;"><span class="intbl">
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<em>5</em>
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<strong>12 </strong>
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</span></td>
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</tr>
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</table>
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</div>
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<h2>Making the Denominators the Same</h2>
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<p>There are two main methods to make the denominator the same:</p>
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<ul>
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<li><a href="numbers/common-denominator.html">Common Denominator Method</a>, or the</li>
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<li><a href="least-common-denominator.html">Least Common Denominator Method</a></li>
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</ul>
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<p>They both work, use which one you prefer!</p>
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<div class="example">
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<h3>Example: Which is larger: <span class="intbl">
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<em>5</em>
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<strong>6</strong>
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</span> or <span class="intbl">
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<em>11</em>
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<strong>15</strong>
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</span> ?</h3>
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<p>Using the <a href="numbers/common-denominator.html">Common Denominator</a> method we multiply each fraction by the denominator of the other:</p>
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<table style="border: 0; margin:auto;">
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<tr>
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<td><table align="center" border="0" cellspacing="3" cellpadding="0">
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<tr align="center">
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<td> </td>
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<td><b>× 15</b></td>
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<td> </td>
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</tr>
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<tr align="center">
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<td colspan="3"><img src="images/style/right-over-arrow.gif" width="75" height="25" alt="right over arrow" /></td>
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</tr>
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<tr align="center">
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<td>5</td>
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<td rowspan="2"> = </td>
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<td>75</td>
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</tr>
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<tr align="center">
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<td style="border-top: 1px solid black;">6</td>
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<td style="border-top: 1px solid black;">90</td>
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</tr>
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<tr align="center">
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<td colspan="3"><img src="images/style/right-under-arrow.gif" width="75" height="25" alt="right under arrow" /></td>
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</tr>
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<tr align="center">
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<td> </td>
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<td><b>× 15</b></td>
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<td> </td>
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</tr>
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</table></td>
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<td width="100" align="center">and</td>
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<td><table align="center" border="0" cellspacing="3" cellpadding="0">
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<tr align="center">
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<td> </td>
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<td><b>× 6</b></td>
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<td> </td>
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</tr>
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<tr align="center">
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<td colspan="3"><img src="images/style/right-over-arrow.gif" width="75" height="25" alt="right over arrow" /></td>
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</tr>
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<tr align="center">
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<td>11</td>
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<td rowspan="2"> = </td>
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<td>66</td>
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</tr>
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<tr align="center">
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<td style="border-top: 1px solid black;">15</td>
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<td style="border-top: 1px solid black;">90</td>
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</tr>
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<tr align="center">
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<td colspan="3"><img src="images/style/right-under-arrow.gif" width="75" height="25" alt="right under arrow" /></td>
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</tr>
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<tr align="center">
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<td> </td>
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<td><b>× 6</b></td>
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<td> </td>
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</tr>
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</table></td>
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</tr>
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</table>
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<p>We can see that <span class="intbl">
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<em>75</em>
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<strong>90</strong>
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</span> is the larger fraction (because 75 is more than 66)</p>
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<div class="so"> so <span class="intbl">
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<em>5</em>
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<strong>6</strong>
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</span> is the larger
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fraction. </div>
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<table style="border: 0; margin:auto;">
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<tr>
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<td><img src="numbers/images/frac5-6.gif" width="145" height="145" alt="frac 5/6" /></td>
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<td> is more than </td>
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<td><img src="numbers/images/frac11-15.gif" width="145" height="145" alt="frac 11/15" /></td>
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</tr>
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<tr>
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<td style="text-align:center;"><span class="intbl">
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<em>5</em>
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<strong>6</strong>
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</span></td>
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<td style="text-align:center;"> </td>
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<td style="text-align:center;"><span class="intbl">
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<em>11</em>
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<strong>15</strong>
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</span></td>
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</tr>
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</table>
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</div>
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<p> </p>
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<div class="questions">
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<script>getQ(922, 1390, 1677, 923, 1392, 1678, 3552, 3553, 3554, 3555);</script> </div>
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<div class="related">
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<a href="fractions.html">Introduction to Fractions</a>
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<a href="least-common-multiple.html">Least Common Multiple</a>
|
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<a href="least-common-multiple-tool.html">Least Common Multiple Tool</a>
|
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<a href="least-common-denominator.html">Least Common Denominator</a>
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<a href="simplifying-fractions.html">Simplifying Fractions</a>
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<a href="fractions_addition.html">Adding Fractions</a>
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<a href="fractions_subtraction.html">Subtracting Fractions</a>
|
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<a href="fractions-menu.html">Fractions Index</a>
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</div>
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</article>
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