Решение:

1. $$6\frac{5}{13} + 2\frac{8}{13} = (6 + 2) + (\frac{5}{13} + \frac{8}{13}) = 8 + \frac{13}{13} = 8 + 1 = 9$$

   Ответ: 9

2. $$5\frac{4}{7} + 3\frac{6}{7} = (5 + 3) + (\frac{4}{7} + \frac{6}{7}) = 8 + \frac{10}{7} = 8 + 1\frac{3}{7} = 9\frac{3}{7}$$

   Ответ: $$9\frac{3}{7}$$

3. $$1 - \frac{15}{19} = \frac{19}{19} - \frac{15}{19} = \frac{4}{19}$$

   Ответ: $$\frac{4}{19}$$

4. $$8 - 3\frac{4}{9} = 7\frac{9}{9} - 3\frac{4}{9} = (7 - 3) + (\frac{9}{9} - \frac{4}{9}) = 4 + \frac{5}{9} = 4\frac{5}{9}$$

   Ответ: $$4\frac{5}{9}$$

5. $$7\frac{3}{8} - 2\frac{5}{8} = 6\frac{11}{8} - 2\frac{5}{8} = (6 - 2) + (\frac{11}{8} - \frac{5}{8}) = 4 + \frac{6}{8} = 4\frac{3}{4}$$

   Ответ: $$4\frac{3}{4}$$

6. $$14\frac{15}{32} - 9\frac{19}{32} = 13\frac{47}{32} - 9\frac{19}{32} = (13 - 9) + (\frac{47}{32} - \frac{19}{32}) = 4 + \frac{28}{32} = 4\frac{7}{8}$$

   Ответ: $$4\frac{7}{8}$$