6 1/6 - 2 1/2 is same as
6 1/6 - 2 3/6 changed to use a common denominator, is same as
5 7/6 - 2 3/6 (an un-normalized mixed number)
= 3 4/6 = 3 2/3
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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.
1 6ths of 30 is equal to 5
8 5/6 - 2 1/6 = 6 4/6 or 6 2/3
3/6 is 1/2 simplified
6