Solve (-1/2)+(-3/2)div(-4/3)-(-5/6)(frac{6}{7})div(frac{8}{7})

$$( - \frac { 1 } { 2 } ) + ( - \frac { 3 } { 2 } ) \div ( - \frac { 4 } { 3 } ) - ( - \frac { 5 } { 6 } ) ( \frac { 6 } { 7 } ) \div ( \frac { 8 } { 7 } )$$

Evaluate

$$\frac{5}{4}=1.25$$

Solution Steps

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

$$-\frac{1}{2}-\frac{3}{2}\left(-\frac{3}{4}\right)-\frac{-\frac{5}{6}\times \frac{6}{7}}{\frac{8}{7}}$$

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

$$-\frac{1}{2}+\frac{-3\left(-3\right)}{2\times 4}-\frac{-\frac{5}{6}\times \frac{6}{7}}{\frac{8}{7}}$$

Do the multiplications in the fraction \frac{-3\left(-3\right)}{2\times 4}.

$$-\frac{1}{2}+\frac{9}{8}-\frac{-\frac{5}{6}\times \frac{6}{7}}{\frac{8}{7}}$$

Least common multiple of 2 and 8 is 8. Convert -\frac{1}{2} and \frac{9}{8} to fractions with denominator 8.

$$-\frac{4}{8}+\frac{9}{8}-\frac{-\frac{5}{6}\times \frac{6}{7}}{\frac{8}{7}}$$

Since -\frac{4}{8} and \frac{9}{8} have the same denominator, add them by adding their numerators.

$$\frac{-4+9}{8}-\frac{-\frac{5}{6}\times \frac{6}{7}}{\frac{8}{7}}$$

Add -4 and 9 to get 5.

$$\frac{5}{8}-\frac{-\frac{5}{6}\times \frac{6}{7}}{\frac{8}{7}}$$

Multiply -\frac{5}{6} times \frac{6}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5}{8}-\frac{\frac{-5\times 6}{6\times 7}}{\frac{8}{7}}$$

Cancel out 6 in both numerator and denominator.

$$\frac{5}{8}-\frac{\frac{-5}{7}}{\frac{8}{7}}$$

Fraction \frac{-5}{7} can be rewritten as -\frac{5}{7} by extracting the negative sign.

$$\frac{5}{8}-\frac{-\frac{5}{7}}{\frac{8}{7}}$$

Divide -\frac{5}{7} by \frac{8}{7} by multiplying -\frac{5}{7} by the reciprocal of \frac{8}{7}.

$$\frac{5}{8}-\left(-\frac{5}{7}\times \frac{7}{8}\right)$$

Multiply -\frac{5}{7} times \frac{7}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5}{8}-\frac{-5\times 7}{7\times 8}$$

Cancel out 7 in both numerator and denominator.

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

Fraction \frac{-5}{8} can be rewritten as -\frac{5}{8} by extracting the negative sign.

$$\frac{5}{8}-\left(-\frac{5}{8}\right)$$

The opposite of -\frac{5}{8} is \frac{5}{8}.

$$\frac{5}{8}+\frac{5}{8}$$

Since \frac{5}{8} and \frac{5}{8} have the same denominator, add them by adding their numerators.

$$\frac{5+5}{8}$$

Add 5 and 5 to get 10.

$$\frac{10}{8}$$

Reduce the fraction \frac{10}{8} to lowest terms by extracting and canceling out 2.

$$\frac{5}{4}$$

Factor

$$\frac{5}{2 ^ {2}} = 1\frac{1}{4} = 1.25$$