To solve the expression 11/3 times 4/3 plus 5/9, we follow the order of operations (multiplication before addition).

Step 1: Multiply 11/3 by 4/3

(11/3) * (4/3) = (11 * 4) / (3 * 3) = 44/9

Step 2: Add 5/9 to the result

44/9 + 5/9 = (44 + 5) / 9 = 49/9

Therefore, 11/3 times 4/3 plus 5/9 is 49/9.