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

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

Evaluate

$$4$$

Solution Steps

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

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

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

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

Multiply 4 and 5 to get 20.

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

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

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

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

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

Since \frac{5}{8} and \frac{4}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5}{2}}{5\times \frac{5-4}{8}}$$

Subtract 4 from 5 to get 1.

$$\frac{\frac{5}{2}}{5\times \frac{1}{8}}$$

Multiply 5 and \frac{1}{8} to get \frac{5}{8}.

$$\frac{\frac{5}{2}}{\frac{5}{8}}$$

Divide \frac{5}{2} by \frac{5}{8} by multiplying \frac{5}{2} by the reciprocal of \frac{5}{8}.

$$\frac{5}{2}\times \frac{8}{5}$$

Multiply \frac{5}{2} times \frac{8}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 8}{2\times 5}$$

Cancel out 5 in both numerator and denominator.

$$\frac{8}{2}$$

Divide 8 by 2 to get 4.

$$4$$

Factor

$$2^{2}$$