Решение:

1. $$6\frac{5}{13}+2\frac{8}{13} = (6 + 2) + (\frac{5}{13} + \frac{8}{13}) = 8 + \frac{13}{13} = 8 + 1 = 9$$
2. $$5\frac{4}{7}+3\frac{6}{7} = (5 + 3) + (\frac{4}{7} + \frac{6}{7}) = 8 + \frac{10}{7} = 8 + 1\frac{3}{7} = 9\frac{3}{7}$$
3. $$1-\frac{15}{19} = \frac{19}{19} - \frac{15}{19} = \frac{19-15}{19} = \frac{4}{19}$$
4. $$8-3\frac{4}{9} = 8 - \frac{3 \cdot 9 + 4}{9} = 8 - \frac{27 + 4}{9} = 8 - \frac{31}{9} = \frac{8 \cdot 9}{9} - \frac{31}{9} = \frac{72 - 31}{9} = \frac{41}{9} = 4\frac{5}{9}$$
5. $$7\frac{3}{8}-2\frac{5}{8} = \frac{7 \cdot 8 + 3}{8} - \frac{2 \cdot 8 + 5}{8} = \frac{56 + 3}{8} - \frac{16 + 5}{8} = \frac{59}{8} - \frac{21}{8} = \frac{59 - 21}{8} = \frac{38}{8} = \frac{19}{4} = 4\frac{3}{4}$$
6. $$14\frac{15}{32}-9\frac{19}{32} = \frac{14 \cdot 32 + 15}{32} - \frac{9 \cdot 32 + 19}{32} = \frac{448 + 15}{32} - \frac{288 + 19}{32} = \frac{463}{32} - \frac{307}{32} = \frac{463 - 307}{32} = \frac{156}{32} = \frac{39}{8} = 4\frac{7}{8}$$

Ответы:

1. $$9$$
2. $$9\frac{3}{7}$$
3. $$\frac{4}{19}$$
4. $$4\frac{5}{9}$$
5. $$4\frac{3}{4}$$
6. $$4\frac{7}{8}$$