Obviously 1/2 = 0.5 and 1/3 = 0.33 , so what we need to know is which is bigger , 0.5 or 0.33 ,in this case most would think that 0.33 is bigger than 0.5 because its 5 and 33.
Example : if you imaged having apples , wouldn't you want 1 apple out of 2 instead of 1 apple out of 3? yes.We just converted the fractions from 1/2 to 0.5 and 1/3 to 0.33.
Now why would 0.5 also known as 1/2 be greater than 0.33 also known as 1/3, is it because its closer to an whole number? or is 0.33 greater because 33 is simply bigger than 5. Yeah that's what most people think , and that's where they go wrong.
If you look back at the apple example you will have your answer.
now that you looked back at it this means the answer is yes 1/2 is greater than 1/3