Solve (7/8-7/12)div(-7/8)+(-2)^3

$$( \frac { 7 } { 8 } - \frac { 7 } { 12 } ) \div ( - \frac { 7 } { 8 } ) + ( - 2 ) ^ { 3 }$$

Evaluate

$$-\frac{25}{3}\approx -8.333333333$$

Solution Steps

Least common multiple of 8 and 12 is 24. Convert \frac{7}{8} and \frac{7}{12} to fractions with denominator 24.

$$\frac{\frac{21}{24}-\frac{14}{24}}{-\frac{7}{8}}+\left(-2\right)^{3}$$

Since \frac{21}{24} and \frac{14}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{21-14}{24}}{-\frac{7}{8}}+\left(-2\right)^{3}$$

Subtract 14 from 21 to get 7.

$$\frac{\frac{7}{24}}{-\frac{7}{8}}+\left(-2\right)^{3}$$

Divide \frac{7}{24} by -\frac{7}{8} by multiplying \frac{7}{24} by the reciprocal of -\frac{7}{8}.

$$\frac{7}{24}\left(-\frac{8}{7}\right)+\left(-2\right)^{3}$$

Multiply \frac{7}{24} times -\frac{8}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7\left(-8\right)}{24\times 7}+\left(-2\right)^{3}$$

Cancel out 7 in both numerator and denominator.

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

Reduce the fraction \frac{-8}{24} to lowest terms by extracting and canceling out 8.

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

Calculate -2 to the power of 3 and get -8.

$$-\frac{1}{3}-8$$

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

$$-\frac{1}{3}-\frac{24}{3}$$

Since -\frac{1}{3} and \frac{24}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-1-24}{3}$$

Subtract 24 from -1 to get -25.

$$-\frac{25}{3}$$

Factor

$$-\frac{25}{3} = -8\frac{1}{3} = -8.333333333333334$$