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

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

Evaluate

$$-\frac{7}{4}=-1.75$$

Solution Steps

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

$$\frac{3}{12}-\frac{8}{12}-\frac{1}{2}-\frac{5}{6}$$

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

$$\frac{3-8}{12}-\frac{1}{2}-\frac{5}{6}$$

Subtract 8 from 3 to get -5.

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

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, subtract them by subtracting their numerators.

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

Subtract 6 from -5 to get -11.

$$-\frac{11}{12}-\frac{5}{6}$$

Least common multiple of 12 and 6 is 12. Convert -\frac{11}{12} and \frac{5}{6} to fractions with denominator 12.

$$-\frac{11}{12}-\frac{10}{12}$$

Since -\frac{11}{12} and \frac{10}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-11-10}{12}$$

Subtract 10 from -11 to get -21.

$$\frac{-21}{12}$$

Reduce the fraction \frac{-21}{12} to lowest terms by extracting and canceling out 3.

$$-\frac{7}{4}$$

Factor

$$-\frac{7}{4} = -1\frac{3}{4} = -1.75$$