Solve 108*(2/3-3/4+7/9)

$$108 \times ( \frac { 2 } { 3 } - \frac { 3 } { 4 } + \frac { 7 } { 9 } )$$

Evaluate

$$75$$

Solution Steps

Least common multiple of 3 and 4 is 12. Convert \frac{2}{3} and \frac{3}{4} to fractions with denominator 12.

$$108\left(\frac{8}{12}-\frac{9}{12}+\frac{7}{9}\right)$$

Since \frac{8}{12} and \frac{9}{12} have the same denominator, subtract them by subtracting their numerators.

$$108\left(\frac{8-9}{12}+\frac{7}{9}\right)$$

Subtract 9 from 8 to get -1.

$$108\left(-\frac{1}{12}+\frac{7}{9}\right)$$

Least common multiple of 12 and 9 is 36. Convert -\frac{1}{12} and \frac{7}{9} to fractions with denominator 36.

$$108\left(-\frac{3}{36}+\frac{28}{36}\right)$$

Since -\frac{3}{36} and \frac{28}{36} have the same denominator, add them by adding their numerators.

$$108\times \frac{-3+28}{36}$$

Add -3 and 28 to get 25.

$$108\times \frac{25}{36}$$

Express 108\times \frac{25}{36} as a single fraction.

$$\frac{108\times 25}{36}$$

Multiply 108 and 25 to get 2700.

$$\frac{2700}{36}$$

Divide 2700 by 36 to get 75.

$$75$$

Factor

$$3\times 5^{2}$$