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

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

Evaluate

$$-1$$

Solution Steps

Convert -1 to fraction -\frac{2}{2}.

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

Since -\frac{2}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

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

Add -2 and 1 to get -1.

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

Least common multiple of 6 and 3 is 6. Convert -\frac{1}{6} and \frac{2}{3} to fractions with denominator 6.

$$-\frac{1}{2}-\left(-\frac{1}{6}+\frac{4}{6}\right)$$

Since -\frac{1}{6} and \frac{4}{6} have the same denominator, add them by adding their numerators.

$$-\frac{1}{2}-\frac{-1+4}{6}$$

Add -1 and 4 to get 3.

$$-\frac{1}{2}-\frac{3}{6}$$

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

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

Since -\frac{1}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 1 from -1 to get -2.

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

Divide -2 by 2 to get -1.

$$-1$$

Factor

$$-1$$