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

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

Evaluate

$$\frac{23}{30}\approx 0.766666667$$

Solution Steps

Least common multiple of 5 and 2 is 10. Convert \frac{3}{5} and \frac{1}{2} to fractions with denominator 10.

$$\frac{6}{10}-\frac{5}{10}-\left(-\frac{2}{3}\right)$$

Since \frac{6}{10} and \frac{5}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6-5}{10}-\left(-\frac{2}{3}\right)$$

Subtract 5 from 6 to get 1.

$$\frac{1}{10}-\left(-\frac{2}{3}\right)$$

The opposite of -\frac{2}{3} is \frac{2}{3}.

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

Least common multiple of 10 and 3 is 30. Convert \frac{1}{10} and \frac{2}{3} to fractions with denominator 30.

$$\frac{3}{30}+\frac{20}{30}$$

Since \frac{3}{30} and \frac{20}{30} have the same denominator, add them by adding their numerators.

$$\frac{3+20}{30}$$

Add 3 and 20 to get 23.

$$\frac{23}{30}$$

Factor

$$\frac{23}{2 \cdot 3 \cdot 5} = 0.7666666666666667$$