Solve 1/4-2/3-(-1/2)+(-5/6)

$$\frac { 1 } { 4 } - \frac { 2 } { 3 } - ( - \frac { 1 } { 2 } ) + ( - \frac { 5 } { 6 } )$$

Evaluate

$$-\frac{3}{4}=-0.75$$

Solution Steps

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

$$\frac{3}{12}-\frac{8}{12}-\left(-\frac{1}{2}\right)-\frac{5}{6}$$

Since \frac{3}{12} and \frac{8}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-8}{12}-\left(-\frac{1}{2}\right)-\frac{5}{6}$$

Subtract 8 from 3 to get -5.

$$-\frac{5}{12}-\left(-\frac{1}{2}\right)-\frac{5}{6}$$

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

$$-\frac{5}{12}+\frac{1}{2}-\frac{5}{6}$$

Least common multiple of 12 and 2 is 12. Convert -\frac{5}{12} and \frac{1}{2} to fractions with denominator 12.

$$-\frac{5}{12}+\frac{6}{12}-\frac{5}{6}$$

Since -\frac{5}{12} and \frac{6}{12} have the same denominator, add them by adding their numerators.

$$\frac{-5+6}{12}-\frac{5}{6}$$

Add -5 and 6 to get 1.

$$\frac{1}{12}-\frac{5}{6}$$

Least common multiple of 12 and 6 is 12. Convert \frac{1}{12} and \frac{5}{6} to fractions with denominator 12.

$$\frac{1}{12}-\frac{10}{12}$$

Since \frac{1}{12} and \frac{10}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1-10}{12}$$

Subtract 10 from 1 to get -9.

$$\frac{-9}{12}$$

Reduce the fraction \frac{-9}{12} to lowest terms by extracting and canceling out 3.

$$-\frac{3}{4}$$

Factor

$$-\frac{3}{4} = -0.75$$