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337 lines
15 KiB
HTML
337 lines
15 KiB
HTML
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<title>Improper Fractions</title>
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<div id="content" role="main"><!-- #BeginEditable "Body" -->
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<h1 align="center">Improper Fractions</h1>
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<div style="float:left; margin: 0 30px 5px 0;">
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<table border="0">
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<tr>
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<td><img src="images/fractions/pie-4-4.jpg" width="120" height="120" alt="pie 4/4" /><img src="images/fractions/pie-3-4.jpg" width="120" height="120" alt="pie 3/4" /></td>
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</tr>
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<tr>
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<td align="center">
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<span class="large"><span class="intbl"><em>7</em><strong>4</strong></span></span></td>
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</tr>
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<tr>
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<td><i>(seven-fourths or seven-quarters)</i></td>
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</tr>
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</table>
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</div>
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<div>
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<p> </p>
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<p> <span class="larger">An Improper Fraction has a top number
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larger than (or equal to) the bottom number.<br />
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</span> <i><br />
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It is usually "<b>top-heavy</b>"</i></p>
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</div>
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<div style="clear:both"></div>
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<h2>More Examples</h2>
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<table border="0" align="center" cellpadding="10">
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<tr align="center" class="larger">
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<td width="60"><span class="intbl"><em>3</em><strong>2</strong></span></td>
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<td width="60"><span class="intbl"><em>7</em><strong>3</strong></span></td>
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<td width="60"><span class="intbl"><em>16</em><strong>15</strong></span></td>
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<td width="60"><span class="intbl"><em>15</em><strong>15</strong></span></td>
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<td width="60"><span class="intbl"><em>100</em><strong>5</strong></span></td>
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</tr>
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</table>
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<p class="center">See how the top number is bigger than (or equal to) the bottom number?
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<br />
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That makes it an Improper Fraction, (but there is <a href="#notwrong">nothing wrong about Improper Fractions</a>).</p>
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<h2>Three Types of Fractions</h2>
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<p>There are three types of fraction:</p>
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<p align="center"><img src="numbers/images/fraction-types.svg" alt="Fraction Types: Proper, Improper, Mixed" /></p>
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<h2>Fractions</h2>
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<p>A Fraction (such as <span class="frac"><sup>7</sup>/<sub>4</sub></span>) has two numbers:</p>
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<p class="center large"><span class="intbl"><em>Numerator</em><strong>Denominator</strong></span> </p>
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<p>The top number (the Numerator) is the number of <b>parts we have</b>.
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<br /> The bottom number (the Denominator) is the number of <b>parts the whole is divided into</b>.</p>
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<div class="example">
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<p>Example: <span class="frac-large"><sup>7</sup>/<sub>4</sub></span> means:</p>
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<ul>
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<li>We have <b>7</b> parts</li>
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<li>Each part is a <b>quarter</b> (<span class="frac"><sup>1</sup>/<sub>4</sub></span>) of a whole
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<br /> </li>
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</ul>
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</div>
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<p>So we can define the three types of fractions like this:</p>
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<div class="simple">
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<table border="0" align="center">
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<tr>
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<th rowspan="2" valign="top">Proper Fractions:</th>
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<td>The numerator is less than the denominator</td>
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</tr>
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<tr>
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<td>Examples: <span class="frac"><sup>1</sup>/<sub>3</sub></span>, <span class="frac"><sup>3</sup>/<sub>4</sub></span>, <span class="frac"><sup>2</sup>/<sub>7</sub></span></td>
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</tr>
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<tr>
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<td bgcolor="#FFFFFF"> </td>
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<td bgcolor="#FFFFFF"> </td>
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</tr>
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<tr>
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<th rowspan="2" valign="top">Improper Fractions:</th>
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<td>The numerator is greater than (or equal to) the denominator</td>
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</tr>
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<tr>
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<td>Examples: <span class="frac"><sup>4</sup>/<sub>3</sub></span>, <span class="frac"><sup>11</sup>/<sub>4</sub></span>, <span class="frac"><sup>7</sup>/<sub>7</sub></span></td>
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</tr>
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<tr>
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<td bgcolor="#FFFFFF"> </td>
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<td bgcolor="#FFFFFF"> </td>
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</tr>
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<tr>
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<th rowspan="2" valign="top">Mixed Fractions:</th>
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<td>A whole number and proper fraction together</td>
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</tr>
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<tr>
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<td>Examples: 1 <span class="frac"><sup>1</sup>/<sub>3</sub></span>, 2 <span class="frac"><sup>1</sup>/<sub>4</sub></span>, 16 <span class="frac"><sup>2</sup>/<sub>5</sub></span></td>
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</tr>
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</table>
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</div>
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<h2>Improper Fraction</h2>
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<p>So an improper fraction is a fraction where the top number (numerator) is greater than or equal to the bottom number (denominator): it is <b>top-heavy</b>.
