To find the reciprocal of a mixed number, we first need to convert it into an improper fraction.
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Convert \(10 \frac{3}{5}\) to an improper fraction:
- The whole number part is 10, which can be converted as follows: \[ 10 = \frac{10 \times 5}{5} = \frac{50}{5} \]
- Now add the fraction: \[ 10 \frac{3}{5} = \frac{50}{5} + \frac{3}{5} = \frac{50 + 3}{5} = \frac{53}{5} \]
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Now, find the reciprocal of \(\frac{53}{5}\): \[ \text{Reciprocal} = \frac{1}{\frac{53}{5}} = \frac{5}{53} \]
Thus, the reciprocal of \(10 \frac{3}{5}\) is \(\frac{5}{53}\).
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