e39465ad2f
new file: Files/flashplayer_32_sa.exe
new file: favicon.ico
new file: globe.gif
new file: imgs/download.png
new file: imgs/zuck.jpg
new file: index.html
new file: other.ico
new file: script.js
new file: site.webmanifest
new file: sitemap.html
new file: styles/backround.css
new file: styles/border.css
new file: styles/fonts/Titillium_Web/OFL.txt
new file: styles/fonts/Titillium_Web/TitilliumWeb-Black.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-Bold.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-BoldItalic.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-ExtraLight.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-ExtraLightItalic.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-Italic.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-Light.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-LightItalic.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-Regular.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-SemiBold.ttf
new file: styles/fonts/Titillium_Web/TitilliumWeb-SemiBoldItalic.ttf
new file: styles/fonts/webfontkit-20221027-163353/generator_config.txt
new file: styles/fonts/webfontkit-20221027-163353/specimen_files/grid_12-825-55-15.css
new file: styles/fonts/webfontkit-20221027-163353/specimen_files/specimen_stylesheet.css
new file: styles/fonts/webfontkit-20221027-163353/stylesheet.css
new file: styles/fonts/webfontkit-20221027-163353/titilliumweb-extralight-demo.html
new file: styles/fonts/webfontkit-20221027-163353/titilliumweb-extralight-webfont.woff
new file: styles/fonts/webfontkit-20221027-163353/titilliumweb-extralight-webfont.woff2
new file: styles/fonts/webfontkit-20221027-165950/generator_config.txt
new file: styles/fonts/webfontkit-20221027-165950/specimen_files/grid_12-825-55-15.css
new file: styles/fonts/webfontkit-20221027-165950/specimen_files/specimen_stylesheet.css
new file: styles/fonts/webfontkit-20221027-165950/stylesheet.css
new file: styles/fonts/webfontkit-20221027-165950/titilliumweb-bold-demo.html
new file: styles/fonts/webfontkit-20221027-165950/titilliumweb-bold-webfont.woff
new file: styles/fonts/webfontkit-20221027-165950/titilliumweb-bold-webfont.woff2
new file: styles/style.css
new file: tools/2048/.gitignore
new file: tools/2048/.jshintrc
new file: tools/2048/CONTRIBUTING.md
new file: tools/2048/LICENSE.txt
new file: tools/2048/README.md
new file: tools/2048/Rakefile
new file: tools/2048/favicon.ico
new file: tools/2048/index.html
new file: tools/2048/js/animframe_polyfill.js
new file: tools/2048/js/application.js
new file: tools/2048/js/bind_polyfill.js
new file: tools/2048/js/classlist_polyfill.js
new file: tools/2048/js/game_manager.js
new file: tools/2048/js/grid.js
new file: tools/2048/js/html_actuator.js
new file: tools/2048/js/keyboard_input_manager.js
new file: tools/2048/js/local_storage_manager.js
new file: tools/2048/js/tile.js
new file: tools/2048/meta/apple-touch-icon.png
new file: tools/webretro/cores/neocd_libretro.js
new file: tools/webretro/cores/neocd_libretro.wasm
new file: tools/webretro/cores/nestopia_libretro.js
new file: tools/webretro/cores/nestopia_libretro.wasm
new file: tools/webretro/cores/o2em_libretro.js
new file: tools/webretro/cores/o2em_libretro.wasm
new file: tools/webretro/cores/opera_libretro.js
