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147 lines
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HTML
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<div class="video">Ekbjz0LLKxI</div>
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<h1 id="title" align="center">Common Denominator</h1>
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<p class="center">This is the easiest method we know to add or subtract fractions!</p>
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<h2>What is a Denominator?</h2>
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<p style="float:right; margin: 0 0 5px 10px;"><img src="images/fraction.svg" alt="fraction" height="107" width="320"></p>
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<p>The <b>denominator</b> is the bottom number in a fraction.</p>
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<p>It shows how many equal parts the item is divided into.</p>
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<div style="clear:both"></div>
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<p style="float:left; margin: 0 10px 5px 0;"><img src="images/common-denominator.svg" alt="Common Denominator" height="224" width="195"></p>
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<h2>What is a Common Denominator?</h2>
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<p>When the denominators of two or more fractions are the <b>same</b>, they are <b>Common Denominators</b>.</p>
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<div style="clear:both"></div>
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<h2>Why is it Important?</h2>
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<p>Before we can <a href="../fractions_addition.html">add</a> or <a href="../fractions_subtraction.html">subtract</a> fractions, the fractions need to have a <b>common</b> denominator</p>
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<p>In other words the denominators <b>must be the same</b>.</p>
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<h2>Making The Denominators the Same</h2>
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<p>To make the denominators the same we can:</p>
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<p class="center large">Multiply top and bottom of each fraction by the denominator of the other.</p>
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<p>Like in this example <i>(press play button)</i>:</p>
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<script>playerMain("images/common-denominator1.txt",640,250);</script>
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<p>This always works, but we often need to <a href="../simplifying-fractions.html">simplify the fraction</a> afterwards, as in this example <i>(press play button)</i>:</p>
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<script>playerMain("images/common-denominator2.txt",600,250);</script>
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<p>We simplified the fraction <span class="intbl"><em>20</em><strong>32</strong></span> to <span class="intbl"><em>10</em><strong>16</strong></span> , then to <span class="intbl"><em>5</em><strong>8</strong></span> by dividing the top and bottom by 2 each time, and that is as simple as it can get!</p>
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<h2>What Did We Do?</h2>
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<p>1. We multiplied each fraction by the denominator of the other. Let's use letters instead of numbers:</p>
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<p class="center"><img src="images/common-factor-explained.svg" alt="common factor explained"></p>
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<p>2. And because they now have the same denominator, we can add them:</p>
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<p class="center"><img src="images/common-factor-explained2.svg" alt="common factor explained step 2"></p>
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<h3>In One Step!</h3>
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<p>We can do those two things in one step like this:</p>
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<div class="center">
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<img src="images/common-factor-formula.svg" alt="common factor formula">
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</div>
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<p>Which we use like this:</p>
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<div class="example">
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<h3>Example: What is <span class="intbl"><em>2</em><strong>3</strong></span> + <span class="intbl"><em>4</em><strong>5</strong></span> ?</h3>
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<p class="center large"><span class="intbl"><em>2</em><strong>3</strong></span> + <span class="intbl"><em>4</em><strong>5</strong></span> = <span class="intbl"><em>2×5 + 3×4</em><strong>3×5</strong></span> = <span class="intbl"><em>10 + 12</em><strong>15</strong></span> = <span class="intbl"><em>22</em><strong>15
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</strong></span></p>
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<p>(Note: <b>a</b> was 2, <b>b</b> was 3, <b>c</b> was 4 and <b>d</b> was 5.)</p>
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</div>
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<p>That is how the experts do it!</p>
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<p> </p>
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<div class="fun">
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<h3><i>Footnote:</i> Least Common Denominator</h3>
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<p><i>You can also try the <a href="../least-common-denominator.html">Least Common Denominator</a> method.</i></p>
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</div>
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<p> </p>
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<div class="questions">1698, 1699, 1700, 1701</div>
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<div class="related">
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<a href="../fractions_addition.html">Adding Fractions</a>
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<a href="../fractions_subtraction.html">Subtracting Fractions</a>
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<a href="../fractions.html">Fractions</a>
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