To solve each of these calculations:

5/9 + 1/3
First, find a common denominator for 9 and 3, which is 9. The fractions are then converted to have the common denominator. It becomes (5/9) + (3/9) = 8/9.

3 3/7 ÷ 2 2/5
First, convert the mixed numbers to improper fractions:
3 3/7 = (37 + 3)/7 = 24/7
2 2/5 = (25 + 2)/5 = 12/5
Then, divide the fractions: (24/7) ÷ (12/5) = (24/7) * (5/12) = 120/84 = 10/7 = 1 3/7

(6/25 - 1/5) 5/6
First, simplify the subtraction inside the parentheses:
(6/25 - 1/5) = (6/25) - (5/25) = 1/25
Then, multiply by 5/6: (1/25) (5/6) = 5/150 = 1/30

Therefore:

5/9 + 1/3 = 8/93 3/7 ÷ 2 2/5 = 1 3/7(6/25 - 1/5) * 5/6 = 1/30