Solve (5/7-5/8)div5/32

$$( \frac{ 5 }{ 7 } - \frac{ 5 }{ 8 } ) \div \frac{ 5 }{ 32 }$$

Evaluate

$$\frac{4}{7}\approx 0.571428571$$

Solution Steps

Least common multiple of 7 and 8 is 56. Convert \frac{5}{7} and \frac{5}{8} to fractions with denominator 56.

$$\frac{\frac{40}{56}-\frac{35}{56}}{\frac{5}{32}}$$

Since \frac{40}{56} and \frac{35}{56} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{40-35}{56}}{\frac{5}{32}}$$

Subtract 35 from 40 to get 5.

$$\frac{\frac{5}{56}}{\frac{5}{32}}$$

Divide \frac{5}{56} by \frac{5}{32} by multiplying \frac{5}{56} by the reciprocal of \frac{5}{32}.

$$\frac{5}{56}\times \frac{32}{5}$$

Multiply \frac{5}{56} times \frac{32}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 32}{56\times 5}$$

Cancel out 5 in both numerator and denominator.

$$\frac{32}{56}$$

Reduce the fraction \frac{32}{56} to lowest terms by extracting and canceling out 8.

$$\frac{4}{7}$$

Factor

$$\frac{2 ^ {2}}{7} = 0.5714285714285714$$