To find how many ounces are in \( \frac{1}{2} \) of \( \frac{1}{5} \) of a 10-ounce block of cheese, we can follow these steps:
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Calculate \( \frac{1}{5} \) of 10 ounces: \[ \frac{1}{5} \times 10 = \frac{10}{5} = 2 \text{ ounces} \]
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Calculate \( \frac{1}{2} \) of the result from step 1: \[ \frac{1}{2} \times 2 = 1 \text{ ounce} \]
Therefore, \( \frac{1}{2} \) of \( \frac{1}{5} \) of a 10-ounce block of cheese is \( \boxed{1} \) ounce.