Solve (2/3-1/4)div(-1+1/6)

$$( \frac { 2 } { 3 } - \frac { 1 } { 4 } ) \div ( - 1 + \frac { 1 } { 6 } )$$

Evaluate

$$-\frac{1}{2}=-0.5$$

Solution Steps

Least common multiple of 3 and 4 is 12. Convert \frac{2}{3} and \frac{1}{4} to fractions with denominator 12.

$$\frac{\frac{8}{12}-\frac{3}{12}}{-1+\frac{1}{6}}$$

Since \frac{8}{12} and \frac{3}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{8-3}{12}}{-1+\frac{1}{6}}$$

Subtract 3 from 8 to get 5.

$$\frac{\frac{5}{12}}{-1+\frac{1}{6}}$$

Convert -1 to fraction -\frac{6}{6}.

$$\frac{\frac{5}{12}}{-\frac{6}{6}+\frac{1}{6}}$$

Since -\frac{6}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$\frac{\frac{5}{12}}{\frac{-6+1}{6}}$$

Add -6 and 1 to get -5.

$$\frac{\frac{5}{12}}{-\frac{5}{6}}$$

Divide \frac{5}{12} by -\frac{5}{6} by multiplying \frac{5}{12} by the reciprocal of -\frac{5}{6}.

$$\frac{5}{12}\left(-\frac{6}{5}\right)$$

Multiply \frac{5}{12} times -\frac{6}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\left(-6\right)}{12\times 5}$$

Cancel out 5 in both numerator and denominator.

$$\frac{-6}{12}$$

Reduce the fraction \frac{-6}{12} to lowest terms by extracting and canceling out 6.

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

Factor

$$-\frac{1}{2} = -0.5$$