Solve =5/8div[3/5-(1/8+2/5)]

$$= \frac { 5 } { 8 } \div [ \frac { 3 } { 5 } - ( \frac { 1 } { 8 } + \frac { 2 } { 5 } ) ]$$

Evaluate

$$\frac{25}{3}\approx 8.333333333$$

Solution Steps

Least common multiple of 8 and 5 is 40. Convert \frac{1}{8} and \frac{2}{5} to fractions with denominator 40.

$$\frac{\frac{5}{8}}{\frac{3}{5}-\left(\frac{5}{40}+\frac{16}{40}\right)}$$

Since \frac{5}{40} and \frac{16}{40} have the same denominator, add them by adding their numerators.

$$\frac{\frac{5}{8}}{\frac{3}{5}-\frac{5+16}{40}}$$

Add 5 and 16 to get 21.

$$\frac{\frac{5}{8}}{\frac{3}{5}-\frac{21}{40}}$$

Least common multiple of 5 and 40 is 40. Convert \frac{3}{5} and \frac{21}{40} to fractions with denominator 40.

$$\frac{\frac{5}{8}}{\frac{24}{40}-\frac{21}{40}}$$

Since \frac{24}{40} and \frac{21}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5}{8}}{\frac{24-21}{40}}$$

Subtract 21 from 24 to get 3.

$$\frac{\frac{5}{8}}{\frac{3}{40}}$$

Divide \frac{5}{8} by \frac{3}{40} by multiplying \frac{5}{8} by the reciprocal of \frac{3}{40}.

$$\frac{5}{8}\times \frac{40}{3}$$

Multiply \frac{5}{8} times \frac{40}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 40}{8\times 3}$$

Do the multiplications in the fraction \frac{5\times 40}{8\times 3}.

$$\frac{200}{24}$$

Reduce the fraction \frac{200}{24} to lowest terms by extracting and canceling out 8.

$$\frac{25}{3}$$

Factor

$$\frac{5 ^ {2}}{3} = 8\frac{1}{3} = 8.333333333333334$$