Evaluate -3 1/2(-2)+9

$- 3 \frac{1}{2} (- 2) + 9$

Convert $3 \frac{1}{2}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$- (3 + \frac{1}{2}) \cdot - 2 + 9$

Add $3$ and $\frac{1}{2}$ .

To write $3$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- (3 \cdot \frac{2}{2} + \frac{1}{2}) \cdot - 2 + 9$

Combine $3$ and $\frac{2}{2}$ .

$- (\frac{3 \cdot 2}{2} + \frac{1}{2}) \cdot - 2 + 9$

Combine the numerators over the common denominator.

$- \frac{3 \cdot 2 + 1}{2} \cdot - 2 + 9$

Simplify the numerator.

Multiply $3$ by $2$ .

$- \frac{6 + 1}{2} \cdot - 2 + 9$

Add $6$ and $1$ .

$- \frac{7}{2} \cdot - 2 + 9$

Simplify each term.

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{7}{2}$ into the numerator.

$\frac{- 7}{2} \cdot - 2 + 9$

Factor $2$ out of $- 2$ .

$\frac{- 7}{2} \cdot (2 (- 1)) + 9$

Cancel the common factor.

$\frac{- 7}{2} \cdot (2 \cdot - 1) + 9$

Rewrite the expression.

$- 7 \cdot - 1 + 9$

Multiply $- 7$ by $- 1$ .

$7 + 9$

Add $7$ and $9$ .

$16$