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

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

Evaluate

$$\frac{7}{3}\approx 2.333333333$$

Solution Steps

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

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

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

$$\frac{3\times \frac{-21-14}{24}}{-\frac{7}{8}}-\frac{8}{3}$$

Subtract 14 from -21 to get -35.

$$\frac{3\left(-\frac{35}{24}\right)}{-\frac{7}{8}}-\frac{8}{3}$$

Express 3\left(-\frac{35}{24}\right) as a single fraction.

$$\frac{\frac{3\left(-35\right)}{24}}{-\frac{7}{8}}-\frac{8}{3}$$

Multiply 3 and -35 to get -105.

$$\frac{\frac{-105}{24}}{-\frac{7}{8}}-\frac{8}{3}$$

Reduce the fraction \frac{-105}{24} to lowest terms by extracting and canceling out 3.

$$\frac{-\frac{35}{8}}{-\frac{7}{8}}-\frac{8}{3}$$

Divide -\frac{35}{8} by -\frac{7}{8} by multiplying -\frac{35}{8} by the reciprocal of -\frac{7}{8}.

$$-\frac{35}{8}\left(-\frac{8}{7}\right)-\frac{8}{3}$$

Multiply -\frac{35}{8} times -\frac{8}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-35\left(-8\right)}{8\times 7}-\frac{8}{3}$$

Do the multiplications in the fraction \frac{-35\left(-8\right)}{8\times 7}.

$$\frac{280}{56}-\frac{8}{3}$$

Divide 280 by 56 to get 5.

$$5-\frac{8}{3}$$

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

$$\frac{15}{3}-\frac{8}{3}$$

Since \frac{15}{3} and \frac{8}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{15-8}{3}$$

Subtract 8 from 15 to get 7.

$$\frac{7}{3}$$

Factor

$$\frac{7}{3} = 2\frac{1}{3} = 2.3333333333333335$$