Solve (-48)*(12/3-3/8+5/24)

$$( - 48 ) \times ( 1 \frac { 2 } { 3 } - \frac { 3 } { 8 } + \frac { 5 } { 24 } )$$

Evaluate

$$-72$$

Solution Steps

Multiply 1 and 3 to get 3.

$$-48\left(\frac{3+2}{3}-\frac{3}{8}+\frac{5}{24}\right)$$

Add 3 and 2 to get 5.

$$-48\left(\frac{5}{3}-\frac{3}{8}+\frac{5}{24}\right)$$

Least common multiple of 3 and 8 is 24. Convert \frac{5}{3} and \frac{3}{8} to fractions with denominator 24.

$$-48\left(\frac{40}{24}-\frac{9}{24}+\frac{5}{24}\right)$$

Since \frac{40}{24} and \frac{9}{24} have the same denominator, subtract them by subtracting their numerators.

$$-48\left(\frac{40-9}{24}+\frac{5}{24}\right)$$

Subtract 9 from 40 to get 31.

$$-48\left(\frac{31}{24}+\frac{5}{24}\right)$$

Since \frac{31}{24} and \frac{5}{24} have the same denominator, add them by adding their numerators.

$$-48\times \frac{31+5}{24}$$

Add 31 and 5 to get 36.

$$-48\times \frac{36}{24}$$

Reduce the fraction \frac{36}{24} to lowest terms by extracting and canceling out 12.

$$-48\times \frac{3}{2}$$

Express -48\times \frac{3}{2} as a single fraction.

$$\frac{-48\times 3}{2}$$

Multiply -48 and 3 to get -144.

$$\frac{-144}{2}$$

Divide -144 by 2 to get -72.

$$-72$$

Factor

$$-72$$