Solve 3/5-8/3+1/2

$$\frac { 3 } { 5 } - \frac { 8 } { 3 } + \frac { 1 } { 2 }$$

Evaluate

$$-\frac{47}{30}\approx -1.566666667$$

Solution Steps

Least common multiple of 5 and 3 is 15. Convert \frac{3}{5} and \frac{8}{3} to fractions with denominator 15.

$$\frac{9}{15}-\frac{40}{15}+\frac{1}{2}$$

Since \frac{9}{15} and \frac{40}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9-40}{15}+\frac{1}{2}$$

Subtract 40 from 9 to get -31.

$$-\frac{31}{15}+\frac{1}{2}$$

Least common multiple of 15 and 2 is 30. Convert -\frac{31}{15} and \frac{1}{2} to fractions with denominator 30.

$$-\frac{62}{30}+\frac{15}{30}$$

Since -\frac{62}{30} and \frac{15}{30} have the same denominator, add them by adding their numerators.

$$\frac{-62+15}{30}$$

Add -62 and 15 to get -47.

$$-\frac{47}{30}$$

Factor

$$-\frac{47}{30} = -1\frac{17}{30} = -1.5666666666666667$$