To multiply the mixed numbers \(1 \frac{2}{3}\) and \(6 \frac{1}{2}\), we first need to convert them to improper fractions.
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Convert \(1 \frac{2}{3}\): \[ 1 \frac{2}{3} = \frac{3 \times 1 + 2}{3} = \frac{3 + 2}{3} = \frac{5}{3} \]
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Convert \(6 \frac{1}{2}\): \[ 6 \frac{1}{2} = \frac{2 \times 6 + 1}{2} = \frac{12 + 1}{2} = \frac{13}{2} \]
Now multiply the two improper fractions: \[ \frac{5}{3} \times \frac{13}{2} = \frac{5 \times 13}{3 \times 2} = \frac{65}{6} \]
Now we convert \(\frac{65}{6}\) to a mixed number. To do this, divide 65 by 6:
- \(65 \div 6 = 10\) remainder \(5\).
So, \(\frac{65}{6} = 10 \frac{5}{6}\).
Therefore, the answer is: \[ 10 \frac{5}{6} \] This corresponds to the first response option: 10 5/6.
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