The problem asks to identify which of the given ratios are equivalent to the ratio $12:32$. The given ratios are $3:8$, $6:16$, $32:12$, $13:33$, and $14:34$.

1. Problem Description

The problem asks to identify which of the given ratios are equivalent to the ratio $12:32$. The given ratios are $3:8$, $6:16$, $32:12$, $13:33$, and $14:34$.

2. Solution Steps

First, simplify the ratio $12:32$ by dividing both numbers by their greatest common divisor, which is

4. $$12:32 = \frac{12}{4} : \frac{32}{4} = 3:8$$

Now, we need to check which of the given ratios are equivalent to $3:8$.

* $3:8$ - This is already in the simplified form and is equivalent to $3:8$.

* $6:16$ - Simplify this ratio by dividing both numbers by their greatest common divisor, which is

2. $6:16 = \frac{6}{2} : \frac{16}{2} = 3:8$. This ratio is equivalent to $3:8$.

* $32:12$ - This is the reverse of the original ratio, and simplifying it gives us:

$32:12 = \frac{32}{4} : \frac{12}{4} = 8:3$. This is not equivalent to $3:8$.

* $13:33$ - This ratio cannot be simplified further, and it is not equivalent to $3:8$.

* $14:34$ - Simplify this ratio by dividing both numbers by their greatest common divisor, which is

2. $14:34 = \frac{14}{2} : \frac{34}{2} = 7:17$. This is not equivalent to $3:8$.

Therefore, the ratios equivalent to $12:32$ (or $3:8$) are $3:8$ and $6:16$.

3. Final Answer

The ratios equivalent to $12:32$ are $3:8$ and $6:16$.