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

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

Evaluate

$$\frac{5}{9}\approx 0.555555556$$

Solution Steps

Least common multiple of 2 and 6 is 6. Convert -\frac{1}{2} and \frac{5}{6} to fractions with denominator 6.

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

Since -\frac{3}{6} and \frac{5}{6} have the same denominator, add them by adding their numerators.

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

Add -3 and 5 to get 2.

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

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

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

Least common multiple of 9 and 3 is 9. Convert \frac{5}{9} and \frac{1}{3} to fractions with denominator 9.

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

Since \frac{5}{9} and \frac{3}{9} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 3 from 5 to get 2.

$$\frac{2}{9}-\frac{2}{3}+1$$

Least common multiple of 9 and 3 is 9. Convert \frac{2}{9} and \frac{2}{3} to fractions with denominator 9.

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

Since \frac{2}{9} and \frac{6}{9} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 6 from 2 to get -4.

$$-\frac{4}{9}+1$$

Convert 1 to fraction \frac{9}{9}.

$$-\frac{4}{9}+\frac{9}{9}$$

Since -\frac{4}{9} and \frac{9}{9} have the same denominator, add them by adding their numerators.

$$\frac{-4+9}{9}$$

Add -4 and 9 to get 5.

$$\frac{5}{9}$$

Factor

$$\frac{5}{3 ^ {2}} = 0.5555555555555556$$