The problem asks us to select all ratios that are equivalent to the ratio $3:12$. The options are $12:48$, $2:8$, and $5:20$.

1. Problem Description

The problem asks us to select all ratios that are equivalent to the ratio $3:12$. The options are $12:48$, $2:8$, and $5:20$.

2. Solution Steps

First, simplify the given ratio $3:12$.

Divide both sides by their greatest common divisor, which is

3. $\frac{3}{3} : \frac{12}{3} = 1:4$

So, the simplified ratio is $1:4$.

Now, check each option:

Option 1: $12:48$.

Simplify the ratio $12:48$ by dividing both sides by

1

2. $\frac{12}{12} : \frac{48}{12} = 1:4$

Therefore, $12:48$ is equivalent to $1:4$.

Option 2: $2:8$.

Simplify the ratio $2:8$ by dividing both sides by

2. $\frac{2}{2} : \frac{8}{2} = 1:4$

Therefore, $2:8$ is equivalent to $1:4$.

Option 3: $5:20$.

Simplify the ratio $5:20$ by dividing both sides by

5. $\frac{5}{5} : \frac{20}{5} = 1:4$

Therefore, $5:20$ is equivalent to $1:4$.

3. Final Answer

All three ratios, $12:48$, $2:8$, and $5:20$, are equivalent to $3:12$.