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

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

Evaluate

$$-\frac{4}{15}\approx -0.266666667$$

Solution Steps

Since \frac{2}{3} and \frac{5}{3} have the same denominator, add them by adding their numerators.

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

Add 2 and 5 to get 7.

$$-\frac{1}{6}\left(\frac{7}{3}-\left(\frac{1}{5}+\frac{6}{5}\right)+\frac{2}{3}\right)$$

Since \frac{1}{5} and \frac{6}{5} have the same denominator, add them by adding their numerators.

$$-\frac{1}{6}\left(\frac{7}{3}-\frac{1+6}{5}+\frac{2}{3}\right)$$

Add 1 and 6 to get 7.

$$-\frac{1}{6}\left(\frac{7}{3}-\frac{7}{5}+\frac{2}{3}\right)$$

Least common multiple of 3 and 5 is 15. Convert \frac{7}{3} and \frac{7}{5} to fractions with denominator 15.

$$-\frac{1}{6}\left(\frac{35}{15}-\frac{21}{15}+\frac{2}{3}\right)$$

Since \frac{35}{15} and \frac{21}{15} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{6}\left(\frac{35-21}{15}+\frac{2}{3}\right)$$

Subtract 21 from 35 to get 14.

$$-\frac{1}{6}\left(\frac{14}{15}+\frac{2}{3}\right)$$

Least common multiple of 15 and 3 is 15. Convert \frac{14}{15} and \frac{2}{3} to fractions with denominator 15.

$$-\frac{1}{6}\left(\frac{14}{15}+\frac{10}{15}\right)$$

Since \frac{14}{15} and \frac{10}{15} have the same denominator, add them by adding their numerators.

$$-\frac{1}{6}\times \frac{14+10}{15}$$

Add 14 and 10 to get 24.

$$-\frac{1}{6}\times \frac{24}{15}$$

Reduce the fraction \frac{24}{15} to lowest terms by extracting and canceling out 3.

$$-\frac{1}{6}\times \frac{8}{5}$$

Multiply -\frac{1}{6} times \frac{8}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-8}{6\times 5}$$

Do the multiplications in the fraction \frac{-8}{6\times 5}.

$$\frac{-8}{30}$$

Reduce the fraction \frac{-8}{30} to lowest terms by extracting and canceling out 2.

$$-\frac{4}{15}$$

Factor

$$-\frac{4}{15} = -0.26666666666666666$$