Divide to find the quotient of 7/8÷ (4+1/5)

Question

. 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 $\frac{7}{8}÷(4+\frac{1}{5})$, 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: $$\frac{7}{8}÷\frac{21}{5}$$ 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: $$\frac{35÷7}{168÷7}=\frac{5}{24}$$

Thus, the simplified quotient is $\frac{5}{24}$.

The answer from the choices given is: Start Fraction 5 over 24 End Fraction.