Solve (2+1/2)(3/2-3)

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

Evaluate

$$-\frac{15}{4}=-3.75$$

Solution Steps

Convert 2 to fraction \frac{4}{2}.

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

Since \frac{4}{2} and \frac{1}{2} have the same denominator, add them by adding their numerators.

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

Add 4 and 1 to get 5.

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

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

$$\frac{5}{2}\left(\frac{3}{2}-\frac{6}{2}\right)$$

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

$$\frac{5}{2}\times \frac{3-6}{2}$$

Subtract 6 from 3 to get -3.

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

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

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

Do the multiplications in the fraction \frac{5\left(-3\right)}{2\times 2}.

$$\frac{-15}{4}$$

Fraction \frac{-15}{4} can be rewritten as -\frac{15}{4} by extracting the negative sign.

$$-\frac{15}{4}$$

Factor

$$-\frac{15}{4} = -3\frac{3}{4} = -3.75$$