Solve (-1/2)^2div(-1/3)*(1/2-1/3)

$$( - \frac { 1 } { 2 } ) ^ { 2 } \div ( - \frac { 1 } { 3 } ) \times ( \frac { 1 } { 2 } - \frac { 1 } { 3 } )$$

Evaluate

$$-\frac{1}{8}=-0.125$$

Solution Steps

Calculate -\frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$\frac{\frac{1}{4}}{-\frac{1}{3}}\left(\frac{1}{2}-\frac{1}{3}\right)$$

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

$$\frac{1}{4}\left(-3\right)\left(\frac{1}{2}-\frac{1}{3}\right)$$

Multiply \frac{1}{4} and -3 to get \frac{-3}{4}.

$$\frac{-3}{4}\left(\frac{1}{2}-\frac{1}{3}\right)$$

Fraction \frac{-3}{4} can be rewritten as -\frac{3}{4} by extracting the negative sign.

$$-\frac{3}{4}\left(\frac{1}{2}-\frac{1}{3}\right)$$

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

$$-\frac{3}{4}\left(\frac{3}{6}-\frac{2}{6}\right)$$

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

$$-\frac{3}{4}\times \frac{3-2}{6}$$

Subtract 2 from 3 to get 1.

$$-\frac{3}{4}\times \frac{1}{6}$$

Multiply -\frac{3}{4} times \frac{1}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-3}{4\times 6}$$

Do the multiplications in the fraction \frac{-3}{4\times 6}.

$$\frac{-3}{24}$$

Reduce the fraction \frac{-3}{24} to lowest terms by extracting and canceling out 3.

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

Factor

$$-\frac{1}{8} = -0.125$$