To find the unit rate of \( \frac{2 \frac{1}{2}}{1 \frac{3}{4}} \), we first convert the mixed numbers to improper fractions.
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Convert \( 2 \frac{1}{2} \) to an improper fraction: \[ 2 \frac{1}{2} = 2 \times 2 + 1 = 4 + 1 = 5 \quad \Rightarrow \quad \frac{5}{2} \]
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Convert \( 1 \frac{3}{4} \) to an improper fraction: \[ 1 \frac{3}{4} = 1 \times 4 + 3 = 4 + 3 = 7 \quad \Rightarrow \quad \frac{7}{4} \]
Now we can divide \( \frac{5}{2} \) by \( \frac{7}{4} \): \[ \frac{5}{2} \div \frac{7}{4} = \frac{5}{2} \times \frac{4}{7} \]
Multiplying the fractions: \[ \frac{5 \times 4}{2 \times 7} = \frac{20}{14} \]
Now simplify \( \frac{20}{14} \): \[ \frac{20}{14} = \frac{10}{7} \]
Now we have the result in the form \( \frac{10}{7} \). To find the unit rate, we can convert this to a mixed number: \[ \frac{10}{7} = 1 \frac{3}{7} \]
Thus, the unit rate of \( 2 \frac{1}{2} \div 1 \frac{3}{4} \) is \( 1 \frac{3}{7} \).