Solve (-3/4)*[-31/2-(-21/3)]

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

Evaluate

$$\frac{7}{8}=0.875$$

Solution Steps

Multiply 3 and 2 to get 6.

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

Add 6 and 1 to get 7.

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

Multiply 2 and 3 to get 6.

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

Add 6 and 1 to get 7.

$$-\frac{3}{4}\left(-\frac{7}{2}-\left(-\frac{7}{3}\right)\right)$$

The opposite of -\frac{7}{3} is \frac{7}{3}.

$$-\frac{3}{4}\left(-\frac{7}{2}+\frac{7}{3}\right)$$

Least common multiple of 2 and 3 is 6. Convert -\frac{7}{2} and \frac{7}{3} to fractions with denominator 6.

$$-\frac{3}{4}\left(-\frac{21}{6}+\frac{14}{6}\right)$$

Since -\frac{21}{6} and \frac{14}{6} have the same denominator, add them by adding their numerators.

$$-\frac{3}{4}\times \frac{-21+14}{6}$$

Add -21 and 14 to get -7.

$$-\frac{3}{4}\left(-\frac{7}{6}\right)$$

Multiply -\frac{3}{4} times -\frac{7}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-3\left(-7\right)}{4\times 6}$$

Do the multiplications in the fraction \frac{-3\left(-7\right)}{4\times 6}.

$$\frac{21}{24}$$

Reduce the fraction \frac{21}{24} to lowest terms by extracting and canceling out 3.

$$\frac{7}{8}$$

Factor

$$\frac{7}{2 ^ {3}} = 0.875$$