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

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

Evaluate

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

Solution Steps

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

$$\left(\frac{4}{6}-\frac{1}{6}\right)\left(\frac{1}{2}-\frac{3}{4}\right)$$

Since \frac{4}{6} and \frac{1}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4-1}{6}\left(\frac{1}{2}-\frac{3}{4}\right)$$

Subtract 1 from 4 to get 3.

$$\frac{3}{6}\left(\frac{1}{2}-\frac{3}{4}\right)$$

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

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

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

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

Since \frac{2}{4} and \frac{3}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}\times \frac{2-3}{4}$$

Subtract 3 from 2 to get -1.

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

Multiply \frac{1}{2} times -\frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{1\left(-1\right)}{2\times 4}.

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

Fraction \frac{-1}{8} can be rewritten as -\frac{1}{8} by extracting the negative sign.

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

Factor

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