1. Problem: Determine if the given ratios are true or false. 2. For part a: The ratio 3 : 2 is compared to 2 : 3. 3. Recall that ratios a : b and c : d are equal if $\frac{a}{b} = \frac{c}{d}$. 4. Calculate $\frac{3}{2} = 1.5$ and $\frac{2}{3} \approx 0.6667$. 5. Since $1.5 \neq 0.6667$, the ratio 3 : 2 is not the same as 2 : 3. 6. Therefore, part a is False. 7. For part b: Check if $1 : 5 = 3 : 12$. 8. Calculate $\frac{1}{5} = 0.2$ and $\frac{3}{12} = 0.25$. 9. Since $0.2 \neq 0.25$, the ratio 1 : 5 is not equal to 3 : 12. 10. Therefore, part b is False. Final answers: - a) False - b) False