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201 lines
8.2 KiB
HTML
201 lines
8.2 KiB
HTML
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<!-- Mirrored from www.mathsisfun.com/algebra/fractions-algebra.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:48:27 GMT -->
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<head>
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<title>Fractions in Algebra</title>
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<meta name="Description" content="Math explained in easy language, plus puzzles, games, quizzes, worksheets and a forum. For K-12 kids, teachers and parents." />
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<body id="bodybg">
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<div id="logo"><a href="../index.html"><img src="../images/style/logo.svg" alt="Math is Fun" /></a></div>
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<div id="content" role="main"><!-- #BeginEditable "Body" -->
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<h1 align="center">Fractions in Algebra</h1>
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<p>We can add, subtract, multiply and divide fractions in algebra in the same way we do in simple arithmetic.</p>
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<h2>Adding Fractions</h2>
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<p>To <a href="../fractions_addition.html">add fractions</a> there is a simple rule:</p>
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<p align="center"><img src="images/fractions-adding.gif" alt="adding fractions rule" width="245" height="53" /></p>
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<p align="center">(See why this works on the <a href="../numbers/common-denominator.html">Common Denominator</a> page).</p>
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<div class="example">
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<h3>Example: </h3>
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<p class="center larger"> <span class="intbl">
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<em>x</em>
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<strong>2</strong>
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</span> + <span class="intbl">
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<em>y</em>
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<strong>5</strong>
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</span> = <span class="intbl">
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<em>(x)(5) + (2)(y)</em>
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<strong>(2)(5)</strong>
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</span> </p>
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<p class="center larger"> = <span class="intbl">
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<em>5x+2y</em>
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<strong>10</strong>
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</span></p>
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</div>
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<div class="example">
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<h3>Example: </h3>
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<p class="center larger"> <span class="intbl">
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<em>x + 4</em>
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<strong>3</strong>
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</span> + <span class="intbl">
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<em>x − 3</em>
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<strong>4</strong>
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</span> = <span class="intbl">
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<em>(x+4)(4) + (3)(x−3)</em>
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<strong>(3)(4)</strong>
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</span></p>
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<p class="center larger"> = <span class="intbl">
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<em>4x+16 + 3x−9</em>
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<strong>12</strong>
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</span></p>
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<p class="center larger"> = <span class="intbl">
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<em>7x+7</em>
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<strong>12</strong>
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</span></p>
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</div>
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<h2>Subtracting Fractions</h2>
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<p><a href="../fractions_subtraction.html">Subtracting fractions</a> is very similar, except that the + is now −</p>
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<p align="center"><img src="images/fractions-subtracting.gif" alt="subtracting fractions" width="244" height="56" /></p>
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<div class="example">
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<h3>Example: </h3>
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<p class="center larger"> <span class="intbl">
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<em>x + 2</em>
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<strong>x</strong>
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</span> − <span class="intbl">
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<em>x</em>
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<strong>x − 2</strong>
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</span> = <span class="intbl">
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<em>(x+2)(x−2) − (x)(x)</em>
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<strong>x(x−2)</strong>
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</span> </p>
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<p class="center larger">= <span class="intbl">
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<em>(x<sup>2 </sup>− 2<sup>2</sup>) − x<sup>2</sup></em>
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<strong>x<sup>2</sup> − 2x</strong>
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</span></p>
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<p class="center larger">= <span class="intbl">
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<em>−4</em>
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<strong>x<sup>2</sup> − 2x</strong>
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</span></p>
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</div>
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<p align="center"> </p>
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<h2>Multiplying Fractions</h2>
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<p><a href="../fractions_multiplication.html">Multiplying fractions</a> is the easiest one of all, just multiply the tops together, and the bottoms together:</p>
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<p align="center"><img src="images/fractions-multiplying.gif" alt="Multiplying Fractions Rule" width="184" height="49" /></p>
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<div class="example">
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<h3>Example: </h3>
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<p class="center larger"> <span class="intbl">
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<em>3x</em>
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<strong>x−2</strong>
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</span> × <span class="intbl">
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<em>x</em>
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<strong>3</strong>
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</span> = <span class="intbl">
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<em>(3x)(x)</em>
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<strong>3(x−2)</strong>
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</span> </p>
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<p class="center larger">= <span class="intbl">
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<em>3x<sup>2</sup></em>
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<strong>3(x−2)</strong>
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</span> </p>
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<p class="center larger">= <span class="intbl">
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<em>x<sup>2</sup></em>
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<strong>x−2</strong>
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</span></p>
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</div>
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<h2>Dividing Fractions</h2>
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<p>To <a href="../fractions_division.html">divide fractions</a>, first "flip" the fraction we want to divide by, then use the same method as for multiplying:</p>
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<p align="center"><img src="images/fractions-divide.gif" alt="divide fractions" width="326" height="53" /></p>
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<div class="example">
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<h3>Example: </h3>
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<div class="clear">
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<div class="example2">
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<p class="example2 center larger"> <span class="intbl">
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<em>3y<sup>2</sup></em>
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<strong>x+1</strong>
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</span> ÷ <span class="intbl">
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<em>y</em>
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<strong>2</strong>
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</span> = <span class="intbl">
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<em>3y<sup>2</sup></em>
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<strong>x+1</strong>
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</span> × <span class="intbl">
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<em>2</em>
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<strong>y</strong>
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</span> </p>
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<p class="center larger">= <span class="intbl">
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<em>(3y<sup>2</sup>)(2)</em>
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<strong>(x+1)(y)</strong>
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</span></p>
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<p class="center larger">= <span class="intbl">
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<em>6y<sup>2</sup></em>
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<strong>(x+1)(y)</strong>
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</span> </p>
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<p class="center larger">= <span class="intbl">
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<em>6y</em>
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<strong>x+1</strong>
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</span></p>
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</div>
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</div>
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</div>
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<p> </p>
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<div class="questions">
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<script type="text/javascript">getQ(3881, 3879, 3880, 3882, 337, 336, 2268, 2269);</script><br />
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Hard: <script type="text/javascript">getQ(190, 240, 241, 242, 257);</script> </div>
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<div class="related"> <a href="rational-numbers-operations.html">Using Rational Numbers</a> <a href="index.html">Algebra Index</a> </div>
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<div id="copyrt">
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Copyright © 2017 MathsIsFun.com
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