Solve -1/2+(-1/6)-(-1/4)-(+2/3)

$$- \frac { 1 } { 2 } + ( - \frac { 1 } { 6 } ) - ( - \frac { 1 } { 4 } ) - ( + \frac { 2 } { 3 } )$$

Evaluate

$$-\frac{13}{12}\approx -1.083333333$$

Solution Steps

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

$$-\frac{3}{6}-\frac{1}{6}-\left(-\frac{1}{4}\right)-\frac{2}{3}$$

Since -\frac{3}{6} and \frac{1}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-3-1}{6}-\left(-\frac{1}{4}\right)-\frac{2}{3}$$

Subtract 1 from -3 to get -4.

$$\frac{-4}{6}-\left(-\frac{1}{4}\right)-\frac{2}{3}$$

Reduce the fraction \frac{-4}{6} to lowest terms by extracting and canceling out 2.

$$-\frac{2}{3}-\left(-\frac{1}{4}\right)-\frac{2}{3}$$

The opposite of -\frac{1}{4} is \frac{1}{4}.

$$-\frac{2}{3}+\frac{1}{4}-\frac{2}{3}$$

Least common multiple of 3 and 4 is 12. Convert -\frac{2}{3} and \frac{1}{4} to fractions with denominator 12.

$$-\frac{8}{12}+\frac{3}{12}-\frac{2}{3}$$

Since -\frac{8}{12} and \frac{3}{12} have the same denominator, add them by adding their numerators.

$$\frac{-8+3}{12}-\frac{2}{3}$$

Add -8 and 3 to get -5.

$$-\frac{5}{12}-\frac{2}{3}$$

Least common multiple of 12 and 3 is 12. Convert -\frac{5}{12} and \frac{2}{3} to fractions with denominator 12.

$$-\frac{5}{12}-\frac{8}{12}$$

Since -\frac{5}{12} and \frac{8}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-5-8}{12}$$

Subtract 8 from -5 to get -13.

$$-\frac{13}{12}$$

Factor

$$-\frac{13}{12} = -1\frac{1}{12} = -1.0833333333333333$$