Solve ((-3/4)+(2/3)^3div(-8/9)-(-2/3))*((-frac{1}{8})+(-frac{4}{5}))

$$( ( - \frac { 3 } { 4 } ) + ( \frac { 2 } { 3 } ) ^ { 3 } \div ( - \frac { 8 } { 9 } ) - ( - \frac { 2 } { 3 } ) ) \times ( ( - \frac { 1 } { 8 } ) + ( - \frac { 4 } { 5 } ) )$$

Evaluate

$$\frac{37}{96}\approx 0.385416667$$

Solution Steps

Calculate \frac{2}{3} to the power of 3 and get \frac{8}{27}.

$$\left(-\frac{3}{4}+\frac{\frac{8}{27}}{-\frac{8}{9}}-\left(-\frac{2}{3}\right)\right)\left(-\frac{1}{8}-\frac{4}{5}\right)$$

Divide \frac{8}{27} by -\frac{8}{9} by multiplying \frac{8}{27} by the reciprocal of -\frac{8}{9}.

$$\left(-\frac{3}{4}+\frac{8}{27}\left(-\frac{9}{8}\right)-\left(-\frac{2}{3}\right)\right)\left(-\frac{1}{8}-\frac{4}{5}\right)$$

Multiply \frac{8}{27} times -\frac{9}{8} by multiplying numerator times numerator and denominator times denominator.

$$\left(-\frac{3}{4}+\frac{8\left(-9\right)}{27\times 8}-\left(-\frac{2}{3}\right)\right)\left(-\frac{1}{8}-\frac{4}{5}\right)$$

Cancel out 8 in both numerator and denominator.

$$\left(-\frac{3}{4}+\frac{-9}{27}-\left(-\frac{2}{3}\right)\right)\left(-\frac{1}{8}-\frac{4}{5}\right)$$

Reduce the fraction \frac{-9}{27} to lowest terms by extracting and canceling out 9.

$$\left(-\frac{3}{4}-\frac{1}{3}-\left(-\frac{2}{3}\right)\right)\left(-\frac{1}{8}-\frac{4}{5}\right)$$

Least common multiple of 4 and 3 is 12. Convert -\frac{3}{4} and \frac{1}{3} to fractions with denominator 12.

$$\left(-\frac{9}{12}-\frac{4}{12}-\left(-\frac{2}{3}\right)\right)\left(-\frac{1}{8}-\frac{4}{5}\right)$$

Since -\frac{9}{12} and \frac{4}{12} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{-9-4}{12}-\left(-\frac{2}{3}\right)\right)\left(-\frac{1}{8}-\frac{4}{5}\right)$$

Subtract 4 from -9 to get -13.

$$\left(-\frac{13}{12}-\left(-\frac{2}{3}\right)\right)\left(-\frac{1}{8}-\frac{4}{5}\right)$$

The opposite of -\frac{2}{3} is \frac{2}{3}.

$$\left(-\frac{13}{12}+\frac{2}{3}\right)\left(-\frac{1}{8}-\frac{4}{5}\right)$$

Least common multiple of 12 and 3 is 12. Convert -\frac{13}{12} and \frac{2}{3} to fractions with denominator 12.

$$\left(-\frac{13}{12}+\frac{8}{12}\right)\left(-\frac{1}{8}-\frac{4}{5}\right)$$

Since -\frac{13}{12} and \frac{8}{12} have the same denominator, add them by adding their numerators.

$$\frac{-13+8}{12}\left(-\frac{1}{8}-\frac{4}{5}\right)$$

Add -13 and 8 to get -5.

$$-\frac{5}{12}\left(-\frac{1}{8}-\frac{4}{5}\right)$$

Least common multiple of 8 and 5 is 40. Convert -\frac{1}{8} and \frac{4}{5} to fractions with denominator 40.

$$-\frac{5}{12}\left(-\frac{5}{40}-\frac{32}{40}\right)$$

Since -\frac{5}{40} and \frac{32}{40} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{5}{12}\times \frac{-5-32}{40}$$

Subtract 32 from -5 to get -37.

$$-\frac{5}{12}\left(-\frac{37}{40}\right)$$

Multiply -\frac{5}{12} times -\frac{37}{40} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-5\left(-37\right)}{12\times 40}$$

Do the multiplications in the fraction \frac{-5\left(-37\right)}{12\times 40}.

$$\frac{185}{480}$$

Reduce the fraction \frac{185}{480} to lowest terms by extracting and canceling out 5.

$$\frac{37}{96}$$

Factor

$$\frac{37}{2 ^ {5} \cdot 3} = 0.3854166666666667$$