Solve (-6/8+9/8):5/8+(2/7-frac{5}{14}):frac{5}{28}-(frac{5}{6}-frac{1}{12}):(-frac{3}{2})

$$( - \frac { 6 } { 8 } + \frac { 9 } { 8 } ) : \frac { 5 } { 8 } + ( \frac { 2 } { 7 } - \frac { 5 } { 14 } ) : \frac { 5 } { 28 } - ( \frac { 5 } { 6 } - \frac { 1 } { 12 } ) : ( - \frac { 3 } { 2 } )$$

Evaluate

$$\frac{7}{10}=0.7$$

Solution Steps

Since -\frac{6}{8} and \frac{9}{8} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-6+9}{8}}{\frac{5}{8}}+\frac{\frac{2}{7}-\frac{5}{14}}{\frac{5}{28}}-\frac{\frac{5}{6}-\frac{1}{12}}{-\frac{3}{2}}$$

Add -6 and 9 to get 3.

$$\frac{\frac{3}{8}}{\frac{5}{8}}+\frac{\frac{2}{7}-\frac{5}{14}}{\frac{5}{28}}-\frac{\frac{5}{6}-\frac{1}{12}}{-\frac{3}{2}}$$

Divide \frac{3}{8} by \frac{5}{8} by multiplying \frac{3}{8} by the reciprocal of \frac{5}{8}.

$$\frac{3}{8}\times \frac{8}{5}+\frac{\frac{2}{7}-\frac{5}{14}}{\frac{5}{28}}-\frac{\frac{5}{6}-\frac{1}{12}}{-\frac{3}{2}}$$

Multiply \frac{3}{8} times \frac{8}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 8}{8\times 5}+\frac{\frac{2}{7}-\frac{5}{14}}{\frac{5}{28}}-\frac{\frac{5}{6}-\frac{1}{12}}{-\frac{3}{2}}$$

Cancel out 8 in both numerator and denominator.

$$\frac{3}{5}+\frac{\frac{2}{7}-\frac{5}{14}}{\frac{5}{28}}-\frac{\frac{5}{6}-\frac{1}{12}}{-\frac{3}{2}}$$

Least common multiple of 7 and 14 is 14. Convert \frac{2}{7} and \frac{5}{14} to fractions with denominator 14.

$$\frac{3}{5}+\frac{\frac{4}{14}-\frac{5}{14}}{\frac{5}{28}}-\frac{\frac{5}{6}-\frac{1}{12}}{-\frac{3}{2}}$$

Since \frac{4}{14} and \frac{5}{14} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{5}+\frac{\frac{4-5}{14}}{\frac{5}{28}}-\frac{\frac{5}{6}-\frac{1}{12}}{-\frac{3}{2}}$$

Subtract 5 from 4 to get -1.

$$\frac{3}{5}+\frac{-\frac{1}{14}}{\frac{5}{28}}-\frac{\frac{5}{6}-\frac{1}{12}}{-\frac{3}{2}}$$

Divide -\frac{1}{14} by \frac{5}{28} by multiplying -\frac{1}{14} by the reciprocal of \frac{5}{28}.

$$\frac{3}{5}-\frac{1}{14}\times \frac{28}{5}-\frac{\frac{5}{6}-\frac{1}{12}}{-\frac{3}{2}}$$

Multiply -\frac{1}{14} times \frac{28}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{5}+\frac{-28}{14\times 5}-\frac{\frac{5}{6}-\frac{1}{12}}{-\frac{3}{2}}$$

Do the multiplications in the fraction \frac{-28}{14\times 5}.

$$\frac{3}{5}+\frac{-28}{70}-\frac{\frac{5}{6}-\frac{1}{12}}{-\frac{3}{2}}$$

Reduce the fraction \frac{-28}{70} to lowest terms by extracting and canceling out 14.

$$\frac{3}{5}-\frac{2}{5}-\frac{\frac{5}{6}-\frac{1}{12}}{-\frac{3}{2}}$$

Since \frac{3}{5} and \frac{2}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3-2}{5}-\frac{\frac{5}{6}-\frac{1}{12}}{-\frac{3}{2}}$$

Subtract 2 from 3 to get 1.

$$\frac{1}{5}-\frac{\frac{5}{6}-\frac{1}{12}}{-\frac{3}{2}}$$

Least common multiple of 6 and 12 is 12. Convert \frac{5}{6} and \frac{1}{12} to fractions with denominator 12.

$$\frac{1}{5}-\frac{\frac{10}{12}-\frac{1}{12}}{-\frac{3}{2}}$$

Since \frac{10}{12} and \frac{1}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{5}-\frac{\frac{10-1}{12}}{-\frac{3}{2}}$$

Subtract 1 from 10 to get 9.

$$\frac{1}{5}-\frac{\frac{9}{12}}{-\frac{3}{2}}$$

Reduce the fraction \frac{9}{12} to lowest terms by extracting and canceling out 3.

$$\frac{1}{5}-\frac{\frac{3}{4}}{-\frac{3}{2}}$$

Divide \frac{3}{4} by -\frac{3}{2} by multiplying \frac{3}{4} by the reciprocal of -\frac{3}{2}.

$$\frac{1}{5}-\frac{3}{4}\left(-\frac{2}{3}\right)$$

Multiply \frac{3}{4} times -\frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{5}-\frac{3\left(-2\right)}{4\times 3}$$

Cancel out 3 in both numerator and denominator.

$$\frac{1}{5}-\frac{-2}{4}$$

Reduce the fraction \frac{-2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{1}{5}-\left(-\frac{1}{2}\right)$$

The opposite of -\frac{1}{2} is \frac{1}{2}.

$$\frac{1}{5}+\frac{1}{2}$$

Least common multiple of 5 and 2 is 10. Convert \frac{1}{5} and \frac{1}{2} to fractions with denominator 10.

$$\frac{2}{10}+\frac{5}{10}$$

Since \frac{2}{10} and \frac{5}{10} have the same denominator, add them by adding their numerators.

$$\frac{2+5}{10}$$

Add 2 and 5 to get 7.

$$\frac{7}{10}$$

Factor

$$\frac{7}{2 \cdot 5} = 0.7$$