The problem asks us to select all ratios that are equivalent to the ratio 6:33. The possible ratios are 2:11, 4:22, and 1:3.

1. Problem Description

The problem asks us to select all ratios that are equivalent to the ratio 6:

3

3. The possible ratios are 2:11, 4:22, and 1:

3.

2. Solution Steps

First, we simplify the ratio 6:33 by finding the greatest common divisor (GCD) of 6 and

3

3. The GCD of 6 and 33 is

3. We divide both numbers by 3:

$6/3 = 2$

$33/3 = 11$

So the simplified ratio is 2:

1

1.

Now we check the given ratios:

- 2:11 is the simplified form of 6:33, so it is equivalent.

- 4:22 can be simplified by dividing both numbers by 2:

$4/2 = 2$

$22/2 = 11$

So 4:22 simplifies to 2:11, which is equivalent to 6:

3

3. - 1:3 is not equal to 2:

1

1. Therefore, 1:3 is not equivalent to 6:

3

3.

3. Final Answer

The ratios equivalent to 6:33 are 2:11 and 4:

2

2.