To solve the problem, we first need to interpret the fractions correctly.
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We have \( 12 \frac{1}{2} \) of \( 15 \frac{1}{5} \) of a 10-ounce block of cheese.
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Let's convert the mixed numbers to improper fractions:
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\( 12 \frac{1}{2} \) can be converted to: \[ 12 \times 2 + 1 = 24 + 1 = 25/2 \]
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\( 15 \frac{1}{5} \) can be converted to: \[ 15 \times 5 + 1 = 75 + 1 = 76/5 \]
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Now we can calculate \( \frac{25}{2} \) of \( \frac{76}{5} \) of a 10-ounce block of cheese.
First, calculate \( \frac{76}{5} \) of 10 ounces: \[ \frac{76}{5} \times 10 = \frac{76 \times 10}{5} = \frac{760}{5} = 152 \text{ ounces} \]
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Next, we need to find \( \frac{25}{2} \) of 152 ounces: \[ \frac{25}{2} \times 152 = \frac{25 \times 152}{2} = \frac{3800}{2} = 1900 \text{ ounces} \]
Thus, the answer is \( 1900 \) ounces.