Solve (4)(-7/8)div(13/4-7/8-7/12)

$$( 4 ) ( - \frac { 7 } { 8 } ) \div ( 1 \frac { 3 } { 4 } - \frac { 7 } { 8 } - \frac { 7 } { 12 } )$$

Evaluate

$$-12$$

Solution Steps

Express 4\left(-\frac{7}{8}\right) as a single fraction.

$$\frac{\frac{4\left(-7\right)}{8}}{\frac{1\times 4+3}{4}-\frac{7}{8}-\frac{7}{12}}$$

Multiply 4 and -7 to get -28.

$$\frac{\frac{-28}{8}}{\frac{1\times 4+3}{4}-\frac{7}{8}-\frac{7}{12}}$$

Reduce the fraction \frac{-28}{8} to lowest terms by extracting and canceling out 4.

$$\frac{-\frac{7}{2}}{\frac{1\times 4+3}{4}-\frac{7}{8}-\frac{7}{12}}$$

Multiply 1 and 4 to get 4.

$$\frac{-\frac{7}{2}}{\frac{4+3}{4}-\frac{7}{8}-\frac{7}{12}}$$

Add 4 and 3 to get 7.

$$\frac{-\frac{7}{2}}{\frac{7}{4}-\frac{7}{8}-\frac{7}{12}}$$

Least common multiple of 4 and 8 is 8. Convert \frac{7}{4} and \frac{7}{8} to fractions with denominator 8.

$$\frac{-\frac{7}{2}}{\frac{14}{8}-\frac{7}{8}-\frac{7}{12}}$$

Since \frac{14}{8} and \frac{7}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{7}{2}}{\frac{14-7}{8}-\frac{7}{12}}$$

Subtract 7 from 14 to get 7.

$$\frac{-\frac{7}{2}}{\frac{7}{8}-\frac{7}{12}}$$

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

$$\frac{-\frac{7}{2}}{\frac{21}{24}-\frac{14}{24}}$$

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

$$\frac{-\frac{7}{2}}{\frac{21-14}{24}}$$

Subtract 14 from 21 to get 7.

$$\frac{-\frac{7}{2}}{\frac{7}{24}}$$

Divide -\frac{7}{2} by \frac{7}{24} by multiplying -\frac{7}{2} by the reciprocal of \frac{7}{24}.

$$-\frac{7}{2}\times \frac{24}{7}$$

Multiply -\frac{7}{2} times \frac{24}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-7\times 24}{2\times 7}$$

Do the multiplications in the fraction \frac{-7\times 24}{2\times 7}.

$$\frac{-168}{14}$$

Divide -168 by 14 to get -12.

$$-12$$

Factor

$$-12$$