Solve (-11/4-5/8+9/12)*(-24)

$$( - 1 \frac { 1 } { 4 } - \frac { 5 } { 8 } + \frac { 9 } { 12 } ) \times ( - 24 )$$

Evaluate

$$27$$

Solution Steps

Multiply 1 and 4 to get 4.

$$\left(-\frac{4+1}{4}-\frac{5}{8}+\frac{9}{12}\right)\left(-24\right)$$

Add 4 and 1 to get 5.

$$\left(-\frac{5}{4}-\frac{5}{8}+\frac{9}{12}\right)\left(-24\right)$$

Least common multiple of 4 and 8 is 8. Convert -\frac{5}{4} and \frac{5}{8} to fractions with denominator 8.

$$\left(-\frac{10}{8}-\frac{5}{8}+\frac{9}{12}\right)\left(-24\right)$$

Since -\frac{10}{8} and \frac{5}{8} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{-10-5}{8}+\frac{9}{12}\right)\left(-24\right)$$

Subtract 5 from -10 to get -15.

$$\left(-\frac{15}{8}+\frac{9}{12}\right)\left(-24\right)$$

Reduce the fraction \frac{9}{12} to lowest terms by extracting and canceling out 3.

$$\left(-\frac{15}{8}+\frac{3}{4}\right)\left(-24\right)$$

Least common multiple of 8 and 4 is 8. Convert -\frac{15}{8} and \frac{3}{4} to fractions with denominator 8.

$$\left(-\frac{15}{8}+\frac{6}{8}\right)\left(-24\right)$$

Since -\frac{15}{8} and \frac{6}{8} have the same denominator, add them by adding their numerators.

$$\frac{-15+6}{8}\left(-24\right)$$

Add -15 and 6 to get -9.

$$-\frac{9}{8}\left(-24\right)$$

Express -\frac{9}{8}\left(-24\right) as a single fraction.

$$\frac{-9\left(-24\right)}{8}$$

Multiply -9 and -24 to get 216.

$$\frac{216}{8}$$

Divide 216 by 8 to get 27.

$$27$$

Factor

$$3^{3}$$