To solve these calculations, we will need to find a common denominator for each pair of fractions, perform the operation, and simplify the result.

2/9 + 7/18:
Common denominator = 18
(4/18) + (7/18) = 11/18

5/18 - 1/3:
Common denominator = 18
(5/18) - (6/18) = -1/18

17/18 - 5/9:
Common denominator = 18
(17/18) - (10/18) = 7/18

Therefore, the results are:

2/9 + 7/18 = 11/185/18 - 1/3 = -1/1817/18 - 5/9 = 7/18