Solve -3/2[-1/2(2/3+2)-2/3(frac{-3}{4})(-frac{1}{2})]:frac{3}{2}

$$\frac { - 3 } { 2 } [ - \frac { 1 } { 2 } ( \frac { 2 } { 3 } + 2 ) - \frac { 2 } { 3 } ( \frac { - 3 } { 4 } ) ( - \frac { 1 } { 2 } ) ] : \frac { 3 } { 2 }$$

Evaluate

$$\frac{19}{12}\approx 1.583333333$$

Solution Steps

Fraction \frac{-3}{2} can be rewritten as -\frac{3}{2} by extracting the negative sign.

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

Convert 2 to fraction \frac{6}{3}.

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

Since \frac{2}{3} and \frac{6}{3} have the same denominator, add them by adding their numerators.

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

Add 2 and 6 to get 8.

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

Multiply -\frac{1}{2} times \frac{8}{3} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{-8}{2\times 3}.

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

Reduce the fraction \frac{-8}{6} to lowest terms by extracting and canceling out 2.

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

Fraction \frac{-3}{4} can be rewritten as -\frac{3}{4} by extracting the negative sign.

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

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

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

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

$$\frac{-\frac{3}{2}\left(-\frac{4}{3}-\frac{-6}{12}\left(-\frac{1}{2}\right)\right)}{\frac{3}{2}}$$

Reduce the fraction \frac{-6}{12} to lowest terms by extracting and canceling out 6.

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

Multiply -\frac{1}{2} times -\frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{-\left(-1\right)}{2\times 2}.

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

Least common multiple of 3 and 4 is 12. Convert -\frac{4}{3} and \frac{1}{4} to fractions with denominator 12.

$$\frac{-\frac{3}{2}\left(-\frac{16}{12}-\frac{3}{12}\right)}{\frac{3}{2}}$$

Since -\frac{16}{12} and \frac{3}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\frac{3}{2}\times \frac{-16-3}{12}}{\frac{3}{2}}$$

Subtract 3 from -16 to get -19.

$$\frac{-\frac{3}{2}\left(-\frac{19}{12}\right)}{\frac{3}{2}}$$

Multiply -\frac{3}{2} times -\frac{19}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{-3\left(-19\right)}{2\times 12}}{\frac{3}{2}}$$

Do the multiplications in the fraction \frac{-3\left(-19\right)}{2\times 12}.

$$\frac{\frac{57}{24}}{\frac{3}{2}}$$

Reduce the fraction \frac{57}{24} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{19}{8}}{\frac{3}{2}}$$

Divide \frac{19}{8} by \frac{3}{2} by multiplying \frac{19}{8} by the reciprocal of \frac{3}{2}.

$$\frac{19}{8}\times \frac{2}{3}$$

Multiply \frac{19}{8} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{19\times 2}{8\times 3}$$

Do the multiplications in the fraction \frac{19\times 2}{8\times 3}.

$$\frac{38}{24}$$

Reduce the fraction \frac{38}{24} to lowest terms by extracting and canceling out 2.

$$\frac{19}{12}$$

Factor

$$\frac{19}{2 ^ {2} \cdot 3} = 1\frac{7}{12} = 1.5833333333333333$$