1. **State the problem:** Given that $\frac{a}{b} = \frac{3}{5}$ and $\frac{b}{c} = \frac{2}{3}$, find the value of $a \times c$. 2. **Write down the given ratios:** $$\frac{a}{b} = \frac{3}{5} \quad \text{and} \quad \frac{b}{c} = \frac{2}{3}$$ 3. **Express $a$ and $b$ in terms of $c$:** From $\frac{b}{c} = \frac{2}{3}$, we get $$b = \frac{2}{3} c$$ From $\frac{a}{b} = \frac{3}{5}$, substitute $b$: $$a = \frac{3}{5} b = \frac{3}{5} \times \frac{2}{3} c$$ 4. **Simplify $a$:** $$a = \frac{3}{5} \times \frac{2}{3} c = \frac{\cancel{3}}{5} \times \frac{2}{\cancel{3}} c = \frac{2}{5} c$$ 5. **Calculate $a \times c$:** $$a \times c = \left( \frac{2}{5} c \right) \times c = \frac{2}{5} c^2$$ 6. **Interpretation:** Without a specific value for $c$, $a \times c$ is expressed as $\frac{2}{5} c^2$. If $c$ is known, substitute to find a numeric value. **Final answer:** $$a \times c = \frac{2}{5} c^2$$