new file: tools/webretro/cores/opera_libretro.wasm
384 lines
13 KiB
HTML
384 lines
13 KiB
HTML
<!doctype html>
|
|
<html lang="en">
|
|
<!-- #BeginTemplate "/Templates/Main.dwt" --><!-- DW6 -->
|
|
<!-- Mirrored from www.mathsisfun.com/fractions_subtraction.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:36:06 GMT -->
|
|
<head>
|
|
<meta http-equiv="content-type" content="text/html; charset=utf-8">
|
|
<!-- #BeginEditable "doctitle" -->
|
|
<title>Subtracting Fractions</title>
|
|
<script src="video.js" type="text/javascript"></script>
|
|
<script src="images/player.js" type="text/javascript"></script>
|
|
<link rel="stylesheet" type="text/css" href="stylejs.css" />
|
|
<!-- #EndEditable -->
|
|
<meta name="keywords" content="math, maths, mathematics, school, homework, education">
|
|
<meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=yes">
|
|
<meta name="HandheldFriendly" content="true">
|
|
<meta name="referrer" content="always">
|
|
<link rel="stylesheet" type="text/css" href="style3.css">
|
|
<script src="main3.js"></script>
|
|
</head>
|
|
|
|
<body id="bodybg">
|
|
<div class="bg">
|
|
<div id="stt"></div>
|
|
<header>
|
|
<div id="hdr"></div>
|
|
<div id="logo"><a href="index.html"><img src="images/style/logo.svg" alt="Math is Fun"></a></div>
|
|
<div id="gtran">
|
|
<script>document.write(getTrans());</script>
|
|
</div>
|
|
<div id="adTopOuter" class="centerfull noprint">
|
|
<div id="adTop">
|
|
<script>document.write(getAdTop());</script>
|
|
</div>
|
|
</div>
|
|
<div id="adHide">
|
|
<div id="showAds1"><a href="javascript:showAds()">Show Ads</a></div>
|
|
<div id="hideAds1"><a href="javascript:hideAds()">Hide Ads</a><br>
|
|
<a href="about-ads.html">About Ads</a></div>
|
|
</div>
|
|
</header>
|
|
<nav>
|
|
<div id="menuWide" class="menu">
|
|
<script>document.write(getMenu(0));</script>
|
|
</div>
|
|
<div id="linkto">
|
|
<div id="linktort">
|
|
<script>document.write(getLinks());</script>
|
|
</div>
|
|
</div>
|
|
<div id="search" role="search">
|
|
<script>document.write(getSearch());</script>
|
|
</div>
|
|
<div id="menuSlim" class="menu">
|
|
<script>document.write(getMenu(1));</script>
|
|
</div>
|
|
<div id="menuTiny" class="menu">
|
|
<script>document.write(getMenu(2));</script>
|
|
</div>
|
|
</nav>
|
|
<div id="extra"></div>
|
|
</div>
|
|
<article id="content" role="main">
|
|
<!-- #BeginEditable "Body" -->
|
|
|
|
<h1 class="center" id="title">Subtracting Fractions</h1>
|
|
|
|
<span id="video"></span>
|
|
<script>initVideo('lXkppDjNwtA');</script>
|
|
<p class="center">You might like to read <a href="fractions_addition.html">Adding Fractions</a> first.</p>
|
|
<h3>There are 3 simple steps to subtract fractions</h3>
|
|
<ul>
|
|
<div class="bigul">
|
|
<li>Step 1. Make sure the bottom numbers (the denominators) are the same</li>
|
|
<li>Step 2. Subtract the top numbers (the numerators). Put the answer over the same denominator.</li>
|
|
<li>Step 3. Simplify the fraction (if needed).</li>
|
|
</div>
|
|
</ul>
|
|
<div class="example">
|
|
<h3>Example 1:
|
|
<p class="center large"><span class="intbl">
|
|
<em>3</em>
|
|
<strong>4</strong>
|
|
</span> − <span class="intbl">
|
|
<em>1</em>
|
|
<strong>4</strong>
|
|
</span></p></h3>
|
|
<p><b>Step 1</b>. The bottom numbers are already the same. Go straight to step 2.</p>
