To find out how many \( \frac{3}{4} \)-pound bags Briona can make with \( 37 \frac{1}{2} \) pounds of hot chocolate powder, we first need to convert \( 37 \frac{1}{2} \) into an improper fraction.
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Convert \( 37 \frac{1}{2} \) to an improper fraction: \[ 37 \frac{1}{2} = \frac{37 \times 2 + 1}{2} = \frac{74 + 1}{2} = \frac{75}{2} \]
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Now, we need to divide \( \frac{75}{2} \) by \( \frac{3}{4} \) to find out how many \( \frac{3}{4} \)-pound bags can be made: \[ \text{Number of bags} = \frac{75/2}{3/4} \]
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Dividing by a fraction is the same as multiplying by its reciprocal: \[ \frac{75}{2} \div \frac{3}{4} = \frac{75}{2} \times \frac{4}{3} \]
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Multiply the fractions: \[ = \frac{75 \times 4}{2 \times 3} = \frac{300}{6} = 50 \]
So, Briona will have 50 \( \frac{3}{4} \)-pound bags of hot chocolate powder.
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