lets operate is separate parts, the whole parts and the fractions:
9 1/6 - 3 5/8
= (9 - 3) + (1/6 - 5/8)
so now we have separated the operations, but now we need to get the fractions to the same denominator using the minimum common multiple of 6 and 8, which is 48 so we convert those fractions to be divided by 48:
1/6 = (8/8)(1/6) = (8*1)/(8*6) = 8/48
5/8 = (6/6)/(5/8) = (6*5)/(6*8) = 30/48
Lets substitute those fractions and subtract:
= (9 - 3) + (1/6 - 5/8)
= (9 - 3) + (8/48 - 30/48)
= (6) + (-22/48)
We have a negative fraction and have to subtract it from the whole part, we can convert the whole part to be divided by 48 as well, so the subtraction is easy:
6 = (48/48)(6) = (48*6)/(48) = 288/48
susbstitute:
= (6) + (-22/48)
= (288/48) + (-22/48)
= 288/48 - 22/48
= 266/48
= 5 26/48
= 5 13/24