Solve 1/3+(-5/6)-(-1/2)-2/3

$$\frac { 1 } { 3 } + ( - \frac { 5 } { 6 } ) - ( - \frac { 1 } { 2 } ) - \frac { 2 } { 3 }$$

Evaluate

$$-\frac{2}{3}\approx -0.666666667$$

Solution Steps

Least common multiple of 3 and 6 is 6. Convert \frac{1}{3} and \frac{5}{6} to fractions with denominator 6.

$$\frac{2}{6}-\frac{5}{6}-\left(-\frac{1}{2}\right)-\frac{2}{3}$$

Since \frac{2}{6} and \frac{5}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2-5}{6}-\left(-\frac{1}{2}\right)-\frac{2}{3}$$

Subtract 5 from 2 to get -3.

$$\frac{-3}{6}-\left(-\frac{1}{2}\right)-\frac{2}{3}$$

Reduce the fraction \frac{-3}{6} to lowest terms by extracting and canceling out 3.

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

The opposite of -\frac{1}{2} is \frac{1}{2}.

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

Add -\frac{1}{2} and \frac{1}{2} to get 0.

$$0-\frac{2}{3}$$

Subtract \frac{2}{3} from 0 to get -\frac{2}{3}.

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

Factor

$$-\frac{2}{3} = -0.6666666666666666$$