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<h1 align="center">Proper Fractions</h1>
<table border="0" align="center">
<tr align="center">
<td><img src="images/fractions/pie-3-8.jpg" width="120" height="120" alt="pie 3/8" /></td>
<td rowspan="3">&nbsp;</td>
<td rowspan="3"><p class="larger">A Proper Fraction has a
top number<br />
less than its bottom number</p></td>
</tr>
<tr align="center">
<td><span class="intbl largest"><em>3</em><strong>8</strong></span></td>
</tr>
<tr align="center">
<td><div align="center">(Three-Eighths)</div></td>
</tr>
</table>
<h2>Examples</h2>
<div class="simple">
<table border="0" align="center" cellpadding="10">
<tr align="center" class="larger">
<td width="60"><span class="intbl"><em>3</em><strong>8</strong></span></td>
<td width="60"><span class="intbl"><em>1</em><strong>4</strong></span></td>
<td width="60"><span class="intbl"><em>14</em><strong>15</strong></span></td>
<td width="60"><span class="intbl"><em>4</em><strong>5</strong></span></td>
</tr>
</table>
</div>
<p>See how the top number is smaller than the bottom number in each example? That makes it a Proper Fraction.</p>
<h2>Three Types of Fractions</h2>
<p>There are three types of fraction:</p>
<p align="center"><img src="numbers/images/fraction-types.svg" alt="Fraction Types" /></p>
<h2>Fractions</h2>
<p>A Fraction (such as <span class="frac"><sup>3</sup>/<sub>8</sub></span>) has two numbers:
</p>
<p class="center large"><span class="intbl"><em>Numerator</em><strong>Denominator</strong></span></p>
<p>The top number is the Numerator, it is the number of <b>parts you have</b>.<br />
The bottom number is the Denominator, it is the number of <b>parts the whole is divided into</b>.</p>
<div class="example"><p style="float:right; margin: 0 0 5px 10px;"><img src="images/fractions/pie-3-4.jpg" width="120" height="120" alt="pie 3/4" /></p>
<h3>Example: <span class="frac-large"><sup>3</sup>/<sub>4</sub></span> means:</h3>
<ul>
<li>We have <b>3</b> parts</li>
<li>Each part is a <b>quarter</b> (<span class="frac"><sup>1</sup>/<sub>4</sub></span>) of a whole<br />
</li>
</ul>
</div>
<p>So we can define the three types of fractions like this:</p>
<div class="simple">
<table border="0" align="center">
<tr>
<th rowspan="2" valign="top">Proper Fractions:</th>
<td>The numerator is less than the denominator</td>
</tr>
<tr>
<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>
</tr>
<tr>
<td bgcolor="#FFFFFF">&nbsp;</td>
<td bgcolor="#FFFFFF">&nbsp;</td>
</tr>
<tr>
<th rowspan="2" valign="top">Improper Fractions:</th>
<td>The numerator is greater than (or equal to) the denominator</td>
</tr>
<tr>
<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>
</tr>
<tr>
<td bgcolor="#FFFFFF">&nbsp;</td>
<td bgcolor="#FFFFFF">&nbsp;</td>
</tr>
<tr>
<th rowspan="2" valign="top">Mixed Fractions:</th>
<td>A whole number and proper fraction together</td>
</tr>
<tr>
<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>
</tr>
</table>
</div>
<h2>Proper Fractions</h2>
<p>So, a proper fraction is just a fraction where the numerator (the top number) is less than the denominator (the bottom number). Here are some examples of proper fractions:</p>
<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>&nbsp;</p>
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<div class="related"> <a href="fractions.html">Introduction to Fractions</a> <a href="improper-fractions.html">Improper 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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