To add the mixed numbers \(6 \frac{1}{3}\) and \(7 \frac{1}{2}\), follow these steps:
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Convert the mixed numbers to improper fractions.
- For \(6 \frac{1}{3}\): \[ 6 \frac{1}{3} = \frac{6 \times 3 + 1}{3} = \frac{18 + 1}{3} = \frac{19}{3} \]
- For \(7 \frac{1}{2}\): \[ 7 \frac{1}{2} = \frac{7 \times 2 + 1}{2} = \frac{14 + 1}{2} = \frac{15}{2} \]
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Find a common denominator to add the fractions. The least common multiple of 3 and 2 is 6.
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Convert the fractions to have a common denominator:
- For \(\frac{19}{3}\): \[ \frac{19}{3} = \frac{19 \times 2}{3 \times 2} = \frac{38}{6} \]
- For \(\frac{15}{2}\): \[ \frac{15}{2} = \frac{15 \times 3}{2 \times 3} = \frac{45}{6} \]
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Now, add the two fractions: \[ \frac{38}{6} + \frac{45}{6} = \frac{38 + 45}{6} = \frac{83}{6} \]
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Convert the improper fraction back to a mixed number: \[ \frac{83}{6} = 13 \frac{5}{6} \quad \text{(since } 83 \div 6 = 13 \text{ remainder } 5\text{)} \]
Therefore, the sum of \(6 \frac{1}{3} + 7 \frac{1}{2}\) is \(13 \frac{5}{6}\).