Solve (1/3-1/12)div(1/8-1/2)

$$( \frac { 1 } { 3 } - \frac { 1 } { 12 } ) \div ( \frac { 1 } { 8 } - \frac { 1 } { 2 } )$$

Evaluate

$$-\frac{2}{3}\approx -0.666666667$$

Solution Steps

Least common multiple of 3 and 12 is 12. Convert \frac{1}{3} and \frac{1}{12} to fractions with denominator 12.

$$\frac{\frac{4}{12}-\frac{1}{12}}{\frac{1}{8}-\frac{1}{2}}$$

Since \frac{4}{12} and \frac{1}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{4-1}{12}}{\frac{1}{8}-\frac{1}{2}}$$

Subtract 1 from 4 to get 3.

$$\frac{\frac{3}{12}}{\frac{1}{8}-\frac{1}{2}}$$

Reduce the fraction \frac{3}{12} to lowest terms by extracting and canceling out 3.

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

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

$$\frac{\frac{1}{4}}{\frac{1}{8}-\frac{4}{8}}$$

Since \frac{1}{8} and \frac{4}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{1}{4}}{\frac{1-4}{8}}$$

Subtract 4 from 1 to get -3.

$$\frac{\frac{1}{4}}{-\frac{3}{8}}$$

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

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

Multiply \frac{1}{4} times -\frac{8}{3} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{1\left(-8\right)}{4\times 3}.

$$\frac{-8}{12}$$

Reduce the fraction \frac{-8}{12} to lowest terms by extracting and canceling out 4.

$$-\frac{2}{3}$$

Factor

$$-\frac{2}{3} = -0.6666666666666666$$