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230 lines
9.3 KiB
HTML
230 lines
9.3 KiB
HTML
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<!-- Mirrored from www.mathsisfun.com/equivalent_fractions.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:36:01 GMT -->
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<!-- #BeginEditable "Body" -->
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<h1 id="title" align="center">Equivalent Fractions</h1>
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<span id="video"></span>
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<script>initVideo('RbKFgYm6bE0');</script>
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<p class="center"><b><i>Equivalent Fractions</i></b><i> have the same value, even though they may look different.</i></p>
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<p>These fractions are really the same:</p>
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<p class="center large"><span class="intbl">
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<em>1</em>
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<strong>2</strong>
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</span> = <span class="intbl">
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<em>2</em>
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<strong>4</strong>
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</span> = <span class="intbl">
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<em>4</em>
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<strong>8</strong>
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</span></p>
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<p><b>Why are they the same?</b> Because when you multiply or divide <b>both</b> the top and bottom by the same number, the fraction keeps it's value.</p>
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<p>The rule to remember is:</p>
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<p class="center larger"><i>"Change the bottom using multiply or divide,<br>
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And the same to the top must be applied"</i></p>
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<p>Here is why those fractions are really the same:</p>
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<table align="center" cellspacing="3" cellpadding="0" border="0">
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<tbody>
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<tr align="center">
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<td style="width:30px;"> </td>
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<td class="larger" style="width:40px;"><b>× 2</b></td>
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<td style="width:30px;"> </td>
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<td class="larger" style="width:40px;"><b>× 2</b></td>
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<td style="width:30px;"> </td>
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</tr>
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<tr align="center">
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<td colspan="5">
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<div class="center larger"><img src="images/style/right-over-arrow.gif" alt="right over arrow" height="25" width="75"> <img src="images/style/right-over-arrow.gif" alt="right over arrow" height="25" width="75"></div></td>
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</tr>
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<tr align="center">
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<td class="larger">1</td>
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<td rowspan="2"> = </td>
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<td class="larger">2</td>
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<td rowspan="2"> = </td>
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<td class="larger">4</td>
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</tr>
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<tr align="center">
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<td class="larger" style="border-top: 1px solid black;">2</td>
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<td class="larger" style="border-top: 1px solid black;">4</td>
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<td class="larger" style="border-top: 1px solid black;">8</td>
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</tr>
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<tr align="center">
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<td colspan="5">
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<div class="center larger"><img src="images/style/right-under-arrow.gif" alt="right under arrow" height="25" width="75"> <img src="images/style/right-under-arrow.gif" alt="right under arrow" height="25" width="75"></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 class="larger" style="width:40px;"><b>× 2</b></td>
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<td> </td>
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<td class="larger" style="width:40px;"><b>× 2</b></td>
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<td> </td>
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</tr>
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</tbody></table>
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And visually it looks like this:<br>
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<br>
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<table style="border: 0; margin:auto;">
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<tbody>
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<tr align="center">
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<td style="width:124px;"><span class="frac-large"><sup>1</sup>/<sub>2</sub></span></td>
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<td style="width:40px;"> </td>
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<td style="width:143px;"><span class="frac-large"><sup>2</sup>/<sub>4</sub></span></td>
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<td style="width:40px;"> </td>
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<td style="width:145px;"><span class="frac-large"><sup>4</sup>/<sub>8</sub></span></td>
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</tr>
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<tr align="center">
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<td style="width:124px;"><img src="images/fractions/pie-1-2.jpg" alt="pie 1/2" height="120" width="120"></td>
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<td class="large" style="width:40px;">=</td>
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<td style="width:143px;"><img src="images/fractions/pie-2-4.jpg" alt="pie 2/4" height="120" width="120"></td>
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<td class="large" style="width:40px;">=</td>
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<td style="width:145px;"><img src="images/fractions/pie-4-8.jpg" alt="pie 4/8" height="120" width="120"></td>
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</tr>
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</tbody></table>
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<p> </p>
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<p class="center">See <a href="numbers/fraction-number-line.html">Fractions on the Number Line</a> ...<br>
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<a href="numbers/fraction-number-line.html"><img src="numbers/images/fraction-number-line-thumb.gif" alt="fraction number line" height="94" width="189" border="0"></a><br>
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...
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it shows many equivalent fractions.</p>
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<div style="clear:both"></div>
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<p>Also see the <a href="numbers/fraction-decimal-chart.html">Chart of Fractions</a> with many examples of equivalent fractions.</p>
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<h2>Dividing</h2>
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<p>Here are some more equivalent fractions, this time by dividing:</p>
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<div class="clear">
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<table align="center" cellspacing="3" cellpadding="0" border="0">
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<tbody>
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<tr align="center">
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<td style="width:30px;"> </td>
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<td class="larger" style="width:40px;">÷ 3</td>
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<td style="width:30px;"> </td>
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<td class="larger" style="width:40px;">÷ 6</td>
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<td style="width:30px;"> </td>
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</tr>
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<tr align="center">
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<td colspan="5" class="larger"><img src="images/style/right-over-arrow.gif" alt="right over arrow" height="25" width="75"> <img src="images/style/right-over-arrow.gif" alt="right over arrow" height="25" width="75"></td>
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</tr>
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<tr align="center">
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<td class="larger">18</td>
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<td rowspan="2"> = </td>
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<td class="larger">6</td>
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<td rowspan="2"> = </td>
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<td class="larger">1</td>
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</tr>
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<tr align="center">
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<td class="larger" style="border-top: 1px solid black;">36</td>
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<td class="larger" style="border-top: 1px solid black;">12</td>
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<td class="larger" style="border-top: 1px solid black;">2</td>
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</tr>
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<tr align="center">
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<td colspan="5" class="larger"><img src="images/style/right-under-arrow.gif" alt="right under arrow" height="25" width="75"> <img src="images/style/right-under-arrow.gif" alt="right under arrow" height="25" width="75"></td>
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</tr>
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<tr align="center">
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<td> </td>
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<td class="larger" style="width:40px;">÷ 3</td>
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<td> </td>
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<td class="larger" style="width:40px;">÷ 6</td>
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<td> </td>
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</tr>
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</tbody></table>
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</div>
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<p>Choose the number you divide by carefully, so that the results (both top and bottom) stay <a href="whole-numbers.html">whole numbers</a>.</p>
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<p>If we keep dividing until we can't go any further, then we have <a href="simplifying-fractions.html">simplified</a> the fraction (made it as simple as possible).</p>
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<p> </p>
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<h2>Summary:</h2>
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<ul>
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<div class="bigul">
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<li>You can make equivalent fractions by multiplying or dividing <b>both top and bottom</b> by the same amount.</li>
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<li>You only multiply or divide, <b>never add or subtract</b>, to get an equivalent fraction.</li>
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<li>Only divide when the top and bottom stay as whole numbers.</li>
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</div>
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</ul>
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<p> </p>
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<div class="questions">
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<script>getQ(907, 908, 1376, 1377, 909, 910, 1378, 3540, 3541, 3542);</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="numbers/fraction-number-line.html">Fraction Number Line</a>
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<a href="numbers/fraction-decimal-chart.html">Fraction/Decimal Chart</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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Copyright © 2020 MathsIsFun.com
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