1. The problem is to calculate $-15 \times 3 \frac{2}{5}$ and simplify the answer. 2. First, convert the mixed number $3 \frac{2}{5}$ to an improper fraction. $$3 \frac{2}{5} = \frac{3 \times 5 + 2}{5} = \frac{15 + 2}{5} = \frac{17}{5}$$ 3. Now multiply $-15$ by $\frac{17}{5}$. $$-15 \times \frac{17}{5} = \frac{-15 \times 17}{5} = \frac{-255}{5}$$ 4. Simplify the fraction by dividing numerator and denominator by 5. $$\frac{\cancel{5}1\cancel{5}1}{\cancel{5}1} = -51$$ 5. The simplest form of the product is $-51$.