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<title>Reciprocal of a Fraction</title>
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<h1 class="center">Reciprocal of a Fraction</h1>
<p class="larger">To get the reciprocal of a fraction, just turn it upside down.</p>
<p class="center"><i>Like this:</i></p>
<script>reciprocalMain('3','4');</script>
<h2>Fractions</h2>
A Fraction (such as <span class="intbl"><em>3</em><strong>4</strong></span>) has two numbers:
<p class="center large"><span class="intbl"><em>Numerator</em><strong>Denominator</strong></span></p>
<p>We call the top number the <b>Numerator</b>, it is the number of parts we have.<br>
We call the bottom number the <b>Denominator</b>, it is the number of parts the whole is divided into.</p>
<p style="float:right; margin: 0 0 5px 10px;"><img src="images/art/sage-upside-down.gif" alt="dog upside down" height="114" width="251"></p>
<h2>Reciprocal
of a Fraction</h2>
<p>To get the reciprocal of a fraction, just <b>turn it upside down</b>.<br>
In other words swap over the Numerator and Denominator.</p>
<h3>Examples:</h3>
<div class="simple">
<table align="center" width="300" border="0">
<tbody>
<tr style="text-align:center;">
<th>Fraction</th>
<th>Reciprocal</th>
</tr>
<tr style="text-align:center;">
<td><span class="intbl"><em>3</em><strong>8</strong></span></td>
<td><span class="intbl">
<em>8</em>
<strong>3</strong>
</span></td>
</tr>
<tr style="text-align:center;">
<td><span class="intbl"><em>5</em><strong>6</strong></span></td>
<td><span class="intbl">
<em>6</em>
<strong>5</strong>
</span></td>
</tr>
<tr style="text-align:center;">
<td height="13"><span class="intbl"><em>19</em><strong>7</strong></span></td>
<td><span class="intbl">
<em>7</em>
<strong>19</strong>
</span></td>
</tr>
<tr style="text-align:center;">
<td><span class="intbl"><em>1</em><strong>2</strong></span></td>
<td><span class="intbl"><em>2</em><strong>1</strong></span> = 2</td>
</tr>
</tbody></table>
</div>
<p>That last example was interesting. The reciprocal of <span class="intbl"><em>1</em><strong>2</strong></span> is 2</p>
<p>Likewise the reciprocal of <span class="intbl"><em>1</em><strong>3</strong></span> is 3 and so on.</p>
<h2>Multiplying a Fraction by its Reciprocal</h2>
<p>When we multiply a fraction by its reciprocal we get 1:</p>
<div class="example">
<h3>Examples:</h3>
<p class="center"><span class="intbl"><em>5</em><strong>6</strong></span> × <span class="intbl"><em>6</em><strong>5</strong></span> = 1<br>
<br>
<span class="intbl"><em>1</em><strong>3</strong></span> × 3 = 1</p>
</div>
<h2>Reciprocal of a Mixed Fraction</h2>
<p>To find the reciprocal of a <a href="mixed-fractions.html">Mixed Fraction</a>, we first convert it to an <a href="improper-fractions.html">Improper Fraction</a>, then turn that upside down.</p>
<div class="example">
<h3>Example: What is the reciprocal of 2<span class="intbl"><em>1</em><strong>3</strong></span> (two and one-third)?</h3>
<p>1. Convert it to an improper fraction: 2<span class="intbl"><em>1</em><strong>3</strong></span> = <span class="intbl">
<em>6</em>
<strong>3</strong>
</span> + <span class="intbl">
<em>1</em>
<strong>3</strong>
</span> = <span class="intbl">
<em>7</em>
<strong>3</strong>
</span><br>
2. Turn it upside down: <span class="intbl"><em>3</em><strong>7</strong></span></p>
<p class="center"><b>The Answer is: <span class="intbl"><em>3</em><strong>7</strong></span></b></p>
</div>
<p>&nbsp;</p>
<div class="questions">
<script>getQ(312, 307, 1422, 1423, 1623, 1624, 3588, 3589, 3590, 3591);</script>&nbsp;
</div>
<div class="related">
<a href="fractions.html">Fractions</a>
<a href="reciprocal.html">Reciprocal</a>
<a href="least-common-multiple-tool.html">Least Common Multiple Tool</a>
<a href="comparing-fractions.html">Comparing Fractions</a>
<a href="simplifying-fractions.html">Simplifying Fractions</a>
<a href="equivalent_fractions.html">Equivalent Fractions</a>
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