Solve (1/3-1/2)div5/8

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

Evaluate

$$-\frac{4}{15}\approx -0.266666667$$

Solution Steps

Least common multiple of 3 and 2 is 6. Convert \frac{1}{3} and \frac{1}{2} to fractions with denominator 6.

$$\frac{\frac{2}{6}-\frac{3}{6}}{\frac{5}{8}}$$

Since \frac{2}{6} and \frac{3}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{2-3}{6}}{\frac{5}{8}}$$

Subtract 3 from 2 to get -1.

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

Divide -\frac{1}{6} by \frac{5}{8} by multiplying -\frac{1}{6} by the reciprocal of \frac{5}{8}.

$$-\frac{1}{6}\times \frac{8}{5}$$

Multiply -\frac{1}{6} times \frac{8}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-8}{6\times 5}$$

Do the multiplications in the fraction \frac{-8}{6\times 5}.

$$\frac{-8}{30}$$

Reduce the fraction \frac{-8}{30} to lowest terms by extracting and canceling out 2.

$$-\frac{4}{15}$$

Factor

$$-\frac{4}{15} = -0.26666666666666666$$