Solve 12((1/3-1/2)(1/18-1/2))=

$$12 ( ( \frac { 1 } { 3 } - \frac { 1 } { 2 } ) ( \frac { 1 } { 18 } - \frac { 1 } { 2 } ) ) =$$

Evaluate

$$\frac{8}{9}\approx 0.888888889$$

Solution Steps

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

$$12\left(\frac{2}{6}-\frac{3}{6}\right)\left(\frac{1}{18}-\frac{1}{2}\right)$$

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

$$12\times \frac{2-3}{6}\left(\frac{1}{18}-\frac{1}{2}\right)$$

Subtract 3 from 2 to get -1.

$$12\left(-\frac{1}{6}\right)\left(\frac{1}{18}-\frac{1}{2}\right)$$

Express 12\left(-\frac{1}{6}\right) as a single fraction.

$$\frac{12\left(-1\right)}{6}\left(\frac{1}{18}-\frac{1}{2}\right)$$

Multiply 12 and -1 to get -12.

$$\frac{-12}{6}\left(\frac{1}{18}-\frac{1}{2}\right)$$

Divide -12 by 6 to get -2.

$$-2\left(\frac{1}{18}-\frac{1}{2}\right)$$

Least common multiple of 18 and 2 is 18. Convert \frac{1}{18} and \frac{1}{2} to fractions with denominator 18.

$$-2\left(\frac{1}{18}-\frac{9}{18}\right)$$

Since \frac{1}{18} and \frac{9}{18} have the same denominator, subtract them by subtracting their numerators.

$$-2\times \frac{1-9}{18}$$

Subtract 9 from 1 to get -8.

$$-2\times \frac{-8}{18}$$

Reduce the fraction \frac{-8}{18} to lowest terms by extracting and canceling out 2.

$$-2\left(-\frac{4}{9}\right)$$

Express -2\left(-\frac{4}{9}\right) as a single fraction.

$$\frac{-2\left(-4\right)}{9}$$

Multiply -2 and -4 to get 8.

$$\frac{8}{9}$$

Factor

$$\frac{2 ^ {3}}{3 ^ {2}} = 0.8888888888888888$$