lkarch/lkarch.org
1
1
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity
lkarch.org/tools/mathisfun/www.mathsisfun.com/mixed-fractions-multiply.html
Lucas Kent e39465ad2f Changes to be committed: 
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
2022-11-02 08:40:01 -04:00

196 lines
13 KiB
HTML
Raw Blame History

This file contains ambiguous Unicode characters

This file contains Unicode characters that might be confused with other characters. If you think that this is intentional, you can safely ignore this warning. Use the Escape button to reveal them.

<!DOCTYPE html>
<html lang="en"><!-- #BeginTemplate "/Templates/Main.dwt" --><!-- DW6 -->
<!-- Mirrored from www.mathsisfun.com/mixed-fractions-multiply.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:59:32 GMT -->
<head>
<meta http-equiv="content-type" content="text/html; charset=utf-8">
<!-- #BeginEditable "doctitle" -->
<title>Multiplying Mixed Numbers</title>
<meta name="Description" content="Math explained in easy language, plus puzzles, games, quizzes, worksheets and a forum. For K-12 kids, teachers and parents.">
<!-- #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 http-equiv="pics-label" content="(PICS-1.1 &quot;http://www.classify.org/safesurf/&quot; L gen true for &quot;http://www.mathsisfun.com&quot; r (SS~~000 1))">
<link rel="stylesheet" type="text/css" href="style3.css">
<script src="main3.js" type="text/javascript"></script>
</head>
<body id="bodybg">
<div class="bg">
<div id="stt"></div>
<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 type="text/javascript">document.write(getTrans());</script></div>
<div id="gplus">
<script type="text/javascript">document.write(getGPlus());</script></div>
<div id="adTopOuter" class="centerfull noprint">
<div id="adTop">
<script type="text/javascript">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>
<div id="menuWide" class="menu">
<script type="text/javascript">document.write(getMenu(0));</script>
</div>
<div id="linkto">
<div id="linktort">
<script type="text/javascript">document.write(getLinks());</script></div>
</div>
<div id="search" role="search">
<script type="text/javascript">document.write(getSearch());</script></div>
<div id="menuSlim" class="menu">
<script type="text/javascript">document.write(getMenu(1));</script>
</div>
<div id="menuTiny" class="menu">
<script type="text/javascript">document.write(getMenu(2));</script>
</div>
<div id="extra"></div>
</div>
<div id="content" role="main"><!-- #BeginEditable "Body" -->
<h1 align="center">Multiplying Mixed Fractions</h1>
<p align="center"><i>("Mixed Fractions" are also called "Mixed Numbers")</i></p>
<p>To multiply <a href="mixed-fractions.html">Mixed Fractions</a>:</p>
<ul>
<li>convert to <a href="improper-fractions.html">Improper Fractions</a></li>
<li><a href="fractions_multiplication.html">Multiply the Fractions</a></li>
<li>convert the result back to Mixed Fractions</li>
</ul>
<h2>Example:
What is 1<span class="intbl"><em>3</em><strong>8</strong></span> × 3 ?</h2>
<p>Think of Pizzas.</p>
<table border="0">
<tbody>
<tr>
<td width="270"><img src="images/fractions/pie-1-1.jpg" alt="pie full" height="120" width="120"><img src="images/fractions/pie-3-8.jpg" alt="pie 3/8" height="120" width="120"></td>
<td class="larger">1<span class="intbl"><em>3</em><strong>8</strong></span> is 1 pizza and 3 eighths of another pizza.</td>
</tr>
</tbody></table>
<p>First, convert the mixed fraction (1<span class="intbl"><em>3</em><strong>8</strong></span>) to an improper fraction (<span class="intbl"><em>11</em><strong>8</strong></span>):</p>
<table border="0">
<tbody>
<tr>
<td width="270"><img src="images/fractions/pie-8-8.jpg" alt="pie 8/8" height="120" width="120"><img src="images/fractions/pie-3-8.jpg" alt="pie 3/8" height="120" width="120"></td>
<td>
<p class="larger">Cut the whole pizza into eighths and how many eighths do you have in total?</p>
<p class="larger">1 lot of 8, plus the 3 eighths = 8+3 = 11 eighths.</p></td>
</tr>
</tbody></table>
<p class="large" align="center"><br>
Now multiply that by 3:<br>
</p>
<table border="0">
<tbody>
<tr>
<td width="270"><img src="images/fractions/pie-8-8.jpg" alt="pie 8/8" height="120" width="120"><img src="images/fractions/pie-3-8.jpg" alt="pie 3/8" height="120" width="120"><br>
