To divide the fractions, we first need to convert the mixed number \(4 \frac{1}{5}\) into an improper fraction.
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Convert \(4 \frac{1}{5}\): \[ 4 \frac{1}{5} = 4 \times 5 + 1 = 20 + 1 = 21 \] So, \(4 \frac{1}{5} = \frac{21}{5}\).
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Now we will change the division into multiplication by taking the reciprocal of \(\frac{21}{5}\): \[ \frac{7}{8} \div \frac{21}{5} = \frac{7}{8} \times \frac{5}{21} \]
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Multiply the fractions: \[ \frac{7 \times 5}{8 \times 21} = \frac{35}{168} \]
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Now we simplify \(\frac{35}{168}\). To simplify, find the greatest common divisor (GCD) of 35 and 168.
- The prime factorization of \(35\) is \(5 \times 7\).
- The prime factorization of \(168\) is \(2^3 \times 3 \times 7\).
The GCD is \(7\).
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Divide both the numerator and the denominator by their GCD: \[ \frac{35 \div 7}{168 \div 7} = \frac{5}{24} \]
Thus, the quotient of \(7/8 \div 4 \frac{1}{5}\) is \(\frac{5}{24}\).