The problem asks to choose all the ratios from the given list that are equivalent to the ratio $8:1$. The list of ratios is: $32:4$, $6:48$, $48:6$, $24:3$, and $16:2$.

1. Problem Description

The problem asks to choose all the ratios from the given list that are equivalent to the ratio $8:1$. The list of ratios is: $32:4$, $6:48$, $48:6$, $24:3$, and $16:2$.

2. Solution Steps

A ratio $a:b$ is equivalent to $8:1$ if $\frac{a}{b} = \frac{8}{1} = 8$.

We need to check each ratio in the list to see if it simplifies to

8.

* $32:4$ can be written as $\frac{32}{4}$. Since $32 = 8 \times 4$, we have $\frac{32}{4} = 8$. Therefore, $32:4$ is equivalent to $8:1$.

* $6:48$ can be written as $\frac{6}{48}$. Since $48 = 8 \times 6$, we have $\frac{6}{48} = \frac{1}{8}$. Therefore, $6:48$ is not equivalent to $8:1$.

* $48:6$ can be written as $\frac{48}{6}$. Since $48 = 8 \times 6$, we have $\frac{48}{6} = 8$. Therefore, $48:6$ is equivalent to $8:1$.

* $24:3$ can be written as $\frac{24}{3}$. Since $24 = 8 \times 3$, we have $\frac{24}{3} = 8$. Therefore, $24:3$ is equivalent to $8:1$.

* $16:2$ can be written as $\frac{16}{2}$. Since $16 = 8 \times 2$, we have $\frac{16}{2} = 8$. Therefore, $16:2$ is equivalent to $8:1$.

3. Final Answer

The ratios equivalent to $8:1$ are $32:4$, $48:6$, $24:3$, and $16:2$.