6. Выполните действия: 1) 6 + \frac{5}{13}; 3) 6 \frac{4}{9} + 5 \frac{2}{9}; 5) 8 \frac{7}{18} + 7 \frac{5}{18} - 4 \frac{11}{18}; 2) \frac{6}{57} + 4; 4) 11 \frac{8}{11} - 3 \frac{5}{11}; 6) 13 \frac{6}{10} - 5 \frac{3}{10} + 16 \frac{1}{10}.

1) $$6 + \frac{5}{13} = 6 \frac{5}{13}$$

3) $$6 \frac{4}{9} + 5 \frac{2}{9} = (6 + 5) + (\frac{4}{9} + \frac{2}{9}) = 11 + \frac{6}{9} = 11 + \frac{2}{3} = 11 \frac{2}{3}$$

5) $$8 \frac{7}{18} + 7 \frac{5}{18} - 4 \frac{11}{18} = (8 + 7 - 4) + (\frac{7}{18} + \frac{5}{18} - \frac{11}{18}) = 11 + \frac{1}{18} = 11 \frac{1}{18}$$

2) $$\frac{6}{57} + 4 = 4 \frac{6}{57} = 4 \frac{2}{19}$$

4) $$11 \frac{8}{11} - 3 \frac{5}{11} = (11 - 3) + (\frac{8}{11} - \frac{5}{11}) = 8 + \frac{3}{11} = 8 \frac{3}{11}$$

6) $$13 \frac{6}{10} - 5 \frac{3}{10} + 16 \frac{1}{10} = (13 - 5 + 16) + (\frac{6}{10} - \frac{3}{10} + \frac{1}{10}) = 24 + \frac{4}{10} = 24 + \frac{2}{5} = 24 \frac{2}{5}$$

Ответ: 1) 6 \frac{5}{13}; 3) 11 \frac{2}{3}; 5) 11 \frac{1}{18}; 2) 4 \frac{2}{19}; 4) 8 \frac{3}{11}; 6) 24 \frac{2}{5}.