Solve (5/3-7/2)+(3/2-8/3)

$$( \frac { 5 } { 3 } - \frac { 7 } { 2 } ) + ( \frac { 3 } { 2 } - \frac { 8 } { 3 } )$$

Evaluate

$$-3$$

Solution Steps

Least common multiple of 3 and 2 is 6. Convert \frac{5}{3} and \frac{7}{2} to fractions with denominator 6.

$$\frac{10}{6}-\frac{21}{6}+\frac{3}{2}-\frac{8}{3}$$

Since \frac{10}{6} and \frac{21}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10-21}{6}+\frac{3}{2}-\frac{8}{3}$$

Subtract 21 from 10 to get -11.

$$-\frac{11}{6}+\frac{3}{2}-\frac{8}{3}$$

Least common multiple of 6 and 2 is 6. Convert -\frac{11}{6} and \frac{3}{2} to fractions with denominator 6.

$$-\frac{11}{6}+\frac{9}{6}-\frac{8}{3}$$

Since -\frac{11}{6} and \frac{9}{6} have the same denominator, add them by adding their numerators.

$$\frac{-11+9}{6}-\frac{8}{3}$$

Add -11 and 9 to get -2.

$$\frac{-2}{6}-\frac{8}{3}$$

Reduce the fraction \frac{-2}{6} to lowest terms by extracting and canceling out 2.

$$-\frac{1}{3}-\frac{8}{3}$$

Since -\frac{1}{3} and \frac{8}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-1-8}{3}$$

Subtract 8 from -1 to get -9.

$$\frac{-9}{3}$$

Divide -9 by 3 to get -3.

$$-3$$

Factor

$$-3$$