Solve 1/2-5/9+5/6

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

Evaluate

$$\frac{7}{9}\approx 0.777777778$$

Solution Steps

Least common multiple of 2 and 9 is 18. Convert \frac{1}{2} and \frac{5}{9} to fractions with denominator 18.

$$\frac{9}{18}-\frac{10}{18}+\frac{5}{6}$$

Since \frac{9}{18} and \frac{10}{18} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9-10}{18}+\frac{5}{6}$$

Subtract 10 from 9 to get -1.

$$-\frac{1}{18}+\frac{5}{6}$$

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

$$-\frac{1}{18}+\frac{15}{18}$$

Since -\frac{1}{18} and \frac{15}{18} have the same denominator, add them by adding their numerators.

$$\frac{-1+15}{18}$$

Add -1 and 15 to get 14.

$$\frac{14}{18}$$

Reduce the fraction \frac{14}{18} to lowest terms by extracting and canceling out 2.

$$\frac{7}{9}$$

Factor

$$\frac{7}{3 ^ {2}} = 0.7777777777777778$$