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312 lines
11 KiB
HTML
312 lines
11 KiB
HTML
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<!-- #BeginEditable "Body" -->
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<h1 class="center">Adding and Subtracting Mixed Fractions</h1>
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<p class="center"><i>A <a href="../mixed-fractions.html">Mixed Fraction</a> is a<br>
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</i> <i>whole number and a fraction combined:</i></p>
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<table style="border: 0; margin:auto;">
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<tbody>
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<tr style="text-align:center;">
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<td><img src="../images/fractions/pizza-1-1.svg" alt="1 whole pizza" height="" width=""><img src="../images/fractions/pizza-3-4.svg" alt="3/4" height="" width=""></td>
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<td rowspan="3">
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<br></td>
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</tr>
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<tr style="text-align:center;">
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<td class="larger">1 <span class="intbl"><em>3</em><strong>4</strong></span></td>
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</tr>
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<tr style="text-align:center;">
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<td><i>(one and three-quarters)</i></td>
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</tr>
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</tbody></table>
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<p>To make it easy to add and subtract them, just convert to Improper Fractions first:</p>
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<p class="center"><i>An <a href="../improper-fractions.html">Improper fraction</a> has a<br>
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top number larger than or equal to<br>
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the bottom number:</i><i></i></p>
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<table style="border: 0; margin:auto;">
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<tbody>
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<tr style="text-align:center;">
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<td><img src="../images/fractions/pizza-4-4.svg" alt="4/4" height="120" width="120"><img src="../images/fractions/pizza-3-4.svg" alt="3/4" height="" width=""></td>
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<td rowspan="3">
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<br></td>
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</tr>
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<tr style="text-align:center;">
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<td class="larger"><span class="intbl"><em>7</em><strong>4</strong></span></td>
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</tr>
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<tr style="text-align:center;">
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<td><i>(seven-fourths or seven-quarters)</i></td>
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</tr>
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</tbody></table>
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<p>Can you see that <span class="larger">1<span class="intbl"><em>3</em><strong>4</strong></span></span> is the same as <span class="larger intbl"><em>7</em><strong>4</strong></span> ?</p>
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<p>In other words "one and three quarters" is the same as "seven quarters".</p>
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<p><i>(You may like to read how to <a href="../mixed-fractions.html">Convert from or to Mixed Fractions</a>)</i></p>
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<p></p>
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<h2>Adding Mixed Fractions</h2>
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<p>To add mixed fractions:</p>
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<ul>
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<li>convert them to <a href="../improper-fractions.html">Improper Fractions</a></li>
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<li>then add them (using <a href="../fractions_addition.html">Addition of Fractions</a>)</li>
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<li>then convert back to Mixed Fractions</li>
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</ul>Like this:<br><div class="example">
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<h3>Example: What is 2 <span class="intbl">
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<em>3</em>
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<strong>4</strong>
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</span> + 3 <span class="intbl">
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<em>1</em>
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<strong>2</strong>
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</span> ?</h3>
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<p>Convert to Improper Fractions:</p>
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<p class="center">2 <span class="intbl">
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<em>3</em>
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<strong>4</strong>
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</span> = <span class="intbl">
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<em>11</em>
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<strong>4</strong>
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</span></p>
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<p class="center">3 <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>7</em>
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<strong>2</strong>
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</span></p>
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<p><a href="common-denominator.html">Common denominator</a> of 4:</p>
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<p class="center"><span class="intbl">
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<em>11</em>
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<strong>4</strong>
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</span> stays as <span class="intbl">
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<em>11</em>
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<strong>4</strong>
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</span></p>
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<p class="center"><span class="intbl">
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<em>7</em>
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<strong>2</strong>
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</span> becomes <span class="intbl">
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<em>14</em>
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<strong>4</strong>
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</span><br>
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<i>(by multiplying top and bottom by 2)</i></p>
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<p>Now Add:</p>
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<p class="center"><span class="intbl">
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<em>11</em>
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<strong>4</strong>
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</span> + <span class="intbl">
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<em>14</em>
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<strong>4</strong>
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</span> = <span class="intbl">
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<em>25</em>
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<strong>4</strong>
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</span></p>
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<p>Convert back to Mixed Fractions:</p>
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<p class="center"><span class="intbl">
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<em>25</em>
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<strong>4</strong>
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</span> = 6 <span class="intbl">
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<em>1</em>
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<strong>4</strong>
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</span></p>
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</div>
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<p>When you get more experience you can do it faster like this example:</p>
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<div class="example">
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<h3>Example: What is 3 <span class="intbl">
