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Original
2026-01-01
Modified
2026-02-28
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<p>When adding and subtracting fractions with different denominators, we must convert the unlike fractions into like fractions. First, we change the different denominators to a<a>common denominator</a>. Adding or subtracting the numerators, while keeping the denominator the same, are as follows - </p>
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<p>When adding and subtracting fractions with different denominators, we must convert the unlike fractions into like fractions. First, we change the different denominators to a<a>common denominator</a>. Adding or subtracting the numerators, while keeping the denominator the same, are as follows - </p>
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<p>For instance, add and \( \frac{1}{3},\quad \frac{3}{4} \)</p>
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<p>For instance, add and \( \frac{1}{3},\quad \frac{3}{4} \)</p>
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<p>First, we must change the unlike denominators to a common denominator. For that, we need to find the<a>least common multiple</a>of 3 and 4. </p>
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<p>First, we must change the unlike denominators to a common denominator. For that, we need to find the<a>least common multiple</a>of 3 and 4. </p>
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<p>Multiples of 3 include 3, 6, 9, 12, 15, 18, ...</p>
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<p>Multiples of 3 include 3, 6, 9, 12, 15, 18, ...</p>
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<p>Multiples of 4 include 4, 8, 12, 16, 20, …</p>
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<p>Multiples of 4 include 4, 8, 12, 16, 20, …</p>
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<p>Here, the smallest common multiple that appears in both lists is 12. Hence, 12 is the LCD of 3 and 4. </p>
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<p>Here, the smallest common multiple that appears in both lists is 12. Hence, 12 is the LCD of 3 and 4. </p>
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<p>Next, we can convert the fractions to get a denominator of 12.</p>
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<p>Next, we can convert the fractions to get a denominator of 12.</p>
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<p>Convert : (1 × 4) / (3 × 4) = \(\frac{4}{12} \)</p>
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<p>Convert : (1 × 4) / (3 × 4) = \(\frac{4}{12} \)</p>
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<p>Convert: (3 × 3) / (4 × 3) = \(\frac{9}{12} \)</p>
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<p>Convert: (3 × 3) / (4 × 3) = \(\frac{9}{12} \)</p>
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<p>Now the denominators are the same. Next, add the numerators together.</p>
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<p>Now the denominators are the same. Next, add the numerators together.</p>
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<p> \(\frac{4}{12} + \frac{9}{12} \)+ = (4 + 9) / 12 = \(\frac{13}{12} \)</p>
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<p> \(\frac{4}{12} + \frac{9}{12} \)+ = (4 + 9) / 12 = \(\frac{13}{12} \)</p>
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<p>is an improper fraction, so convert it into a<a>mixed fraction</a>.</p>
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<p>is an improper fraction, so convert it into a<a>mixed fraction</a>.</p>
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<p>Divide 13 by 12: 13 ÷ 12</p>
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<p>Divide 13 by 12: 13 ÷ 12</p>
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<p>Quotient = 1</p>
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<p>Quotient = 1</p>
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<p>Remainder = 1</p>
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<p>Remainder = 1</p>
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<p>Fraction can be expressed as a mixed fraction in the following way: Q</p>
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<p>Fraction can be expressed as a mixed fraction in the following way: Q</p>
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<p>Here, Q is the<a>quotient</a>, R is the<a>remainder</a>, and D is the denominator. </p>
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<p>Here, Q is the<a>quotient</a>, R is the<a>remainder</a>, and D is the denominator. </p>
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<p> So \(\frac{13}{12} \) can be written as 1 \(\frac{1}{12} \)</p>
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<p> So \(\frac{13}{12} \) can be written as 1 \(\frac{1}{12} \)</p>
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<p><strong>Subtracting fractions with unlike denominators</strong></p>
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<p><strong>Subtracting fractions with unlike denominators</strong></p>
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<p>The rules to add unlike fractions can also be applied to subtract unlike fractions. For a better understanding, take a look at this example. </p>
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<p>The rules to add unlike fractions can also be applied to subtract unlike fractions. For a better understanding, take a look at this example. </p>
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<p>Subtract- \(\frac{4}{5} - \frac{1}{4} \)</p>
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<p>Subtract- \(\frac{4}{5} - \frac{1}{4} \)</p>
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<p>Find the LCD of 5 and 4. </p>
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<p>Find the LCD of 5 and 4. </p>
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<p>20 is the least common multiple of both 5 and 4. So, we can convert the unlike fractions into like fractions. </p>
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<p>20 is the least common multiple of both 5 and 4. So, we can convert the unlike fractions into like fractions. </p>
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<p>Convert :\( \frac{4 \times 4}{5 \times 4} \) = \(\frac{16}{12} \)</p>
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<p>Convert :\( \frac{4 \times 4}{5 \times 4} \) = \(\frac{16}{12} \)</p>
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<p>Convert : \(\frac{1 \times 5}{4 \times 5} \) = \(\frac{5}{20} \)</p>
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<p>Convert : \(\frac{1 \times 5}{4 \times 5} \) = \(\frac{5}{20} \)</p>
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<p>Next, subtract the numerators.</p>
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<p>Next, subtract the numerators.</p>
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<p> \(\frac{16}{20} - \frac{5}{20} \) - = \(\frac{16 - 5}{20} \) = \( \frac{11}{20} \)</p>
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<p> \(\frac{16}{20} - \frac{5}{20} \) - = \(\frac{16 - 5}{20} \) = \( \frac{11}{20} \)</p>
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<p>Thus, - = \(\frac{16}{20} - \frac{5}{20} = \frac{11}{20} \)</p>
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<p>Thus, - = \(\frac{16}{20} - \frac{5}{20} = \frac{11}{20} \)</p>
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