To simplify these addition problems, we need to find a common denominator.

1) 5/9 + 2/3
Common denominator is 9.
(5/9) + (6/9) = 11/9

2) 1/12 + 3/4
Common denominator is 12.
(1/12) + (9/12) = 10/12 = 5/6

3) 1/2 + 3/8
Common denominator is 8.
(4/8) + (3/8) = 7/8

4) 17/1000 + 81/100
Common denominator is 1000.
(17/1000) + (810/1000) = 827/1000

Therefore,
5/9 + 2/3 = 11/9
1/12 + 3/4 = 5/6
1/2 + 3/8 = 7/8
17/1000 + 81/100 = 827/1000