To divide \( \frac{5}{8} \) by \( \frac{3}{4} \), you can multiply by the reciprocal of the second fraction.
Here are the steps:
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Write the division as multiplication by the reciprocal: \[ \frac{5}{8} \div \frac{3}{4} = \frac{5}{8} \times \frac{4}{3} \]
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Multiply the numerators and the denominators: \[ = \frac{5 \times 4}{8 \times 3} = \frac{20}{24} \]
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Simplify the fraction: \[ \frac{20}{24} = \frac{5}{6} \quad \text{(by dividing both the numerator and denominator by 4)} \]
Thus, \( \frac{5}{8} \div \frac{3}{4} = \frac{5}{6} \).