Solve (+2/3)+(-1/2)+(-5/9)+(+5/6)

$$( + \frac { 2 } { 3 } ) + ( - \frac { 1 } { 2 } ) + ( - \frac { 5 } { 9 } ) + ( + \frac { 5 } { 6 } )$$

Evaluate

$$\frac{4}{9}\approx 0.444444444$$

Solution Steps

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

$$\frac{4}{6}-\frac{3}{6}-\frac{5}{9}+\frac{5}{6}$$

Since \frac{4}{6} and \frac{3}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4-3}{6}-\frac{5}{9}+\frac{5}{6}$$

Subtract 3 from 4 to get 1.

$$\frac{1}{6}-\frac{5}{9}+\frac{5}{6}$$

Least common multiple of 6 and 9 is 18. Convert \frac{1}{6} and \frac{5}{9} to fractions with denominator 18.

$$\frac{3}{18}-\frac{10}{18}+\frac{5}{6}$$

Since \frac{3}{18} and \frac{10}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-10}{18}+\frac{5}{6}$$

Subtract 10 from 3 to get -7.

$$-\frac{7}{18}+\frac{5}{6}$$

Least common multiple of 18 and 6 is 18. Convert -\frac{7}{18} and \frac{5}{6} to fractions with denominator 18.

$$-\frac{7}{18}+\frac{15}{18}$$

Since -\frac{7}{18} and \frac{15}{18} have the same denominator, add them by adding their numerators.

$$\frac{-7+15}{18}$$

Add -7 and 15 to get 8.

$$\frac{8}{18}$$

Reduce the fraction \frac{8}{18} to lowest terms by extracting and canceling out 2.

$$\frac{4}{9}$$

Factor

$$\frac{2 ^ {2}}{3 ^ {2}} = 0.4444444444444444$$