To add the mixed numbers \( 6 \frac{1}{3} \) and \( 7 \frac{1}{2} \), we can 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:
- The denominators are 3 and 2. The least common multiple (LCM) 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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Add the 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:
- Divide 83 by 6:
- \( 83 \div 6 = 13 \) remainder \( 5 \).
- So, \( \frac{83}{6} = 13 \frac{5}{6} \).
- Divide 83 by 6:
Therefore, the sum of \( 6 \frac{1}{3} + 7 \frac{1}{2} \) is \( 13 \frac{5}{6} \).