To solve \( \frac{7}{8} \div \left(4 + \frac{1}{5}\right) \), we need to first simplify \( 4 + \frac{1}{5} \).
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Convert 4 to a fraction: \[ 4 = \frac{20}{5} \] So: \[ 4 + \frac{1}{5} = \frac{20}{5} + \frac{1}{5} = \frac{21}{5} \]
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Now, we can rewrite the division: \[ \frac{7}{8} \div \frac{21}{5} \] This is the same as multiplying by the reciprocal: \[ \frac{7}{8} \times \frac{5}{21} \]
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Now multiply the fractions: \[ \frac{7 \times 5}{8 \times 21} = \frac{35}{168} \]
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Simplify \( \frac{35}{168} \):
- Find the greatest common divisor (GCD) of 35 and 168, which is 7.
- Divide both the numerator and the denominator by their GCD: \[ \frac{35 \div 7}{168 \div 7} = \frac{5}{24} \]
Thus, the simplified quotient is \( \frac{5}{24} \).
The answer from the choices given is: Start Fraction 5 over 24 End Fraction.
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