To find the sum of 1 1/3 and 2 2/9, we need to convert both fractions to have the same denominator. The least common multiple of 3 and 9 is 9. So, we convert 1 1/3 to 3/3 + 1/3 = 4/3, and 2 2/9 to 18/9 + 2/9 = 20/9. Now, we can add the fractions: 4/3 + 20/9 = (4*3)/(3*3) + 20/9 = 12/9 + 20/9 = 32/9. We can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 1. Therefore, the simplified answer is 32/9. In mixed fraction form, this is 3 5/9.