Solve [(-3/2)*5/3-(-1/2)]div[(-3/4)*3+frac{3}{2}]

$$[ ( - \frac { 3 } { 2 } ) \cdot \frac { 5 } { 3 } - ( - \frac { 1 } { 2 } ) ] \div [ ( - \frac { 3 } { 4 } ) \cdot 3 + \frac { 3 } { 2 } ]$$

Evaluate

$$\frac{8}{3}\approx 2.666666667$$

Solution Steps

Multiply -\frac{3}{2} times \frac{5}{3} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{-3\times 5}{2\times 3}.

$$\frac{\frac{-15}{6}-\left(-\frac{1}{2}\right)}{-\frac{3}{4}\times 3+\frac{3}{2}}$$

Reduce the fraction \frac{-15}{6} to lowest terms by extracting and canceling out 3.

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

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

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

Since -\frac{5}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

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

Add -5 and 1 to get -4.

$$\frac{\frac{-4}{2}}{-\frac{3}{4}\times 3+\frac{3}{2}}$$

Divide -4 by 2 to get -2.

$$\frac{-2}{-\frac{3}{4}\times 3+\frac{3}{2}}$$

Express -\frac{3}{4}\times 3 as a single fraction.

$$\frac{-2}{\frac{-3\times 3}{4}+\frac{3}{2}}$$

Multiply -3 and 3 to get -9.

$$\frac{-2}{\frac{-9}{4}+\frac{3}{2}}$$

Fraction \frac{-9}{4} can be rewritten as -\frac{9}{4} by extracting the negative sign.

$$\frac{-2}{-\frac{9}{4}+\frac{3}{2}}$$

Least common multiple of 4 and 2 is 4. Convert -\frac{9}{4} and \frac{3}{2} to fractions with denominator 4.

$$\frac{-2}{-\frac{9}{4}+\frac{6}{4}}$$

Since -\frac{9}{4} and \frac{6}{4} have the same denominator, add them by adding their numerators.

$$\frac{-2}{\frac{-9+6}{4}}$$

Add -9 and 6 to get -3.

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

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

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

Express -2\left(-\frac{4}{3}\right) as a single fraction.

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

Multiply -2 and -4 to get 8.

$$\frac{8}{3}$$

Factor

$$\frac{2 ^ {3}}{3} = 2\frac{2}{3} = 2.6666666666666665$$