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<em>5</em>
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<strong>8</strong>
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</span> + 1 <span class="intbl">
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<em>3</em>
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<strong>4</strong>
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</span></h3>
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<p>Convert them to improper fractions:</p>
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<p class="center">3 <span class="intbl">
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<em>5</em>
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<strong>8</strong>
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</span> = <span class="intbl">
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<em>29</em>
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<strong>8</strong>
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</span><br>
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1 <span class="intbl">
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<em>3</em>
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<strong>4</strong>
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</span> = <span class="intbl">
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<em>7</em>
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<strong>4</strong>
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</span></p>
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<p>Make same denominator: <span class="intbl">
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<em>7</em>
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<strong>4</strong>
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</span> becomes <span class="intbl">
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<em>14</em>
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<strong>8</strong>
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</span> (by multiplying top and bottom by 2)</p>
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<p>And add:</p>
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<p class="center"><span class="intbl">
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<em>29</em>
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<strong>8</strong>
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</span> + <span class="intbl">
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<em>14</em>
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<strong>8</strong>
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</span> = <span class="intbl">
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<em>43</em>
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<strong>8</strong>
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</span> = 5 <span class="intbl">
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<em>3</em>
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<strong>8</strong>
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</span></p>
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</div>
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<p> </p>
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<h2>Subtracting Mixed Fractions</h2>
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<p>Just follow the same method, but subtract instead of add:</p>
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<div class="example">
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<h3>Example: What is 15 <span class="intbl">
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<em>3</em>
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<strong>4</strong>
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</span> − 8 <span class="intbl">
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<em>5</em>
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<strong>6</strong>
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</span> ?</h3>
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<p>Convert to Improper Fractions:</p>
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<p class="center">15 <span class="intbl">
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<em>3</em>
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<strong>4</strong>
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</span> = <span class="intbl">
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<em>63</em>
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<strong>4</strong>
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</span></p>
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<p class="center">8 <span class="intbl">
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<em>5</em>
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<strong>6</strong>
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</span> = <span class="intbl">
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<em>53</em>
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<strong>6</strong>
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</span></p>
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<p>Common denominator of 12:</p>
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<p class="center"><span class="intbl">
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<em>63</em>
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<strong>4</strong>
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</span> becomes <span class="intbl">
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<em>189</em>
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<strong>12</strong>
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</span></p>
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<p class="center"><span class="intbl">
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<em>53</em>
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<strong>6</strong>
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</span> becomes <span class="intbl">
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<em>106</em>
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<strong>12</strong>
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</span></p>
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<p>Now Subtract:</p>
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<p class="center"><span class="intbl">
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<em>189</em>
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<strong>12</strong>
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</span> − <span class="intbl">
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<em>106</em>
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<strong>12</strong>
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</span> = <span class="intbl">
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<em>83</em>
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<strong>12</strong>
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</span></p>
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<p>Convert back to Mixed Fractions:</p>
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<p class="center"><span class="intbl">
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<em>83</em>
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<strong>12</strong>
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</span> = 6 <span class="intbl">
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<em>11</em>
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<strong>12</strong>
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</span></p>
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</div>
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<p> </p>
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<div class="questions">935, 1414, 1415, 1416, 936, 1417, 3585, 3586, 3587</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="../simplifying-fractions.html">Simplifying Fractions</a>
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<a href="../equivalent_fractions.html">Equivalent Fractions</a>
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<a href="../least-common-multiple.html">Least Common Multiple</a>
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<a href="../least-common-multiple-tool.html">Least Common Multiple Tool</a>
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<a href="../least-common-denominator.html">Least Common Denominator</a>
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<a href="../fractions_subtraction.html">Subtracting Fractions</a>
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<a href="../fractions_multiplication.html">Multiplying Fractions</a>
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<a href="../fractions_division.html">Dividing Fractions</a>
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<a href="../fractions-menu.html">Fractions Index</a>
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</div>
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<!-- #EndEditable -->
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