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

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

Evaluate

$$\frac{1}{30}\approx 0.033333333$$

Solution Steps

Least common multiple of 5 and 3 is 15. Convert \frac{1}{5} and \frac{2}{3} to fractions with denominator 15.

$$\frac{3}{15}-\frac{10}{15}+\frac{1}{2}$$

Since \frac{3}{15} and \frac{10}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-10}{15}+\frac{1}{2}$$

Subtract 10 from 3 to get -7.

$$-\frac{7}{15}+\frac{1}{2}$$

Least common multiple of 15 and 2 is 30. Convert -\frac{7}{15} and \frac{1}{2} to fractions with denominator 30.

$$-\frac{14}{30}+\frac{15}{30}$$

Since -\frac{14}{30} and \frac{15}{30} have the same denominator, add them by adding their numerators.

$$\frac{-14+15}{30}$$

Add -14 and 15 to get 1.

$$\frac{1}{30}$$

Factor

$$\frac{1}{2 \cdot 3 \cdot 5} = 0.03333333333333333$$