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<br /> </p>
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<div style="float:left; margin: 0 10px 5px 0;">
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<table border="0" align="center">
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<tr>
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<td align="center"><img src="images/fractions/pie-4-4.jpg" alt="4/4" width="120" height="120" />
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<br /><span class="large"><span class="intbl"><em>4</em><strong>4</strong></span></span></td>
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</tr>
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</table>
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</div>
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<h2>Can be Equal</h2>
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<p>What about when the numerator is equal to the denominator? For example <span class="frac"><sup>4</sup>/<sub>4</sub></span> ?</p>
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<p>Well it is the same as a whole, but it is written as a fraction, so most people agree it is a type of improper fraction.</p>
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<p> </p>
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<h2>Improper Fractions or Mixed Fractions </h2>
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<p>We can use either an improper fraction or a mixed fraction to show the same amount. </p>
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<p>For example 1<span class="intbl"><em>3</em><strong>4</strong></span> = <span class="intbl"><em>7</em><strong>4</strong></span>, as shown here: </p>
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<p> </p>
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<table border="0" align="center">
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<tr align="center" class="large">
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<td>1<span class="intbl"><em>3</em><strong>4</strong></span></td>
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<td> </td>
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<td><span class="intbl"><em>7</em><strong>4</strong></span></td>
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</tr>
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<tr align="center">
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<td><img src="images/fractions/pie-1-1.jpg" width="120" height="120" alt="pie full" /><img src="images/fractions/pie-3-4.jpg" width="120" height="120" alt="pie 3/4" /></td>
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<td class="huge" width="40">=</td>
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<td><img src="images/fractions/pie-4-4.jpg" width="120" height="120" alt="pie 4/4" /><img src="images/fractions/pie-3-4.jpg" width="120" height="120" alt="pie 3/4" /></td>
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</tr>
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</table>
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<p> </p>
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<h2>Converting Improper Fractions to Mixed Fractions<br />
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</h2> To convert an improper fraction to a mixed fraction, follow these steps:
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<br />
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<br />
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<table border="0">
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<tr>
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<td><img src="images/dog-pointing.gif" width="46" height="55" alt="dog looking" /></td>
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<td>
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<ul>
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<li>Divide the numerator by the denominator.</li>
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<li>Write down the whole number answer</li>
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<li>Then write down any remainder above the denominator.</li>
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</ul>
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</td>
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</tr>
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<tr>
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<td> </td>
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<td> </td>
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</tr>
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</table>
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<div class="example">
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<h3>Example: Convert <span class="intbl"><em>11</em><strong>4</strong></span> to a mixed fraction.</h3>
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<p>Divide: </p>
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<div class="so">11 ÷ 4 = 2 with a remainder of 3 </div>
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<p>Write down the 2 and then write down the remainder (3) above the denominator (4).</p>
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<p>Answer: </p>
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<p class="center large">2 <span class="intbl"><em>3</em><strong>4</strong></span></p>
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</div><p>That example can be written like this:</p>
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<p align="center"><img src="numbers/images/fraction-11-4-mixed.svg" alt="Fraction 11/4 = 2 3/4" /></p>
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<div class="example">
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<h3>Example: Convert <span class="intbl"><em>10</em><strong>3</strong></span> to a mixed fraction. </h3>
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<p align="center"><img src="numbers/images/fraction-10-3-mixed.svg" alt="Fraction 11/4 = 2 3/4" /></p>
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<p>Answer: </p>
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<p class="center large">3 <span class="intbl"><em>1</em><strong>3</strong></span></p>
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</div>
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<p> </p>
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<h2>Converting Mixed Fractions to Improper Fractions</h2> To convert a mixed fraction to an improper fraction, follow these steps:
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<br />
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<br />
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<table border="0">
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<tr>
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<td><img src="images/dog-pointing.gif" width="46" height="55" alt="dog looking" /></td>
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<td>
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<ul>
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<li>Multiply the whole number part by the fraction's denominator.</li>
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<li>Add that to the numerator</li>
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<li>Then write the result on top of the denominator.</li>
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</ul>
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</td>
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</tr>
