1. **State the problem:** Given the ratio $\frac{a}{b} = \frac{3}{5}$ and $a = 2$, find the value of $b$. 2. **Formula used:** For ratios, if $\frac{a}{b} = \frac{3}{5}$, then $a$ and $b$ are proportional such that $\frac{a}{b} = \frac{3}{5}$. 3. **Set up the equation:** $$\frac{a}{b} = \frac{3}{5}$$ Substitute $a = 2$: $$\frac{2}{b} = \frac{3}{5}$$ 4. **Solve for $b$:** Cross multiply: $$2 \times 5 = 3 \times b$$ $$10 = 3b$$ Divide both sides by 3: $$\cancel{3}b = \frac{10}{\cancel{3}}$$ $$b = \frac{10}{3}$$ 5. **Final answer:** The value of $b$ when $a = 2$ is $$b = \frac{10}{3}$$