Solve {-1/6+5/9-[2/3-4/6-(frac{4}{3}-frac{5}{6})]-frac{2}{9}}

$$\{ - \frac { 1 } { 6 } + \frac { 5 } { 9 } - [ \frac { 2 } { 3 } - \frac { 4 } { 6 } - ( \frac { 4 } { 3 } - \frac { 5 } { 6 } ) ] - \frac { 2 } { 9 } \}$$

Evaluate

$$\frac{2}{3}\approx 0.666666667$$

Solution Steps

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

$$-\frac{3}{18}+\frac{10}{18}-\left(\frac{2}{3}-\frac{4}{6}-\left(\frac{4}{3}-\frac{5}{6}\right)\right)-\frac{2}{9}$$

Since -\frac{3}{18} and \frac{10}{18} have the same denominator, add them by adding their numerators.

$$\frac{-3+10}{18}-\left(\frac{2}{3}-\frac{4}{6}-\left(\frac{4}{3}-\frac{5}{6}\right)\right)-\frac{2}{9}$$

Add -3 and 10 to get 7.

$$\frac{7}{18}-\left(\frac{2}{3}-\frac{4}{6}-\left(\frac{4}{3}-\frac{5}{6}\right)\right)-\frac{2}{9}$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$\frac{7}{18}-\left(\frac{2}{3}-\frac{2}{3}-\left(\frac{4}{3}-\frac{5}{6}\right)\right)-\frac{2}{9}$$

Subtract \frac{2}{3} from \frac{2}{3} to get 0.

$$\frac{7}{18}-\left(0-\left(\frac{4}{3}-\frac{5}{6}\right)\right)-\frac{2}{9}$$

Least common multiple of 3 and 6 is 6. Convert \frac{4}{3} and \frac{5}{6} to fractions with denominator 6.

$$\frac{7}{18}-\left(0-\left(\frac{8}{6}-\frac{5}{6}\right)\right)-\frac{2}{9}$$

Since \frac{8}{6} and \frac{5}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{7}{18}-\left(0-\frac{8-5}{6}\right)-\frac{2}{9}$$

Subtract 5 from 8 to get 3.

$$\frac{7}{18}-\left(0-\frac{3}{6}\right)-\frac{2}{9}$$

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

$$\frac{7}{18}-\left(0-\frac{1}{2}\right)-\frac{2}{9}$$

Subtract \frac{1}{2} from 0 to get -\frac{1}{2}.

$$\frac{7}{18}-\left(-\frac{1}{2}\right)-\frac{2}{9}$$

The opposite of -\frac{1}{2} is \frac{1}{2}.

$$\frac{7}{18}+\frac{1}{2}-\frac{2}{9}$$

Least common multiple of 18 and 2 is 18. Convert \frac{7}{18} and \frac{1}{2} to fractions with denominator 18.

$$\frac{7}{18}+\frac{9}{18}-\frac{2}{9}$$

Since \frac{7}{18} and \frac{9}{18} have the same denominator, add them by adding their numerators.

$$\frac{7+9}{18}-\frac{2}{9}$$

Add 7 and 9 to get 16.

$$\frac{16}{18}-\frac{2}{9}$$

Reduce the fraction \frac{16}{18} to lowest terms by extracting and canceling out 2.

$$\frac{8}{9}-\frac{2}{9}$$

Since \frac{8}{9} and \frac{2}{9} have the same denominator, subtract them by subtracting their numerators.

$$\frac{8-2}{9}$$

Subtract 2 from 8 to get 6.

$$\frac{6}{9}$$

Reduce the fraction \frac{6}{9} to lowest terms by extracting and canceling out 3.

$$\frac{2}{3}$$

Factor

$$\frac{2}{3} = 0.6666666666666666$$