Solve 3/5div[7/8-(2/5+3/8)]

$$\frac { 3 } { 5 } \div [ \frac { 7 } { 8 } - ( \frac { 2 } { 5 } + \frac { 3 } { 8 } ) ]$$

Evaluate

$$6$$

Solution Steps

Least common multiple of 5 and 8 is 40. Convert \frac{2}{5} and \frac{3}{8} to fractions with denominator 40.

$$\frac{\frac{3}{5}}{\frac{7}{8}-\left(\frac{16}{40}+\frac{15}{40}\right)}$$

Since \frac{16}{40} and \frac{15}{40} have the same denominator, add them by adding their numerators.

$$\frac{\frac{3}{5}}{\frac{7}{8}-\frac{16+15}{40}}$$

Add 16 and 15 to get 31.

$$\frac{\frac{3}{5}}{\frac{7}{8}-\frac{31}{40}}$$

Least common multiple of 8 and 40 is 40. Convert \frac{7}{8} and \frac{31}{40} to fractions with denominator 40.

$$\frac{\frac{3}{5}}{\frac{35}{40}-\frac{31}{40}}$$

Since \frac{35}{40} and \frac{31}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{3}{5}}{\frac{35-31}{40}}$$

Subtract 31 from 35 to get 4.

$$\frac{\frac{3}{5}}{\frac{4}{40}}$$

Reduce the fraction \frac{4}{40} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{3}{5}}{\frac{1}{10}}$$

Divide \frac{3}{5} by \frac{1}{10} by multiplying \frac{3}{5} by the reciprocal of \frac{1}{10}.

$$\frac{3}{5}\times 10$$

Express \frac{3}{5}\times 10 as a single fraction.

$$\frac{3\times 10}{5}$$

Multiply 3 and 10 to get 30.

$$\frac{30}{5}$$

Divide 30 by 5 to get 6.

$$6$$

Factor

$$2\times 3$$