|
|
<p><b>Step 2</b>. Subtract the top numbers and put the answer over the same denominator:</p>
|
|
<p class="center large"><span class="intbl">
|
|
<em>3</em>
|
|
<strong>4</strong>
|
|
</span> − <span class="intbl">
|
|
<em>1</em>
|
|
<strong>4</strong>
|
|
</span> = <span class="intbl">
|
|
<em>3 − 1</em>
|
|
<strong>4</strong>
|
|
</span> = <span class="intbl">
|
|
<em>2</em>
|
|
<strong>4</strong>
|
|
</span></p>
|
|
<p><b><br>
|
|
Step 3</b>. Simplify the fraction:</p>
|
|
<p class="center large"><span class="intbl">
|
|
<em>2</em>
|
|
<strong>4</strong>
|
|
</span> = <span class="intbl">
|
|
<em>1</em>
|
|
<strong>2</strong>
|
|
</span></p>
|
|
<p>(If you are unsure of the last step see <a href="equivalent_fractions.html">Equivalent Fractions</a>.)</p>
|
|
</div>
|
|
<p> <br></p>
|
|
<div class="example">
|
|
<h3>Example 2:
|
|
<p class="center large"><span class="intbl">
|
|
<em>1</em>
|
|
<strong>2</strong>
|
|
</span> − <span class="intbl">
|
|
<em>1</em>
|
|
<strong>6</strong>
|
|
</span></p></h3>
|
|
<p><b>Step 1</b>. The bottom numbers are different. See how the slices are different sizes? We need to make them the same before we can continue, because we <b>can't</b> subtract them like this:</p>
|
|
<table style="border: 0; margin:auto;">
|
|
<tr style="text-align:center;">
|
|
<td><span class="intbl">
|
|
<em>1</em>
|
|
<strong>2</strong>
|
|
</span></td>
|
|
<td style="width:20px;">−</td>
|
|
<td><span class="intbl">
|
|
<em>1</em>
|
|
<strong>6</strong>
|
|
</span></td>
|
|
<td style="width:50px;">=</td>
|
|
<td>?</td>
|
|
</tr>
|
|
<tr style="text-align:center;">
|
|
<td><img src="images/fractions/pizza-1-2.jpg" alt="1/3" width="111" height="111" /></td>
|
|
<td class="large"> </td>
|
|
<td><img src="images/fractions/pizza-1-6.jpg" alt="1/6" width="112" height="111" /></td>
|
|
<td class="large"> </td>
|
|
<td><img src="images/fractions/pie-huh.jpg" width="120" height="120" alt="pie huh?" /></td>
|
|
</tr>
|
|
</table>
|
|
<p> </p>
|
|
<p>To make the bottom numbers the same, multiply the top and bottom of the first fraction (<span class="frac-large"><sup>1</sup>/<sub>2</sub></span>) by <b>3</b> like this:</p>
|
|
<table style="border: 0; margin:auto;">
|
|
<tr>
|
|
<td style="text-align:center;">× 3</td>
|
|
</tr>
|
|
<tr>
|
|
<td><img src="images/style/right-over-arrow.gif" width="75" height="25" alt="right over arrow" /></td>
|
|
</tr>
|
|
</table>
|
|
<table align="center">
|
|
<tr class="large" align="center">
|
|
<td><span class="intbl">
|
|
<em>1</em>
|
|
<strong>2</strong>
|
|
</span></td>
|
|
<td> = </td>
|
|
<td><span class="intbl">
|
|
<em>3</em>
|
|
<strong>6</strong>
|
|
</span></td>
|
|
</tr>
|
|
</table>
|
|
<table style="border: 0; margin:auto;">
|
|
<tr>
|
|
<td><img src="images/style/right-under-arrow.gif" width="75" height="25" alt="right under arrow" /></td>
|
|
</tr>
|
|
<tr>
|
|
<td style="text-align:center;">× 3</td>
|
|
</tr>
|
|
</table>
|
|
|
|
<p>And now our question looks like this:</p>
|
|
<table style="border: 0; margin:auto;">
|
|
<tr style="text-align:center;">
|
|
<td><span class="intbl">
|
|
<em>3</em>
|
|
<strong>6</strong>
|
|
</span></td>
|
|
<td style="width:20px;">−</td>
|
|
<td><span class="intbl">
|
|
<em>1</em>
|
|
<strong>6</strong>
|
