Solve 4/5div[(3/5-1/2)div5/8]

$$\frac { 4 } { 5 } \div [ ( \frac { 3 } { 5 } - \frac { 1 } { 2 } ) \div \frac { 5 } { 8 } ]$$

Evaluate

$$5$$

Solution Steps

Divide \frac{4}{5} by \frac{\frac{3}{5}-\frac{1}{2}}{\frac{5}{8}} by multiplying \frac{4}{5} by the reciprocal of \frac{\frac{3}{5}-\frac{1}{2}}{\frac{5}{8}}.

$$\frac{4\times \frac{5}{8}}{5\left(\frac{3}{5}-\frac{1}{2}\right)}$$

Express 4\times \frac{5}{8} as a single fraction.

$$\frac{\frac{4\times 5}{8}}{5\left(\frac{3}{5}-\frac{1}{2}\right)}$$

Multiply 4 and 5 to get 20.

$$\frac{\frac{20}{8}}{5\left(\frac{3}{5}-\frac{1}{2}\right)}$$

Reduce the fraction \frac{20}{8} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{5}{2}}{5\left(\frac{3}{5}-\frac{1}{2}\right)}$$

Least common multiple of 5 and 2 is 10. Convert \frac{3}{5} and \frac{1}{2} to fractions with denominator 10.

$$\frac{\frac{5}{2}}{5\left(\frac{6}{10}-\frac{5}{10}\right)}$$

Since \frac{6}{10} and \frac{5}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5}{2}}{5\times \frac{6-5}{10}}$$

Subtract 5 from 6 to get 1.

$$\frac{\frac{5}{2}}{5\times \frac{1}{10}}$$

Multiply 5 and \frac{1}{10} to get \frac{5}{10}.

$$\frac{\frac{5}{2}}{\frac{5}{10}}$$

Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{5}{2}}{\frac{1}{2}}$$

Divide \frac{5}{2} by \frac{1}{2} by multiplying \frac{5}{2} by the reciprocal of \frac{1}{2}.

$$\frac{5}{2}\times 2$$

Cancel out 2 and 2.

$$5$$

Factor

$$5$$