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205 lines
7.2 KiB
HTML
205 lines
7.2 KiB
HTML
<!DOCTYPE html>
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<html lang="en"><!-- #BeginTemplate "/Templates/Main.dwt" --><!-- DW6 -->
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<!-- Mirrored from www.mathsisfun.com/reciprocal.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:59:39 GMT -->
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<meta http-equiv="content-type" content="text/html; charset=utf-8">
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<title>Reciprocal</title>
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<div class="bg">
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<div id="hdr"></div>
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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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<script>document.write(getAdTop());</script>
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<a href="about-ads.html">About Ads</a></div>
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</div>
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</header>
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<nav>
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<div id="menuWide" class="menu">
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<script>document.write(getMenu(0));</script>
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<script>document.write(getLinks());</script>
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<article id="content" role="main">
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<!-- #BeginEditable "Body" -->
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<h1 class="center">Reciprocal</h1>
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<p class="center larger"><i>The reciprocal is simply: 1/number</i></p>
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<div class="center"><img src="numbers/images/reciprocal.svg" alt="reciprocal"> </div>
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<p>To get the reciprocal of a number, we divide 1 by the number.</p>
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<div class="example">
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<h3>Example: the reciprocal of 2 is ½ <i>(a half)</i></h3>
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</div>
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<h3>More Examples:</h3>
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<div class="simple">
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<table align="center" width="400" border="0">
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<tbody>
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<tr style="text-align:center;">
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<th>Number</th>
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<th>Reciprocal</th>
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<th>As a Decimal</th>
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</tr>
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<tr style="text-align:center;">
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<td>5</td>
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<td><span class="intbl"><em>1</em><strong>5</strong></span></td>
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<td>= 0.2</td>
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</tr>
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<tr style="text-align:center;">
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<td>8</td>
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<td><span class="intbl"><em>1</em><strong>8</strong></span></td>
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<td>= 0.125</td>
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</tr>
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<tr style="text-align:center;">
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<td>1000</td>
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<td><span class="intbl"><em>1</em><strong>1000</strong></span></td>
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<td>= 0.001</td>
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</tr>
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</tbody></table>
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</div>
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<h2>Like Turning the Number Upside Down</h2>
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<table style="border: 0;">
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<tbody>
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<tr>
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<td><img src="images/art/sage-upside-down.gif" alt="dog upside down" height="114" width="251"></td>
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<td> </td>
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<td>
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<p>We can think of a whole number as being "number/1", so the reciprocal is just like "flipping it over":</p>
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<div class="simple">
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<table align="center" width="400" border="0">
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<tbody>
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<tr style="text-align:center;">
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<th>Number </th>
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<th> </th>
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<th>Reciprocal</th>
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</tr>
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<tr style="text-align:center;">
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<td>5 = <span class="intbl">
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<em>5</em><strong>1</strong></span></td>
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<td> </td>
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<td><span class="intbl">
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<em>1</em>
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<strong>5</strong></span></td>
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</tr>
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<tr style="text-align:center;">
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<td>8 = <span class="intbl">
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<em>8</em><strong>1</strong></span></td>
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<td> </td>
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<td><span class="intbl">
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<em>1</em>
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<strong>8</strong></span></td>
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</tr>
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<tr style="text-align:center;">
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<td>1000 = <span class="intbl">
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<em>1000</em><strong>1</strong></span></td>
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<td> </td>
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<td><span class="intbl">
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<em>1</em>
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<strong>1000</strong></span></td>
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</tr>
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</tbody></table>
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</div>
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</td>
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</tr>
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</tbody></table>
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<h2>For Fractions, Flip the Whole Fraction Over</h2>
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<div class="example">
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<p>Example: the reciprocal of <span class="frac"><sup>3</sup>/<sub>4</sub></span> is <span class="frac"><sup>4</sup>/<sub>3</sub></span></p>
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</div>
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<p>Read more at <a href="reciprocal-fraction.html">Reciprocal of a Fraction</a>.</p>
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<p style="float:left; margin: 0 10px 5px 0;"><img src="images/art/sage-flipping-frisbee.gif" alt="dog flipping frisbee" height="200" width="140"></p>
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<h2>Flipping a Flip</h2>
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<p>The reciprocal of a reciprocal takes us <b>back to where we started</b>:</p>
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<p class="center"><img src="numbers/images/reciprocal-reciprocal.svg" alt="Reciprocals"></p>
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<div style="clear:both"></div>
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<div class="example">
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<h3>Example:</h3>
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<p>The reciprocal of <span class="large">4</span> is <span class="frac"><sup>1</sup>/<sub>4</sub></span></p>
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<p>The reciprocal of <span class="frac"><sup>1</sup>/<sub>4</sub></span> is <span class="large">4 </span>(back to 4 again)</p>
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</div>
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<p>It may help to remember that "Reciprocal" comes from the Latin <i>reciprocus</i> meaning <i>returning</i>. Like going to the shops and then <i>returning</i> home again.</p>
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<h2>But Not Zero</h2>
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<p>Every number has a reciprocal except 0 (<a href="numbers/dividing-by-zero.html">1/0 is undefined</a>)</p>
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<h2>Multiplying a Number by Its Reciprocal </h2>
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<p>Let us try multiplying a number by its reciprocal:</p>
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<div class="center80">2 × (<span class="frac"><sup>1</sup>/<sub>2</sub></span>) = 2 x 0.5 = <b>1</b></div>
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<p>How about another:</p>
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<div class="center80">10 × (<span class="frac"><sup>1</sup>/<sub>10</sub></span>) = 10 x 0.1 = <b>1</b></div>
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<p>Try some more yourself! You should always get <b>1</b></p>
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<p>And that is a way to define Reciprocal:</p>
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<div class="def">
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<p class="center large">Reciprocal: what to multiply a value by to get 1</p>
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</div><p> </p>
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<p class="words">The reciprocal is also called the "<a href="numbers/inverse.html">Multiplicative Inverse</a>".</p>
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<p> </p>
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<div class="questions">
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<script>getQ(312, 1619, 313, 1620);</script>
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</div>
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<div class="related">
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<a href="algebra/reciprocal.html">Reciprocal in Algebra</a>
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<a href="reciprocal-fraction.html">Reciprocal of a Fraction</a>
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<a href="numbers/index.html">Numbers Index</a>
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</div>
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</article>
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Copyright © 2020 MathsIsFun.com
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