1. **State the problem:** We need to find which ratios are equivalent to $1:4$. 2. **Recall the rule for equivalent ratios:** Two ratios $a:b$ and $c:d$ are equivalent if $\frac{a}{b} = \frac{c}{d}$. 3. **Check each ratio:** - For $6:24$, calculate $\frac{6}{24} = \frac{6 \div 6}{24 \div 6} = \frac{1}{4}$, so $6:24$ is equivalent to $1:4$. - For $3:12$, calculate $\frac{3}{12} = \frac{3 \div 3}{12 \div 3} = \frac{1}{4}$, so $3:12$ is equivalent to $1:4$. - For $24:6$, calculate $\frac{24}{6} = 4$, which is not equal to $\frac{1}{4}$, so $24:6$ is not equivalent. - For $4:16$, calculate $\frac{4}{16} = \frac{4 \div 4}{16 \div 4} = \frac{1}{4}$, so $4:16$ is equivalent. - For $2:8$, calculate $\frac{2}{8} = \frac{2 \div 2}{8 \div 2} = \frac{1}{4}$, so $2:8$ is equivalent. 4. **Final answer:** The ratios equivalent to $1:4$ are $6:24$, $3:12$, $4:16$, and $2:8$.