If you convert both numbers into 6ths it is easier to work out. 1 and 1/2 is 9/6ths and 2/3rds is 4/6ths. so, 9/6ths - 4/6ths = 5/6ths.
4/6ths plus 1/2 = 9/6ths or: 1 & 1/2
4 6th of 12 is 54 divided by 12 so it will be 54 over 12
You have to find the common denominator for the fractions, so multiply the "half" (2) by the "thirds" (3). These two numbers multiplied with give 6 as a common denominator. Then multiply the 1 by the 3, which will give 3/6ths, and the 2 by the other 2, which will give 4/6ths. Hmmm! it seems that 4/6ths is greater than 3/6ths, so you have to add a whole to the 3/6ths to make a big enough fraction to subtract. Doing that will give you 9/6ths and you can subtract the 4/6ths. So the answer would be 5/6ths. Try it.
2/3rds would be 4/6ths. Therefore the answer is 5/6ths