|
</span></td>
|
|
</tr>
|
|
<tr style="text-align:center;">
|
|
<td><img src="images/fractions/pizza-3-6.jpg" alt="2/6" width="112" height="112" /></td>
|
|
<td class="large"> </td>
|
|
<td><img src="images/fractions/pizza-1-6.jpg" alt="1/6" width="112" height="111" /></td>
|
|
</tr>
|
|
</table>
|
|
|
|
<p>The bottom numbers (the denominators) are the same, so we can go to step 2.</p>
|
|
<p> </p>
|
|
<p><b>Step 2</b>. Subtract the top numbers and put the answer over the same denominator:</p>
|
|
<p class="center large"><span class="intbl">
|
|
<em>3</em>
|
|
<strong>6</strong>
|
|
</span> − <span class="intbl">
|
|
<em>1</em>
|
|
<strong>6</strong>
|
|
</span> = <span class="intbl">
|
|
<em>3 − 1</em>
|
|
<strong>6</strong>
|
|
</span> = <span class="intbl">
|
|
<em>2</em>
|
|
<strong>6</strong>
|
|
</span></p>
|
|
<p>In picture form it looks like this:</p>
|
|
<table style="border: 0; margin:auto;">
|
|
<tr style="text-align:center;">
|
|
<td><span class="intbl">
|
|
<em>3</em>
|
|
<strong>6</strong>
|
|
</span></td>
|
|
<td style="width:20px;">−</td>
|
|
<td><span class="intbl">
|
|
<em>1</em>
|
|
<strong>6</strong>
|
|
</span></td>
|
|
<td style="width:50px;">=</td>
|
|
<td><span class="intbl">
|
|
<em>2</em>
|
|
<strong>6</strong>
|
|
</span></td>
|
|
</tr>
|
|
<tr style="text-align:center;">
|
|
<td><img src="images/fractions/pizza-3-6.jpg" alt="2/6" width="112" height="112" /></td>
|
|
<td class="large"> </td>
|
|
<td><img src="images/fractions/pizza-1-6.jpg" alt="1/6" width="112" height="111" /></td>
|
|
<td class="large"> </td>
|
|
<td><img src="images/fractions/pizza-2-6.jpg" alt="3/6" width="112" height="111" /></td>
|
|
</tr>
|
|
</table>
|
|
<p><br>
|
|
<b>Step 3</b>. Simplify the fraction:</p>
|
|
<p class="center large"><span class="intbl">
|
|
<em>2</em>
|
|
<strong>6</strong>
|
|
</span> = <span class="intbl">
|
|
<em>1</em>
|
|
<strong>3</strong>
|
|
</span></p>
|
|
</div>
|
|
<h3>With Pen and Paper</h3>
|
|
<p>And here is how to do it with a pen and paper (press the play button):</p>
|
|
<script>playerMain("numbers/images/fractions-sub-a.txt",600,220,'');</script>
|
|
|
|
<p> </p>
|
|
<div class="simple">
|
|
<table style="border: 0; margin:auto;">
|
|
<tr>
|
|
<td><a href="numbers/fractions-subtraction-animation.html"><img src="numbers/images/adding-fractions-thumb.gif" width="150" height="114" border="0" alt="adding fractions thumb" /></a></td>
|
|
<td> </td>
|
|
<td><h3>Play with it!</h3>
|
|
<p>Try <a href="numbers/fractions-subtraction-animation.html">Subtracting Fractions Illustrated</a>.</p></td>
|
|
</tr>
|
|
</table>
|
|
</div>
|
|
|
|
|
|
<h2>Subtracting Mixed Fractions</h2>
|
|
<p>I have a special page on <a href="numbers/fractions-mixed-addition.html">Adding and Subtracting Mixed Fractions</a>.</p>
|
|
<h2>Making the Denominators the Same</h2>
|
|
<p>In the previous example it was easy to make the denominators the same, but it can be harder ... so you may need to use either the</p>
|
|
<ul>
|
|
<li><a href="numbers/common-denominator.html">Common Denominator Method</a>, or the</li>
|
|
<li><a href="least-common-denominator.html">Least Common Denominator Method</a></li>
|
|
</ul>
|
|
<p>They both work, use which one you prefer!</p>
|
|
<div class="example">
|
|
