Solve (1/6-2/3+5/12)*(-36)

$$( \frac { 1 } { 6 } - \frac { 2 } { 3 } + \frac { 5 } { 12 } ) \times ( - 36 )$$

Evaluate

$$3$$

Solution Steps

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

$$\left(\frac{1}{6}-\frac{4}{6}+\frac{5}{12}\right)\left(-36\right)$$

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

$$\left(\frac{1-4}{6}+\frac{5}{12}\right)\left(-36\right)$$

Subtract 4 from 1 to get -3.

$$\left(\frac{-3}{6}+\frac{5}{12}\right)\left(-36\right)$$

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

$$\left(-\frac{1}{2}+\frac{5}{12}\right)\left(-36\right)$$

Least common multiple of 2 and 12 is 12. Convert -\frac{1}{2} and \frac{5}{12} to fractions with denominator 12.

$$\left(-\frac{6}{12}+\frac{5}{12}\right)\left(-36\right)$$

Since -\frac{6}{12} and \frac{5}{12} have the same denominator, add them by adding their numerators.

$$\frac{-6+5}{12}\left(-36\right)$$

Add -6 and 5 to get -1.

$$-\frac{1}{12}\left(-36\right)$$

Express -\frac{1}{12}\left(-36\right) as a single fraction.

$$\frac{-\left(-36\right)}{12}$$

Multiply -1 and -36 to get 36.

$$\frac{36}{12}$$

Divide 36 by 12 to get 3.

$$3$$

Factor

$$3$$