Решение:

1) $$4\frac{3}{5}+2\frac{4}{5}= (4+2) + (\frac{3}{5} + \frac{4}{5}) = 6 + \frac{7}{5} = 6 + 1\frac{2}{5} = 7\frac{2}{5}$$

Ответ: $$7\frac{2}{5}$$

2) $$7\frac{7}{12}-3\frac{5}{12}= (7-3) + (\frac{7}{12} - \frac{5}{12}) = 4 + \frac{2}{12} = 4 + \frac{1}{6} = 4\frac{1}{6}$$

Ответ: $$4\frac{1}{6}$$

3) $$5\frac{1}{6}+3\frac{2}{9} = 5\frac{3}{18}+3\frac{4}{18}= (5+3) + (\frac{3}{18} + \frac{4}{18}) = 8 + \frac{7}{18} = 8\frac{7}{18}$$

Ответ: $$8\frac{7}{18}$$