The problem asks to select the ratios that are equivalent to the ratio 12:3. The options are 4:1, 18:5, and 16:4.

1. Problem Description

The problem asks to select the ratios that are equivalent to the ratio 12:

3. The options are 4:1, 18:5, and 16:

4.

2. Solution Steps

First, we can simplify the ratio 12:3 by dividing both sides by their greatest common divisor, which is

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

Therefore, the simplified ratio is 4:

1. Now, we need to check which of the given ratios are equivalent to 4:

1. Ratio 1: 4:

1. This is the same as the simplified ratio, so it is equivalent.

Ratio 2: 18:

5. To check if this is equivalent, we would need to have $\frac{18}{5} = \frac{4}{1}$. This simplifies to $18 = 4 \times 5 = 20$, which is false. Therefore, 18:5 is not equivalent to 12:

3. Ratio 3: 16:

4. We can simplify this ratio by dividing both sides by their greatest common divisor, which is

4. $\frac{16}{4} = \frac{16 \div 4}{4 \div 4} = \frac{4}{1}$

Therefore, the simplified ratio is 4:1, which is equivalent to 12:

3.

3. Final Answer

The ratios equivalent to 12:3 are 4:1 and 16:4.