To divide \( \frac{7}{8} \) by \( 4 \frac{1}{5} \), we first convert the mixed number \( 4 \frac{1}{5} \) into an improper fraction.
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Convert \( 4 \frac{1}{5} \) to an improper fraction: \[ 4 \frac{1}{5} = 4 \times 5 + 1 = 20 + 1 = 21 \] So, \( 4 \frac{1}{5} = \frac{21}{5} \).
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Now, to divide \( \frac{7}{8} \) by \( \frac{21}{5} \), we multiply by the reciprocal of \( \frac{21}{5} \): \[ \frac{7}{8} \div \frac{21}{5} = \frac{7}{8} \times \frac{5}{21} \]
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Now, multiply the fractions: \[ \frac{7 \times 5}{8 \times 21} = \frac{35}{168} \]
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Next, we simplify \( \frac{35}{168} \). To do this, we find the greatest common divisor (GCD) of 35 and 168. The GCD is 7. \[ \frac{35 \div 7}{168 \div 7} = \frac{5}{24} \]
Thus, the final simplified quotient of \( \frac{7}{8} \div 4 \frac{1}{5} \) is \( \frac{5}{24} \).