By creating a common denominator, you can compare different numbers to the same ratio. For example:
Take 2/3 and 3/4
Now 3/4 is the same as 9/12
And 2/3 is the same as 8/12
Now that they have the same denominator, you can tell that 9/12 is clearly greater than 8/12, meaning 3/4 is greater than 2/3.