If your teacher asks you to subtract 2/3 from 2 & 2/3 but she tells you to use the circular method, which would turn 2 & 2/3 into 7/3 should and the answer is 5/3. Then she asks you to compare, do you compare 2 & 2/3 with 2/3 or 7/3 with 2/3 ?
Note 2 + 2/3 = [3*2 + 2] / 3 = [ 6 + 2] / 3 = 8/3
So....
8/3 - 2/3 = 6/3 = 2
This makes sense....... [2 + 2/3 - 2/3] should = 2 !!!