Solve -2/3(3/2-5/2+7/2)

$$- \frac { 2 } { 3 } ( \frac { 3 } { 2 } - \frac { 5 } { 2 } + \frac { 7 } { 2 } )$$

Evaluate

$$-\frac{5}{3}\approx -1.666666667$$

Solution Steps

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

$$-\frac{2}{3}\left(\frac{3-5}{2}+\frac{7}{2}\right)$$

Subtract 5 from 3 to get -2.

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

Divide -2 by 2 to get -1.

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

Convert -1 to fraction -\frac{2}{2}.

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

Since -\frac{2}{2} and \frac{7}{2} have the same denominator, add them by adding their numerators.

$$-\frac{2}{3}\times \frac{-2+7}{2}$$

Add -2 and 7 to get 5.

$$-\frac{2}{3}\times \frac{5}{2}$$

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

$$\frac{-2\times 5}{3\times 2}$$

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

$$\frac{-10}{6}$$

Reduce the fraction \frac{-10}{6} to lowest terms by extracting and canceling out 2.

$$-\frac{5}{3}$$

Factor

$$-\frac{5}{3} = -1\frac{2}{3} = -1.6666666666666667$$