1. **Problem:** Determine if the given ratios are true or false. 2. **Part a:** Is the ratio 3 : 2 the same as 2 : 3? - Ratios are equal if their fractions are equal: $$\frac{3}{2} \stackrel{?}{=} \frac{2}{3}$$ - Cross multiply: $$3 \times 3 = 9$$ and $$2 \times 2 = 4$$ - Since 9 \neq 4, the ratios are not equal. 3. **Answer for a:** False. 4. **Part b:** Is the ratio 1 : 5 equal to 3 : 12? - Write as fractions: $$\frac{1}{5} \stackrel{?}{=} \frac{3}{12}$$ - Simplify $$\frac{3}{12}$$ by canceling common factor 3: $$\frac{\cancel{3}}{\cancel{12}} = \frac{1}{4}$$ - Now compare $$\frac{1}{5}$$ and $$\frac{1}{4}$$. - Since denominators differ, $$\frac{1}{5} \neq \frac{1}{4}$$. 5. **Answer for b:** False. **Final answers:** - a) False - b) False