Question

Divide to find the quotient of 7/8÷ (4+1/5)
. Simplify the answer, if possible. (1 point)
Responses

524
Start Fraction 5 over 24 End Fraction

445
4 Start Fraction 4 over 5 End Fraction

32740
3 Start Fraction 27 over 40 End Fraction

40147

Answer 1

To solve \( \frac{7}{8} \div \left(4 + \frac{1}{5}\right) \), we need to first simplify \( 4 + \frac{1}{5} \).

1. Convert 4 to a fraction:
\[
4 = \frac{20}{5}
\]
So:
\[
4 + \frac{1}{5} = \frac{20}{5} + \frac{1}{5} = \frac{21}{5}
\]

2. Now, we can rewrite the division:
\[
\frac{7}{8} \div \frac{21}{5}
\]
This is the same as multiplying by the reciprocal:
\[
\frac{7}{8} \times \frac{5}{21}
\]

3. Now multiply the fractions:
\[
\frac{7 \times 5}{8 \times 21} = \frac{35}{168}
\]

4. 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**.