To compute \(1 \frac{1}{6} \div \frac{1}{2}\), we can follow these steps:
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Convert the mixed number \(1 \frac{1}{6}\) to an improper fraction: \[ 1 \frac{1}{6} = 1 + \frac{1}{6} = \frac{6}{6} + \frac{1}{6} = \frac{7}{6} \]
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Now, we need to divide \(\frac{7}{6}\) by \(\frac{1}{2}\). Dividing by a fraction is the same as multiplying by its reciprocal: \[ \frac{7}{6} \div \frac{1}{2} = \frac{7}{6} \times 2 = \frac{7 \times 2}{6} = \frac{14}{6} \]
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Now, simplify \(\frac{14}{6}\): \[ \frac{14}{6} = \frac{7}{3} \]
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Convert \(\frac{7}{3}\) to a mixed number:
- Divide 7 by 3 which gives 2 with a remainder of 1.
- Thus, \(\frac{7}{3} = 2 \frac{1}{3}\).
So, the final answer in simplest mixed number form is: \[ \boxed{2 \frac{1}{3}} \]