1. The problem is to multiply the mixed numbers $-2 \frac{1}{2}$ and $3 \frac{2}{5}$ and express the answer as a simplified mixed number. 2. First, convert the mixed numbers to improper fractions. $$-2 \frac{1}{2} = -\left(2 + \frac{1}{2}\right) = -\frac{5}{2}$$ $$3 \frac{2}{5} = 3 + \frac{2}{5} = \frac{17}{5}$$ 3. Multiply the improper fractions: $$-\frac{5}{2} \times \frac{17}{5} = -\frac{5 \times 17}{2 \times 5} = -\frac{85}{10}$$ 4. Simplify the fraction by canceling common factors: $$-\frac{\cancel{85}}{\cancel{10}} = -\frac{17}{2}$$ 5. Convert the improper fraction back to a mixed number: $$-\frac{17}{2} = -\left(8 + \frac{1}{2}\right) = -8 \frac{1}{2}$$ 6. Final answer: $-8 \frac{1}{2}$