Solve (1/6+8/12)*(15/14-11/7)+(frac{10}{8}-frac{7}{6}):(-frac{1}{3})^3

$$( \frac { 1 } { 6 } + \frac { 8 } { 12 } ) \cdot ( \frac { 15 } { 14 } - \frac { 11 } { 7 } ) + ( \frac { 10 } { 8 } - \frac { 7 } { 6 } ) : ( - \frac { 1 } { 3 } ) ^ { 3 }$$

Evaluate

$$-\frac{8}{3}\approx -2.666666667$$

Solution Steps

Reduce the fraction \frac{8}{12} to lowest terms by extracting and canceling out 4.

$$\left(\frac{1}{6}+\frac{2}{3}\right)\left(\frac{15}{14}-\frac{11}{7}\right)+\frac{\frac{10}{8}-\frac{7}{6}}{\left(-\frac{1}{3}\right)^{3}}$$

Least common multiple of 6 and 3 is 6. Convert \frac{1}{6} and \frac{2}{3} to fractions with denominator 6.

$$\left(\frac{1}{6}+\frac{4}{6}\right)\left(\frac{15}{14}-\frac{11}{7}\right)+\frac{\frac{10}{8}-\frac{7}{6}}{\left(-\frac{1}{3}\right)^{3}}$$

Since \frac{1}{6} and \frac{4}{6} have the same denominator, add them by adding their numerators.

$$\frac{1+4}{6}\left(\frac{15}{14}-\frac{11}{7}\right)+\frac{\frac{10}{8}-\frac{7}{6}}{\left(-\frac{1}{3}\right)^{3}}$$

Add 1 and 4 to get 5.

$$\frac{5}{6}\left(\frac{15}{14}-\frac{11}{7}\right)+\frac{\frac{10}{8}-\frac{7}{6}}{\left(-\frac{1}{3}\right)^{3}}$$

Least common multiple of 14 and 7 is 14. Convert \frac{15}{14} and \frac{11}{7} to fractions with denominator 14.

$$\frac{5}{6}\left(\frac{15}{14}-\frac{22}{14}\right)+\frac{\frac{10}{8}-\frac{7}{6}}{\left(-\frac{1}{3}\right)^{3}}$$

Since \frac{15}{14} and \frac{22}{14} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5}{6}\times \frac{15-22}{14}+\frac{\frac{10}{8}-\frac{7}{6}}{\left(-\frac{1}{3}\right)^{3}}$$

Subtract 22 from 15 to get -7.

$$\frac{5}{6}\times \frac{-7}{14}+\frac{\frac{10}{8}-\frac{7}{6}}{\left(-\frac{1}{3}\right)^{3}}$$

Reduce the fraction \frac{-7}{14} to lowest terms by extracting and canceling out 7.

$$\frac{5}{6}\left(-\frac{1}{2}\right)+\frac{\frac{10}{8}-\frac{7}{6}}{\left(-\frac{1}{3}\right)^{3}}$$

Multiply \frac{5}{6} times -\frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\left(-1\right)}{6\times 2}+\frac{\frac{10}{8}-\frac{7}{6}}{\left(-\frac{1}{3}\right)^{3}}$$

Do the multiplications in the fraction \frac{5\left(-1\right)}{6\times 2}.

$$\frac{-5}{12}+\frac{\frac{10}{8}-\frac{7}{6}}{\left(-\frac{1}{3}\right)^{3}}$$

Fraction \frac{-5}{12} can be rewritten as -\frac{5}{12} by extracting the negative sign.

$$-\frac{5}{12}+\frac{\frac{10}{8}-\frac{7}{6}}{\left(-\frac{1}{3}\right)^{3}}$$

Reduce the fraction \frac{10}{8} to lowest terms by extracting and canceling out 2.

$$-\frac{5}{12}+\frac{\frac{5}{4}-\frac{7}{6}}{\left(-\frac{1}{3}\right)^{3}}$$

Least common multiple of 4 and 6 is 12. Convert \frac{5}{4} and \frac{7}{6} to fractions with denominator 12.

$$-\frac{5}{12}+\frac{\frac{15}{12}-\frac{14}{12}}{\left(-\frac{1}{3}\right)^{3}}$$

Since \frac{15}{12} and \frac{14}{12} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{5}{12}+\frac{\frac{15-14}{12}}{\left(-\frac{1}{3}\right)^{3}}$$

Subtract 14 from 15 to get 1.

$$-\frac{5}{12}+\frac{\frac{1}{12}}{\left(-\frac{1}{3}\right)^{3}}$$

Calculate -\frac{1}{3} to the power of 3 and get -\frac{1}{27}.

$$-\frac{5}{12}+\frac{\frac{1}{12}}{-\frac{1}{27}}$$

Divide \frac{1}{12} by -\frac{1}{27} by multiplying \frac{1}{12} by the reciprocal of -\frac{1}{27}.

$$-\frac{5}{12}+\frac{1}{12}\left(-27\right)$$

Multiply \frac{1}{12} and -27 to get \frac{-27}{12}.

$$-\frac{5}{12}+\frac{-27}{12}$$

Reduce the fraction \frac{-27}{12} to lowest terms by extracting and canceling out 3.

$$-\frac{5}{12}-\frac{9}{4}$$

Least common multiple of 12 and 4 is 12. Convert -\frac{5}{12} and \frac{9}{4} to fractions with denominator 12.

$$-\frac{5}{12}-\frac{27}{12}$$

Since -\frac{5}{12} and \frac{27}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-5-27}{12}$$

Subtract 27 from -5 to get -32.

$$\frac{-32}{12}$$

Reduce the fraction \frac{-32}{12} to lowest terms by extracting and canceling out 4.

$$-\frac{8}{3}$$

Factor

$$-\frac{8}{3} = -2\frac{2}{3} = -2.6666666666666665$$