Here is a quick way of subtracting this fraction and finding the correct answer.
You see 1/2 well you know in order to subtract this fraction there has to be a common denominator. Now with that what is the lowest common multiple between 2 and 3. It is 6. So 1/2 of 6 is 3/6. 1/3 of 6 is 2/6. Now you can do the subtracting.
