1. **State the problem:** Solve the equation $\frac{b}{5} = \frac{8}{16}$ for $b$. 2. **Use the cross-multiplication method:** When two fractions are equal, their cross products are equal. So, $$b \times 16 = 8 \times 5$$ 3. **Calculate the products:** $$16b = 40$$ 4. **Isolate $b$ by dividing both sides by 16:** $$b = \frac{40}{16}$$ 5. **Simplify the fraction:** $$b = \frac{\cancel{40}^{5 \times 8}}{\cancel{16}^{2 \times 8}} = \frac{5}{2}$$ 6. **Final answer:** $$b = \frac{5}{2}$$ This means $b$ equals two and a half or 2.5.