Solve (1/12-3/4-1/6)*(-24)

$$( \frac { 1 } { 12 } - \frac { 3 } { 4 } - \frac { 1 } { 6 } ) \times ( - 24 )$$

Evaluate

$$20$$

Solution Steps

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

$$\left(\frac{1}{12}-\frac{9}{12}-\frac{1}{6}\right)\left(-24\right)$$

Since \frac{1}{12} and \frac{9}{12} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{1-9}{12}-\frac{1}{6}\right)\left(-24\right)$$

Subtract 9 from 1 to get -8.

$$\left(\frac{-8}{12}-\frac{1}{6}\right)\left(-24\right)$$

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

$$\left(-\frac{2}{3}-\frac{1}{6}\right)\left(-24\right)$$

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

$$\left(-\frac{4}{6}-\frac{1}{6}\right)\left(-24\right)$$

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

$$\frac{-4-1}{6}\left(-24\right)$$

Subtract 1 from -4 to get -5.

$$-\frac{5}{6}\left(-24\right)$$

Express -\frac{5}{6}\left(-24\right) as a single fraction.

$$\frac{-5\left(-24\right)}{6}$$

Multiply -5 and -24 to get 120.

$$\frac{120}{6}$$

Divide 120 by 6 to get 20.

$$20$$

Factor

$$2^{2}\times 5$$