Ratio is a comparison of two numbers or values. It is usually expressed as "A is to B" or "A:B" and indicates how many times A contains B.

From the given options, the smallest ratio is 1 : 3.

To understand this, let us consider an example. If there are 6 apples and 18 oranges, then the ratio of apples to oranges is 6 : 18 or 1 : 3.

The other ratios given in the question can be written as follows:
1. 1 : 2 = 3 : 6
2. 2 : 1 = 6 : 3
3. 3 : 1 = 9 : 3

Now, if we compare the ratios, it is clear that 1 : 3 is the smallest ratio.

To compare two ratios, we can use the following steps:
1. Convert the ratios into fractions.
2. Simplify the fractions.
3. Compare the simplified fractions.

For example, let us compare the ratios 2 : 1 and 1 : 3:
1. 2 : 1 = 2/1 and 1 : 3 = 1/3
2. 2/1 = 2 and 1/3 = 1/3
3. 2 > 1/3

Hence, 2 : 1 is greater than 1 : 3.

In conclusion, the smallest ratio out of 1 : 2, 2 : 1, 1 : 3 and 3 : 1 is 1 : 3.

If you think the solution is wrong then please provide your own solution below in the comments section .