To solve each of these addition problems, we must find a common denominator and then add the fractions together.

17/75 + 2/25
Common denominator: 75
(17/75) 1 = 17/75
(2/25) 3 = 6/75
Adding both fractions together: 17/75 + 6/75 = 23/75

14/15 + 3/2 + 16/15 + 1/2
Common denominator: 30
(14/15) 2 = 28/30
(3/2) 15 = 45/30
(16/15) 2 = 32/30
(1/2) 15 = 15/30
Adding all fractions together: 28/30 + 45/30 + 32/30 + 15/30 = 120/30 = 4

Therefore:
17/75 + 2/25 = 23/75
14/15 + 3/2 + 16/15 + 1/2 = 4