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

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

Evaluate

$$9$$

Solution Steps

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

$$-1-\left(\frac{4}{12}-\frac{1}{12}+\frac{1}{6}\right)\left(-24\right)$$

Since \frac{4}{12} and \frac{1}{12} have the same denominator, subtract them by subtracting their numerators.

$$-1-\left(\frac{4-1}{12}+\frac{1}{6}\right)\left(-24\right)$$

Subtract 1 from 4 to get 3.

$$-1-\left(\frac{3}{12}+\frac{1}{6}\right)\left(-24\right)$$

Reduce the fraction \frac{3}{12} to lowest terms by extracting and canceling out 3.

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

Least common multiple of 4 and 6 is 12. Convert \frac{1}{4} and \frac{1}{6} to fractions with denominator 12.

$$-1-\left(\frac{3}{12}+\frac{2}{12}\right)\left(-24\right)$$

Since \frac{3}{12} and \frac{2}{12} have the same denominator, add them by adding their numerators.

$$-1-\frac{3+2}{12}\left(-24\right)$$

Add 3 and 2 to get 5.

$$-1-\frac{5}{12}\left(-24\right)$$

Express \frac{5}{12}\left(-24\right) as a single fraction.

$$-1-\frac{5\left(-24\right)}{12}$$

Multiply 5 and -24 to get -120.

$$-1-\frac{-120}{12}$$

Divide -120 by 12 to get -10.

$$-1-\left(-10\right)$$

The opposite of -10 is 10.

$$-1+10$$

Add -1 and 10 to get 9.

$$9$$

Factor

$$3^{2}$$