1. The problem asks us to find which ratios are equivalent to $3:9$. 2. Two ratios $a:b$ and $c:d$ are equivalent if $\frac{a}{b} = \frac{c}{d}$. 3. Simplify the ratio $3:9$ by dividing both terms by their greatest common divisor, which is 3: $$\frac{3}{9} = \frac{\cancel{3}^1}{\cancel{9}^3} = \frac{1}{3}$$ 4. Check each given ratio by simplifying and comparing to $\frac{1}{3}$: - $1:7 \Rightarrow \frac{1}{7}$ (not equal to $\frac{1}{3}$) - $1:3 \Rightarrow \frac{1}{3}$ (equal) - $12:36 \Rightarrow \frac{12}{36} = \frac{\cancel{12}^1}{\cancel{36}^3} = \frac{1}{3}$ (equal) - $6:18 \Rightarrow \frac{6}{18} = \frac{\cancel{6}^1}{\cancel{18}^3} = \frac{1}{3}$ (equal) - $27:9 \Rightarrow \frac{27}{9} = \frac{\cancel{27}^3}{\cancel{9}^1} = 3$ (not equal) 5. Therefore, the ratios equivalent to $3:9$ are $1:3$, $12:36$, and $6:18$.