<p style="float:right; margin: 10px;"><img src="images/cupcakes.jpg" width="185" height="117" alt="cupcakes" /></p>
|
|
<h3>Example: Cupcakes
|
|
<p>You want to sell cupcakes at a market:</p>
|
|
<ul>
|
|
<li>You get paid <span class="intbl">
|
|
<em>2</em>
|
|
<strong>5</strong>
|
|
</span> of total sales</li>
|
|
<li>But you have to pay <span class="intbl">
|
|
<em>1</em>
|
|
<strong>4</strong>
|
|
</span> of total sales for the stall</li>
|
|
</ul>
|
|
<p>How much do you get?</p></h3>
|
|
<p> </p>
|
|
<p>We need to subtract <span class="intbl">
|
|
<em>1</em>
|
|
<strong>4</strong>
|
|
</span> from <span class="intbl">
|
|
<em>2</em>
|
|
<strong>5</strong>
|
|
</span></p>
|
|
<p class="center large"><span class="intbl">
|
|
<em>2</em>
|
|
<strong>5</strong>
|
|
</span> − <span class="intbl">
|
|
<em>1</em>
|
|
<strong>4</strong>
|
|
</span> = <span class="intbl">
|
|
<em>?</em>
|
|
<strong>?</strong>
|
|
</span></p>
|
|
<p><b>First</b> make the bottom numbers (the denominators) the same.</p>
|
|
<p>Multiply top and bottom of <sup>2</sup>/<sub>5</sub> by <b>4</b>:</p>
|
|
<p class="center large"><span class="intbl">
|
|
<em>2 × 4</em>
|
|
<strong>5 × 4</strong>
|
|
</span> − <span class="intbl">
|
|
<em>1</em>
|
|
<strong>4</strong>
|
|
</span> = <span class="intbl">
|
|
<em>?</em>
|
|
<strong>?</strong>
|
|
</span></p>
|
|
<p>And multiply top and bottom of <sup>1</sup>/<sub>4</sub> by <b>5</b>:</p>
|
|
<p class="center large"><span class="intbl">
|
|
<em>2 × 4</em>
|
|
<strong>5 × 4</strong>
|
|
</span> − <span class="intbl">
|
|
<em>1 × 5</em>
|
|
<strong>4 × 5</strong>
|
|
</span> = <span class="intbl">
|
|
<em>?</em>
|
|
<strong>?</strong>
|
|
</span></p>
|
|
<p><b>Now</b> do the calculations:</p>
|
|
<p class="center large"><span class="intbl">
|
|
<em>8</em>
|
|
<strong>20</strong>
|
|
</span> − <span class="intbl">
|
|
<em>5</em>
|
|
<strong>20</strong>
|
|
</span> = <span class="intbl">
|
|
<em>8 − 5</em>
|
|
<strong>20</strong>
|
|
</span> = <span class="intbl">
|
|
<em>3</em>
|
|
<strong>20</strong>
|
|
</span></p>
|
|
<p>Answer: you get to keep<b> <span class="intbl">
|
|
<em>3</em>
|
|
<strong>20</strong>
|
|
</span> </b>of total sales.</p>
|
|
</div>
|
|
<p> </p>
|
|
<div class="questions"><a href="worksheets/fractions.html">Worksheets</a>
|
|
<script>getQ(436, 433, 1403, 1404, 1405, 934, 1406, 3566, 3567, 3568);</script> </div>
|
|
|
|
<div class="related">
|
|
<a href="fractions.html">Introduction to Fractions</a>
|
|
<a href="numbers/fractions-subtraction-animation.html">Subtracting Fractions Illustrated</a>
|
|
<a href="simplifying-fractions.html">Simplifying Fractions</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="fractions-menu.html">Fractions Index</a>
|
|
</div>
|
|
<!-- #EndEditable -->
|
|
|
|
</article>
|
|
<div id="adend" class="centerfull noprint">
|
|
<script>document.write(getAdEnd());</script>
|
|
</div>
|
|
<footer id="footer" class="centerfull noprint">
|
|
<script>document.write(getFooter());</script>
|
|
</footer>
|
|
<div id="copyrt">
|
|
Copyright © 2020 MathsIsFun.com
|
|
</div>
|
|
<script>document.write(getBodyEnd());</script>
|
|
</body>
|
|
<!-- #EndTemplate -->
|
|
|
|
<!-- Mirrored from www.mathsisfun.com/fractions_subtraction.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:36:08 GMT -->
|
|
</html>
|