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<!doctype html>
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<!-- Mirrored from www.mathsisfun.com/fractions.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:35:57 GMT -->
<head>
<!-- #BeginEditable "doctitle" -->
<title>Fractions</title>
<script src="numbers/images/ani-frac-pick.js" type="text/javascript"></script>
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<h1 align="center">Fractions</h1>
<p align="center"><i>How many equal parts of a whole</i></p>
<h3>Slice a pizza, and we get fractions:</h3>
<table width="450" border="0" align="center">
<tr align="center">
<td width="124"> <img src="images/fractions/pie-1-2.jpg" width="120" height="120" alt="pie 1/2" /></td>
<td width="143"> <img src="images/fractions/pie-1-4.jpg" width="120" height="120" alt="pie 1/4" /></td>
<td width="145"> <img src="images/fractions/pie-3-8.jpg" width="120" height="120" alt="pie 3/8" /></td>
</tr>
<tr align="center">
<td width="124"> <span class="frac-large"><sup>1</sup>/<sub>2</sub></span> </td>
<td width="143"> <span class="frac-large"><sup>1</sup>/<sub>4</sub></span> </td>
<td width="145"> <span class="frac-large"><sup>3</sup>/<sub>8</sub></span> </td>
</tr>
<tr align="center">
<td width="124">
<div align="center"><b>(One-Half)</b></div> </td>
<td width="143">
<div align="center"><b>(One-Quarter)</b></div> </td>
<td width="145">
<div align="center"><b>(Three-Eighths)</b></div> </td>
</tr>
</table>
<p class="center">The top number says how many slices we <b>have. </b><br />
The bottom number says how many equal slices the whole pizza was <b>cut into</b>.
</p>
<h3>Have a try yourself:</h3>
<script type="text/javascript">anifracpickMain('');</script>
<h2>Equivalent Fractions</h2>
<p>Some fractions may look different, but are really the same, for example: <br />
<br />
</p>
<table border="0" align="center">
<tr align="center">
<td width="124"><span class="frac-large"><sup>4</sup>/<sub>8</sub></span> </td>
<td width="40">=</td>
<td width="143"><span class="frac-large"><sup>2</sup>/<sub>4</sub></span> </td>
<td width="40">=</td>
<td width="145"><span class="frac-large"><sup>1</sup>/<sub>2</sub></span> </td>
</tr>
<tr align="center">
<td width="124">(Four-Eighths)</td>
<td width="40">&nbsp;</td>
<td width="143">(Two-Quarters)</td>
<td width="40">&nbsp;</td>
<td width="145">(One-Half)</td>
</tr>
<tr align="center">
<td width="124"><img src="images/fractions/pie-4-8.jpg" width="120" height="120" alt="pie 4/8" /></td>
<td width="40" class="large">=</td>
<td width="143"><img src="images/fractions/pie-2-4.jpg" width="120" height="120" alt="pie 2/4" /></td>
<td width="40" class="large">=</td>
<td width="145"><img src="images/fractions/pie-1-2.jpg" width="120" height="120" alt="pie 1/2" /></td>
</tr>
</table>
<p>It is usually best to show an answer using the simplest fraction ( <span class="frac-large"><sup>1</sup>/<sub>2</sub></span> in this case ).
That is called <i><b>Simplifying</b></i>, or <i><b>Reducing</b></i> the Fraction
</p>
<h2>Numerator / Denominator</h2>
<p>We call the top number the <b>Numerator</b>, it is the number of parts we <b>have</b>.<br />
We call the bottom number the <b>Denominator</b>, it is the number of parts the whole is <b>divided into</b>.</p>
<p class="center large"><span class="intbl"><em>Numerator</em><strong>Denominator</strong></span></p>
<p>You just have to remember those names! (If you forget just think &quot;Down&quot;-ominator)</p>
<h2>Adding Fractions</h2>
<p>It is easy to add fractions with the <b>same denominator</b> (same bottom number): </p>
<div class="center">
<table border="0" align="center">
<tr align="center">
<td width="20%"><span class="frac-large"><sup>1</sup>/<sub>4</sub></span> </td>
<td>+</td>
<td width="20%"><span class="frac-large"><sup>1</sup>/<sub>4</sub></span> </td>
<td>=</td>
<td width="20%"><span class="frac-large"><sup>2</sup>/<sub>4</sub></span> </td>
<td>=</td>
<td width="20%"><span class="frac-large"><sup>1</sup>/<sub>2</sub></span> </td>
</tr>
<tr align="center">
<td>(One-Quarter)</td>
<td>&nbsp;</td>
<td>(One-Quarter)</td>
<td>&nbsp;</td>
<td>(Two-Quarters)</td>
<td>&nbsp;</td>
<td>(One-Half)</td>
</tr>
<tr align="center">
<td><img src="images/fractions/pie-1-4.jpg" style="width:120px; max-width:100%" alt="pie 1/4" /></td>
<td class="large">+</td>
<td><img src="images/fractions/pie-1-4.jpg" style="width:120px; max-width:100%" alt="pie 1/4" /></td>
<td class="large">=</td>
<td><img src="images/fractions/pie-2-4.jpg" style="width:120px; max-width:100%" alt="pie 2/4" /></td>
<td class="large">=</td>
<td><img src="images/fractions/pie-1-2.jpg" style="width:120px; max-width:100%" alt="pie 1/2" /></td>