<img src="images/fractions/pie-8-8.jpg" alt="pie 8/8" height="120" width="120"><img src="images/fractions/pie-3-8.jpg" alt="pie 3/8" height="120" width="120"><br>
<img src="images/fractions/pie-8-8.jpg" alt="pie 8/8" height="120" width="120"><img src="images/fractions/pie-3-8.jpg" alt="pie 3/8" height="120" width="120"></td>
<td>
<p class="larger">1<span class="intbl"><em>3</em><strong>8</strong></span> × 3 = <span class="intbl"><em>11</em><strong>8</strong></span> × <span class="intbl"><em>3</em><strong>1</strong></span> = <span class="intbl"><em>33</em><strong>8</strong></span></p>
<p class="larger"><br>
You have 33 eighths. </p>
<p>&nbsp;</p></td>
</tr>
</tbody></table>
<p>And, lastly, convert to a mixed fraction (only because the original fraction was in that form):</p>
<table border="0">
<tbody>
<tr>
<td width="270"><img src="images/fractions/pie-8-8.jpg" alt="pie 8/8" height="120" width="120"><img src="images/fractions/pie-8-8.jpg" alt="pie 8/8" height="120" width="120"><br>
<img src="images/fractions/pie-8-8.jpg" alt="pie 8/8" height="120" width="120"><img src="images/fractions/pie-8-8.jpg" alt="pie 8/8" height="120" width="120"><br>
<img src="images/fractions/pie-1-8.jpg" alt="pie 1/8" height="120" width="120"></td>
<td>
<p class="larger">33 eighths is 4 whole pizzas (4×8=32) and 1 eighth left over.</p></td>
</tr>
</tbody></table>
<p><b>And this is what it looks like in one line:</b></p>
<p class="larger" align="center">1<span class="intbl"><em>3</em><strong>8</strong></span> × 3 = <span class="intbl"><em>11</em><strong>8</strong></span> × <span class="intbl"><em>3</em><strong>1</strong></span> = <span class="intbl"><em>33</em><strong>8</strong></span> = 4<span class="intbl"><em>1</em><strong>8</strong></span> </p>
<h2>Another Example:
What is 1<span class="intbl"><em>1</em><strong>2</strong></span> × 2<span class="intbl"><em>1</em><strong>5</strong></span> ?</h2>
<p>Do the steps from above: </p>
<ol>
<li>convert to Improper Fractions</li>
<li>Multiply the Fractions</li>
<li>convert the result back to Mixed Fractions</li>
</ol>
<div align="center"><img src="numbers/images/mixed-fraction-multiply.svg" alt="mixed fractions multiply"></div>
<h3>Step, by step it is:</h3>
<p>Convert Mixed to Improper Fractions:</p>
<p class="larger" align="center">1<span class="intbl"><em>1</em><strong>2</strong></span> = <span class="intbl"><em>2</em><strong>2</strong></span>+<span class="intbl"><em>1</em><strong>2</strong></span> = <span class="intbl"><em>3</em><strong>2</strong></span></p>
<p class="larger" align="center">2<span class="intbl"><em>1</em><strong>5</strong></span> =<em> </em><span class="intbl"><em>10</em><strong>5</strong></span>+<span class="intbl"><em>1</em><strong>5</strong></span> =<em> </em><span class="intbl"><em>11</em><strong>5</strong></span></p>
<p><a href="fractions_multiplication.html">Multiply the fractions</a> (multiply the top numbers, multiply bottom numbers):</p>
<p class="larger" align="center"><span class="intbl"><em>3</em><strong>2</strong></span> × <span class="intbl"><em>11</em><strong>5</strong></span> =
<span class="intbl"><em>3 × 11</em><strong>2 × 5</strong></span> =
<span class="intbl"><em>33</em><strong>10</strong></span></p>
<p>Convert to a mixed number</p>
<p class="larger" align="center"><span class="intbl"><em>33</em><strong>10</strong></span> = <b>3<span class="intbl"><em>3</em><strong>10</strong></span></b></p>
<p>If you are clever you can do it all in one line like this:</p>
<p class="larger" align="center">1<span class="intbl"><em>1</em><strong>2</strong></span> × 2<span class="intbl"><em>1</em><strong>5</strong></span> = <span class="intbl"><em>3</em><strong>2</strong></span> × <span class="intbl"><em>11</em><strong>5</strong></span> = <span class="intbl"><em>33</em><strong>10</strong></span> = <b>3<span class="intbl"><em>3</em><strong>10</strong></span></b></p>
<h2>One More Example:
What is 3<span class="intbl"><em>1</em><strong>4</strong></span> × 3<span class="intbl"><em>1</em><strong>3</strong></span> ?</h2>
<p>Convert Mixed to Improper Fractions:</p>
<p class="larger" align="center">3<span class="intbl"><em>1</em><strong>4</strong></span> = <span class="intbl"><em>13</em><strong>4</strong></span></p>