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<tr>
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<td> </td>
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<td> </td>
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</tr>
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</table>
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<div class="example">
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<h3>Example: Convert 3<span class="intbl"><em>2</em><strong>5</strong></span> to an improper fraction.</h3>
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<p>Multiply the whole number part by the denominator: </p>
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<div class="so">3 × 5 = 15 </div>
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<p>Add that to the numerator: </p>
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<div class="so">15 + 2 = 17 </div>
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<p>Then write that result above the denominator: </p>
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<p class="center large"><span class="intbl"><em>17</em><strong>5</strong></span> </p>
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</div>
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<p>We can do the numerator in one go:</p>
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<p align="center"><img src="numbers/images/fraction-3-2-5-improper.svg" alt="Fraction 2 2/5 = 17/5" /></p>
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<div class="example">
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<h3>Example: Convert 2<span class="intbl"><em>1</em><strong>9</strong></span> to an improper fraction.</h3>
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<p align="center"><img src="numbers/images/fraction-2-1-9-improper.svg" alt="Fraction 2 1/9 = 19/9" /></p>
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</div>
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<p> </p>
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<h2><a name="notwrong" id="notwrong"></a>Are Improper Fractions Bad ?</h2>
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<p>NO, they aren't bad! </p>
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<p>For mathematics they are actually <b>better</b> than mixed fractions. Because mixed fractions can be confusing when we write them in a formula: <i><b>should the two parts be added or multiplied?</b></i></p>
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<table border="0" align="center">
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<tr>
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<th align="right">Mixed Fraction: </th>
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<td width="20"> </td>
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<td align="right">What is:</td>
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<td> </td>
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<td nowrap>1 + 2<span class="intbl"><em>1</em><strong>4</strong></span> ?</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 align="right"> </td>
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<td> </td>
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<td align="right">Is it:</td>
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<td> </td>
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<td nowrap>1 + 2 <span class="hilite">+</span> <span class="intbl"><em>1</em><strong>4</strong></span></td>
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<td> </td>
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<td>= 3<span class="intbl"><em>1</em><strong>4</strong></span> <b>?</b></td>
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</tr>
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<tr>
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<td align="right"> </td>
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<td> </td>
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<td align="right"><i><b>Or</b></i> is it:</td>
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<td> </td>
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<td nowrap>1 + 2 <span class="hilite">×</span> <span class="intbl"><em>1</em><strong>4</strong></span></td>
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<td> </td>
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<td>= 1<span class="intbl"><em>1</em><strong>2</strong></span> <b>?</b></td>
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</tr>
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<tr>
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<td align="right"> </td>
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<td> </td>
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<td align="right"> </td>
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<td> </td>
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<td nowrap> </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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<th align="right">Improper Fraction: </th>
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<th> </th>
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<td align="right">What is:</td>
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<td> </td>
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<td nowrap>1 + <span class="intbl"><em>9</em><strong>4</strong></span> ?</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 align="right"> </td>
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<td> </td>
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<td align="right">It is: </td>
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<td> </td>
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<td nowrap><span class="intbl"><em>4</em><strong>4</strong></span> + <span class="intbl"><em>9</em><strong>4</strong></span> = <span class="intbl"><em>13</em><strong>4</strong></span></td>
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<td> </td>
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<td><img src="images/style/yes.svg" alt="yes"></td>
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</tr>
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</table>
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<p>But, for <b>everyday use</b>, people understand mixed fractions better. </p>
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<div class="example">
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<p>Example: It is easier to say "I ate 2<span class="intbl"><em>1</em><strong>4</strong></span> sausages", than "I ate <span class="intbl"><em>9</em><strong>4</strong></span> sausages"</p>
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<p>We Recommend:</p>
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<li>For Mathematics: Improper Fractions</li>
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<li>For Everyday Use: Mixed Fractions</li>
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<div class="related"> <a href="fractions.html">Introduction to Fractions</a> <a href="proper-fractions.html">Proper Fractions</a> <a href="mixed-fractions.html">Mixed Fractions</a> <a href="fractions_addition.html">Adding Fractions</a> <a href="fractions_subtraction.html">Subtracting Fractions</a> <a href="fractions_multiplication.html">Multiplying Fractions</a> <a href="fractions_division.html">Dividing Fractions</a> <a href="fractions-menu.html">Fractions Index</a></div>
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