</tr>
</table>
One-quarter plus one-quarter equals two-quarters, equals one-half</div>
<p>Another example:</p>
<div class="center">
<table border="0" align="center">
<tr align="center">
<td width="20%" height="7"><span class="frac-large"><sup>5</sup>/<sub>8</sub></span> </td>
<td height="7">+</td>
<td width="20%" height="7"><span class="frac-large"><sup>1</sup>/<sub>8</sub></span> </td>
<td height="7">=</td>
<td width="20%" height="7"><span class="frac-large"><sup>6</sup>/<sub>8</sub></span> </td>
<td height="7">=</td>
<td width="20%" height="7"><span class="frac-large"><sup>3</sup>/<sub>4</sub></span> </td>
</tr>
<tr align="center">
<td><img src="images/fractions/pie-5-8.jpg" style="width:120px; max-width:100%" alt="pie 5/8" /></td>
<td class="large">+</td>
<td><img src="images/fractions/pie-1-8.jpg" style="width:120px; max-width:100%" alt="pie 1/8" /></td>
<td class="large">=</td>
<td><img src="images/fractions/pie-6-8.jpg" style="width:120px; max-width:100%" alt="pie 6/8" /></td>
<td class="large">=</td>
<td><img src="images/fractions/pie-3-4.jpg" style="width:120px; max-width:100%" alt="pie 3/4" /></td>
</tr>
</table>
Five-eighths plus one-eighth equals six-eighths, equals three-quarters
</div>
<br />
<h2>Adding Fractions with Different Denominators</h2>
<p>But what about when the <b>denominators</b> (the bottom numbers) are not the same?
<br />
</p>
<div class="center">
<table border="0" align="center">
<tr align="center">
<td width="124" class="center"><sup>3</sup>/<sub>8</sub></td>
<td width="40" class="center">+</td>
<td width="143" class="center"><sup>1</sup>/<sub>4</sub></td>
<td width="40" class="center">=</td>
<td width="145" class="center">?</td>
</tr>
<tr align="center">
<td width="124" class="center"><img src="images/fractions/pie-3-8.jpg" width="120" height="120" alt="pie 3/8" /></td>
<td width="40" class="center">+</td>
<td width="143" class="center"><img src="images/fractions/pie-1-4.jpg" width="120" height="120" alt="pie 1/4" /></td>
<td width="40" class="center">=</td>
<td width="145" class="center"><img src="images/fractions/pie-huh.jpg" width="120" height="120" alt="pie huh" /></td>
</tr>
</table>
<span class="center">Three-eighths plus one-quarter equals ... what? </span></div>
<p>
We must <i>somehow</i> make the denominators the same. </p>
<p>In this case it is easy, because we know that <span class="frac-large"><sup>1</sup>/<sub>4</sub></span>
is the same as <span class="frac-large"><sup>2</sup>/<sub>8</sub></span> :<br />
<br />
</p>
<div class="center">
<table border="0" align="center">
<tr align="center">
<td width="124"><span class="frac-large"><sup>3</sup>/<sub>8</sub></span> </td>
<td width="40">+</td>
<td width="143"><span class="frac-large"><sup>2</sup>/<sub>8</sub></span> </td>
<td width="40">=</td>
<td width="145"><span class="frac-large"><sup>5</sup>/<sub>8</sub></span> </td>
</tr>
<tr align="center">
<td width="124"><img src="images/fractions/pie-3-8.jpg" width="120" height="120" alt="pie 3/8" /></td>
<td width="40" class="large">+</td>
<td width="143"><img src="images/fractions/pie-2-8.jpg" width="120" height="120" alt="pie 2/8" /></td>
<td width="40" class="large">=</td>
<td width="145"><img src="images/fractions/pie-5-8.jpg" width="120" height="120" alt="pie 5/8" /></td>
</tr>
</table>
Three-eighths plus two-eighths equals five-eighths </div>
<p>&nbsp;</p>
<p>There are two popular methods to <b> make the denominators the same</b>:</p>
<ul>
<li><a href="least-common-denominator.html">Least Common Denominator</a>, or</li>
<li><a href="numbers/common-denominator.html">Common Denominator</a> </li>
</ul>
<p>(They both work nicely, use the one you prefer.) </p>
<h2>Other Things We Can Do With Fractions</h2>
<p>We can also:</p>
<ul>
<li><a href="fractions_subtraction.html">Subtract Fractions</a></li>
<li><a href="fractions_multiplication.html">Multiply Fractions</a></li>
<li><a href="fractions_division.html">Divide Fractions</a></li>
</ul>
<p>Visit the <a href="fractions-menu.html">Fractions Index</a> to find out even more.</p>
<p>&nbsp;</p>
<div class="questions">
<script type="text/javascript">getQ(904, 905, 1367, 1368, 3524, 3525, 3526, 906, 1369, 3527);</script>&nbsp;
</div>
<div class="related">
<a href="fractions-menu.html">Fractions Index</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>
<a href="fractions_multiplication.html">Multiplying Fractions</a>
<a href="fractions_division.html">Dividing Fractions</a>
<a href="greatest-common-factor.html">Greatest Common Factor</a>
<a href="least-common-multiple.html">Least Common Multiple</a></div>
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