Solve 2/9+[-5/6*(4/5-2/3)]

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

Evaluate

$$\frac{1}{9}\approx 0.111111111$$

Solution Steps

Least common multiple of 5 and 3 is 15. Convert \frac{4}{5} and \frac{2}{3} to fractions with denominator 15.

$$\frac{2}{9}-\frac{5}{6}\left(\frac{12}{15}-\frac{10}{15}\right)$$

Since \frac{12}{15} and \frac{10}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2}{9}-\frac{5}{6}\times \frac{12-10}{15}$$

Subtract 10 from 12 to get 2.

$$\frac{2}{9}-\frac{5}{6}\times \frac{2}{15}$$

Multiply -\frac{5}{6} times \frac{2}{15} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2}{9}+\frac{-5\times 2}{6\times 15}$$

Do the multiplications in the fraction \frac{-5\times 2}{6\times 15}.

$$\frac{2}{9}+\frac{-10}{90}$$

Reduce the fraction \frac{-10}{90} to lowest terms by extracting and canceling out 10.

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

Since \frac{2}{9} and \frac{1}{9} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 1 from 2 to get 1.

$$\frac{1}{9}$$

Factor

$$\frac{1}{3 ^ {2}} = 0.1111111111111111$$