34 lines
2.7 KiB
Markdown
34 lines
2.7 KiB
Markdown
---
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title: Example of Subtracting Fractions with Unlike Denominators
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---
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## Example of Subtracting Fractions with Unlike Denominators
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Subtracting fractions with unlike denominators is similar to addition of fractions with unlike denominators. Here are the steps,
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1. Convert the fractions to equivalent fractions with common denominator
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2. To convert two fractions to common denominator, multiply the numerator and denominator of a fraction with the denominator of the other fraction.
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3. Now that the fractions have common denominators, subtract the numerators of both fractions and put the resultant over the denominator
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Consider, <span class="fraction"><sup>a</sup>⁄<sub>b</sub></span> and <span class="fraction"><sup>c</sup>⁄<sub>d</sub></span> are fractions with different denominators, you can subtract these fractions in a single step like below,
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<br>
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<pre> <span class="fraction"><sup>a</sup>⁄<sub>b</sub></span> - <span class="fraction"><sup>c</sup>⁄<sub>d</sub></span> = <span class="fraction"><sup>(a * d) - (b * c)</sup>⁄<sub>(b * d)</sub></span> </pre>
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###### Example
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Consider fractions <span class="fraction"><sup>5</sup>⁄<sub>6</sub></span> and <span class="fraction"><sup>5</sup>⁄<sub>15</sub></span>
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1. The denominators are different. So you need to make the denominators common
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2. Before that, if possible, simplify the fractions. In this case, <span class="fraction"><sup>5</sup>⁄<sub>15</sub></span> can be simplified as <span class="fraction"><sup>1</sup>⁄<sub>3</sub></span>. Here <span class="fraction"><sup>5</sup>⁄<sub>15</sub></span> and <span class="fraction"><sup>1</sup>⁄<sub>3</sub></span> are called equivalent fractions.
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3. After simplification, the fractions are <span class="fraction"><sup>5</sup>⁄<sub>6</sub></span> and <span class="fraction"><sup>1</sup>⁄<sub>3</sub></span>.
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4. Now to subtract these fractions, you must make the denominators common
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5. Multiply the numerator and denominator of a fraction with denominator of the other
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6. For fraction <span class="fraction"><sup>5</sup>⁄<sub>6</sub></span> , the denominator of the other fraction is 3. For fraction <span class="fraction"><sup>1</sup>⁄<sub>3</sub></span> , the denominator of the other fraction is 6
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<pre> <span class="fraction"><sup>((5 * 3) - (1 * 6))</sup>⁄<sub>(6 * 3)</sub></span> = <span class="fraction"><sup>9</sup>⁄<sub>18</sub></span> </pre>
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7. The resultant fraction is <span class="fraction"><sup>9</sup>⁄<sub>18</sub></span>. This can be further simplified as <span class="fraction"><sup>1</sup>⁄<sub>2</sub></span>
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<pre> <span class="fraction"><sup>5</sup>⁄<sub>6</sub></span> - <span class="fraction"><sup>5</sup>⁄<sub>15</sub></span> = <span class="fraction"><sup>1</sup>⁄<sub>2</sub></span> </pre>
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