<p class="larger" align="center"> 3<span class="intbl"><em>1</em><strong>3</strong></span> = <span class="intbl"><em>10</em><strong>3</strong></span></p>
<p>Multiply</p>
<p class="larger" align="center"><span class="intbl"><em>13</em><strong>4</strong></span> × <span class="intbl"><em>10</em><strong>3</strong></span> = <span class="intbl"><em>130</em><strong>12</strong></span></p>
<p>Convert to a mixed number:</p>
<p class="larger" align="center"><span class="intbl"><em>130</em><strong>12</strong></span> = <b>10<span class="intbl"><em>10</em><strong>12</strong></span></b></p>
<p>And <a href="simplifying-fractions.html">simplify</a>:</p>
<p class="larger" align="center">10<span class="intbl"><em>10</em><strong>12</strong></span> = <b>10<span class="intbl"><em>5</em><strong>6</strong></span></b></p>
<p><b>Here it is in one line:</b></p>
<p class="larger" align="center">3<span class="intbl"><em>1</em><strong>4</strong></span> × 3<span class="intbl"><em>1</em><strong>3</strong></span> = <span class="intbl"><em>13</em><strong>4</strong></span> × <span class="intbl"><em>10</em><strong>3</strong></span> = <span class="intbl"><em>130</em><strong>12</strong></span> = 10<span class="intbl"><em>10</em><strong>12</strong></span> = <b>10<span class="intbl"><em>5</em><strong>6</strong></span></b></p>
<h2>This One Has Negatives: What is −1<span class="intbl"><em>5</em><strong>9</strong></span> × −2<span class="intbl"><em>1</em><strong>7</strong></span> ? </h2>
<p>Convert Mixed to Improper Fractions: </p>
<p class="larger" align="center"> 1<span class="intbl"><em>5</em><strong>9</strong></span> = <span class="intbl"><em>9</em><strong>9</strong></span> + <span class="intbl"><em>5</em><strong>9</strong></span> = <span class="intbl"><em>14</em><strong>9</strong></span> <br>
2<span class="intbl"><em>1</em><strong>7</strong></span> = <span class="intbl"><em>14</em><strong>7</strong></span> + <span class="intbl"><em>1</em><strong>7</strong></span> = <span class="intbl"><em>15</em><strong>7</strong></span> </p>
<p> Then multiply the Improper Fractions <i>(Note: <a href="multiplying-negatives.html">negative times negative gives positive</a>) </i>:</p>
<p class="larger" align="center"> <span class="intbl"><em>−14</em><strong>9</strong></span> × <span class="intbl"><em>−15</em><strong>7</strong></span> = <span class="intbl"><em>−14 × −15</em><strong>9 × 7</strong></span> = <span class="intbl"><em>210</em><strong>63</strong></span>&nbsp; <br>
</p>
<p> We can simplify now. Here we use two steps, first by 7 (21 and 63 are both multiples of 7), then again by 3. But it could be done in one step by dividing by 21:</p>
<p class="larger" align="center"> <span class="intbl"><em>210</em><strong>63</strong></span> = <span class="intbl"><em>30</em><strong>9</strong></span> = <span class="intbl"><em>10</em><strong>3</strong></span> <br>
</p>
<p> Finally convert to a Mixed Fraction (because that was the style of the question): </p>
<p class="larger" align="center"> <span class="intbl"><em>10</em><strong>3</strong></span> = <span class="intbl"><em>(9+1)</em><strong>3</strong></span> = <span class="intbl"><em>9</em><strong>3</strong></span> + <span class="intbl"><em>1</em><strong>3</strong></span> = 3<span class="intbl"><em>1</em><strong>3</strong> </span></p>
<p>&nbsp;</p>
<div class="questions">
<script type="text/javascript">getQ(940, 941, 942, 1418, 943, 1419, 1420, 1421, 3573, 3574);</script>&nbsp;
</div>
<div class="related"><a href="mixed-fractions.html">Mixed Fractions</a> <a href="fractions-menu.html">Fractions Index </a></div>
<!-- #EndEditable --></div>
<div id="adend" class="centerfull noprint">
<script type="text/javascript">document.write(getAdEnd());</script>
</div>
<div id="footer" class="centerfull noprint">
<script type="text/javascript">document.write(getFooter());</script>
</div>
<div id="copyrt">
Copyright © 2017 MathsIsFun.com
</div>
<script type="text/javascript">document.write(getBodyEnd());</script>
</body><!-- #EndTemplate -->
<!-- Mirrored from www.mathsisfun.com/mixed-fractions-multiply.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:59:32 GMT -->
</html>
Reference in New Issue View Git Blame Copy Permalink