Final answer:
The smallest ratio among the given options is 2/3. Each ratio is converted to a fraction with a common denominator for comparison, revealing that 2/3 (or 8/12) is the smallest.
Step-by-step explanation:
To determine which is the smallest ratio among the given options, first, we need to express all ratios in the same form. This can be achieved by writing them as fractions. The given ratios and their fractional equivalents are:
3 to 4 is 3/4
2/3 remains as 2/3
10:12 simplifies down to 5/6
2 to 1 is 2/1
Now we can compare these fractions to find the smallest. If we convert all the fractions so they have the same denominator, it becomes easier to compare their relative sizes:
3/4 is equivalent to 9/12
2/3 is equivalent to 8/12
5/6 is equivalent to 10/12
2/1 is equivalent to 24/12
Looking at these equivalents, 8/12 is the smallest fraction, so 2/3 is the smallest ratio among the options given.