Solve (5/6-1/3)div(5/8div1/4)

$$( \frac { 5 } { 6 } - \frac { 1 } { 3 } ) \div ( \frac { 5 } { 8 } \div \frac { 1 } { 4 } )$$

Evaluate

$$\frac{1}{5}=0.2$$

Solution Steps

Least common multiple of 6 and 3 is 6. Convert \frac{5}{6} and \frac{1}{3} to fractions with denominator 6.

$$\frac{\frac{5}{6}-\frac{2}{6}}{\frac{\frac{5}{8}}{\frac{1}{4}}}$$

Since \frac{5}{6} and \frac{2}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{5-2}{6}}{\frac{\frac{5}{8}}{\frac{1}{4}}}$$

Subtract 2 from 5 to get 3.

$$\frac{\frac{3}{6}}{\frac{\frac{5}{8}}{\frac{1}{4}}}$$

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{1}{2}}{\frac{\frac{5}{8}}{\frac{1}{4}}}$$

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

$$\frac{\frac{1}{2}}{\frac{5}{8}\times 4}$$

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

$$\frac{\frac{1}{2}}{\frac{5\times 4}{8}}$$

Multiply 5 and 4 to get 20.

$$\frac{\frac{1}{2}}{\frac{20}{8}}$$

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

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

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

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

Multiply \frac{1}{2} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 2 in both numerator and denominator.

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

Factor

$$\frac{1}{5} = 0.2$$