1. The problem is to calculate $-15 \times 3 \frac{2}{5}$ and simplify the answer. 2. 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. Multiply $-15$ by $\frac{17}{5}$: $$-15 \times \frac{17}{5} = \frac{-15 \times 17}{5} = \frac{-255}{5}$$ 4. Simplify the fraction $\frac{-255}{5}$ by dividing numerator and denominator by 5: $$\frac{-255}{5} = -51$$ 5. The simplest form of the product is $-51$. Final answer: $-51$