Solve (13/4-7/8-7/12)div(-7/8)+(-frac{7}{8})div(1frac{3}{4}-frac{7}{8}-frac{7}{12})

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

Evaluate

$$-\frac{10}{3}\approx -3.333333333$$

Solution Steps

Multiply 1 and 4 to get 4.

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

Add 4 and 3 to get 7.

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

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

$$\frac{\frac{14}{8}-\frac{7}{8}-\frac{7}{12}}{-\frac{7}{8}}+\frac{-\frac{7}{8}}{\frac{1\times 4+3}{4}-\frac{7}{8}-\frac{7}{12}}$$

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

$$\frac{\frac{14-7}{8}-\frac{7}{12}}{-\frac{7}{8}}+\frac{-\frac{7}{8}}{\frac{1\times 4+3}{4}-\frac{7}{8}-\frac{7}{12}}$$

Subtract 7 from 14 to get 7.

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

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

$$\frac{\frac{21}{24}-\frac{14}{24}}{-\frac{7}{8}}+\frac{-\frac{7}{8}}{\frac{1\times 4+3}{4}-\frac{7}{8}-\frac{7}{12}}$$

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

$$\frac{\frac{21-14}{24}}{-\frac{7}{8}}+\frac{-\frac{7}{8}}{\frac{1\times 4+3}{4}-\frac{7}{8}-\frac{7}{12}}$$

Subtract 14 from 21 to get 7.

$$\frac{\frac{7}{24}}{-\frac{7}{8}}+\frac{-\frac{7}{8}}{\frac{1\times 4+3}{4}-\frac{7}{8}-\frac{7}{12}}$$

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

$$\frac{7}{24}\left(-\frac{8}{7}\right)+\frac{-\frac{7}{8}}{\frac{1\times 4+3}{4}-\frac{7}{8}-\frac{7}{12}}$$

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

$$\frac{7\left(-8\right)}{24\times 7}+\frac{-\frac{7}{8}}{\frac{1\times 4+3}{4}-\frac{7}{8}-\frac{7}{12}}$$

Cancel out 7 in both numerator and denominator.

$$\frac{-8}{24}+\frac{-\frac{7}{8}}{\frac{1\times 4+3}{4}-\frac{7}{8}-\frac{7}{12}}$$

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

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

Multiply 1 and 4 to get 4.

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

Add 4 and 3 to get 7.

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

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

$$-\frac{1}{3}+\frac{-\frac{7}{8}}{\frac{14}{8}-\frac{7}{8}-\frac{7}{12}}$$

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

$$-\frac{1}{3}+\frac{-\frac{7}{8}}{\frac{14-7}{8}-\frac{7}{12}}$$

Subtract 7 from 14 to get 7.

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

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

$$-\frac{1}{3}+\frac{-\frac{7}{8}}{\frac{21}{24}-\frac{14}{24}}$$

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

$$-\frac{1}{3}+\frac{-\frac{7}{8}}{\frac{21-14}{24}}$$

Subtract 14 from 21 to get 7.

$$-\frac{1}{3}+\frac{-\frac{7}{8}}{\frac{7}{24}}$$

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

$$-\frac{1}{3}-\frac{7}{8}\times \frac{24}{7}$$

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

$$-\frac{1}{3}+\frac{-7\times 24}{8\times 7}$$

Do the multiplications in the fraction \frac{-7\times 24}{8\times 7}.

$$-\frac{1}{3}+\frac{-168}{56}$$

Divide -168 by 56 to get -3.

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

Convert 3 to fraction \frac{9}{3}.

$$-\frac{1}{3}-\frac{9}{3}$$

Since -\frac{1}{3} and \frac{9}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-1-9}{3}$$

Subtract 9 from -1 to get -10.

$$-\frac{10}{3}$$

Factor

$$-\frac{10}{3} = -3\frac{1}{3} = -3.3333333333333335$$