1. **State the problem:** Multiply the mixed number $2\ 3/5$ by $16$. 2. **Convert the mixed number to an improper fraction:** $$2\ \frac{3}{5} = \frac{2 \times 5 + 3}{5} = \frac{10 + 3}{5} = \frac{13}{5}$$ 3. **Set up the multiplication:** $$\frac{13}{5} \times 16$$ 4. **Rewrite 16 as a fraction:** $$\frac{13}{5} \times \frac{16}{1}$$ 5. **Multiply the numerators and denominators:** $$\frac{13 \times 16}{5 \times 1} = \frac{208}{5}$$ 6. **Convert the improper fraction back to a mixed number:** Divide $208$ by $5$: $$208 \div 5 = 41 \text{ remainder } 3$$ So, $$\frac{208}{5} = 41\ \frac{3}{5}$$ **Final answer:** $$41\ \frac{3}{5}$$