Solve -2^3-(-2)*(-1/3)+(-5/6+5/8)*(-24)

$$- 2 ^ { 3 } - ( - 2 ) \times ( - \frac { 1 } { 3 } ) + ( - \frac { 5 } { 6 } + \frac { 5 } { 8 } ) \times ( - 24 )$$

Evaluate

$$-\frac{11}{3}\approx -3.666666667$$

Solution Steps

Calculate 2 to the power of 3 and get 8.

$$-8-\left(-2\left(-\frac{1}{3}\right)\right)+\left(-\frac{5}{6}+\frac{5}{8}\right)\left(-24\right)$$

Express -2\left(-\frac{1}{3}\right) as a single fraction.

$$-8-\frac{-2\left(-1\right)}{3}+\left(-\frac{5}{6}+\frac{5}{8}\right)\left(-24\right)$$

Multiply -2 and -1 to get 2.

$$-8-\frac{2}{3}+\left(-\frac{5}{6}+\frac{5}{8}\right)\left(-24\right)$$

Convert -8 to fraction -\frac{24}{3}.

$$-\frac{24}{3}-\frac{2}{3}+\left(-\frac{5}{6}+\frac{5}{8}\right)\left(-24\right)$$

Since -\frac{24}{3} and \frac{2}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-24-2}{3}+\left(-\frac{5}{6}+\frac{5}{8}\right)\left(-24\right)$$

Subtract 2 from -24 to get -26.

$$-\frac{26}{3}+\left(-\frac{5}{6}+\frac{5}{8}\right)\left(-24\right)$$

Least common multiple of 6 and 8 is 24. Convert -\frac{5}{6} and \frac{5}{8} to fractions with denominator 24.

$$-\frac{26}{3}+\left(-\frac{20}{24}+\frac{15}{24}\right)\left(-24\right)$$

Since -\frac{20}{24} and \frac{15}{24} have the same denominator, add them by adding their numerators.

$$-\frac{26}{3}+\frac{-20+15}{24}\left(-24\right)$$

Add -20 and 15 to get -5.

$$-\frac{26}{3}-\frac{5}{24}\left(-24\right)$$

Express -\frac{5}{24}\left(-24\right) as a single fraction.

$$-\frac{26}{3}+\frac{-5\left(-24\right)}{24}$$

Multiply -5 and -24 to get 120.

$$-\frac{26}{3}+\frac{120}{24}$$

Divide 120 by 24 to get 5.

$$-\frac{26}{3}+5$$

Convert 5 to fraction \frac{15}{3}.

$$-\frac{26}{3}+\frac{15}{3}$$

Since -\frac{26}{3} and \frac{15}{3} have the same denominator, add them by adding their numerators.

$$\frac{-26+15}{3}$$

Add -26 and 15 to get -11.

$$-\frac{11}{3}$$

Factor

$$-\frac{11}{3} = -3\frac{2}{3} = -3.6666666666666665$$