Solve 1/2-3/7+2/3-5/6

$$\frac { 1 } { 2 } - \frac { 3 } { 7 } + \frac { 2 } { 3 } - \frac { 5 } { 6 }$$

Evaluate

$$-\frac{2}{21}\approx -0.095238095$$

Solution Steps

Least common multiple of 2 and 7 is 14. Convert \frac{1}{2} and \frac{3}{7} to fractions with denominator 14.

$$\frac{7}{14}-\frac{6}{14}+\frac{2}{3}-\frac{5}{6}$$

Since \frac{7}{14} and \frac{6}{14} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7-6}{14}+\frac{2}{3}-\frac{5}{6}$$

Subtract 6 from 7 to get 1.

$$\frac{1}{14}+\frac{2}{3}-\frac{5}{6}$$

Least common multiple of 14 and 3 is 42. Convert \frac{1}{14} and \frac{2}{3} to fractions with denominator 42.

$$\frac{3}{42}+\frac{28}{42}-\frac{5}{6}$$

Since \frac{3}{42} and \frac{28}{42} have the same denominator, add them by adding their numerators.

$$\frac{3+28}{42}-\frac{5}{6}$$

Add 3 and 28 to get 31.

$$\frac{31}{42}-\frac{5}{6}$$

Least common multiple of 42 and 6 is 42. Convert \frac{31}{42} and \frac{5}{6} to fractions with denominator 42.

$$\frac{31}{42}-\frac{35}{42}$$

Since \frac{31}{42} and \frac{35}{42} have the same denominator, subtract them by subtracting their numerators.

$$\frac{31-35}{42}$$

Subtract 35 from 31 to get -4.

$$\frac{-4}{42}$$

Reduce the fraction \frac{-4}{42} to lowest terms by extracting and canceling out 2.

$$-\frac{2}{21}$$

Factor

$$-\frac{2}{21} = -0.09523809523809523$$