Вычисление выражений:

1. $$7\frac{14}{15}+2\frac{1}{15} = (7+2) + (\frac{14}{15} + \frac{1}{15}) = 9 + \frac{15}{15} = 9+1 = 10$$
2. $$9\frac{24}{27}+12\frac{13}{27} = (9+12) + (\frac{24}{27} + \frac{13}{27}) = 21 + \frac{37}{27} = 21 + 1\frac{10}{27} = 22\frac{10}{27}$$
3. $$1-\frac{12}{19} = \frac{19}{19} - \frac{12}{19} = \frac{7}{19}$$
4. $$8-3\frac{6}{15} = 8 - 3\frac{2}{5} = 7\frac{5}{5} - 3\frac{2}{5} = (7-3) + (\frac{5}{5} - \frac{2}{5}) = 4\frac{3}{5}$$
5. $$12-11\frac{6}{11} = 12 - 11\frac{6}{11} = 11\frac{11}{11} - 11\frac{6}{11} = (11-11) + (\frac{11}{11} - \frac{6}{11}) = 0 + \frac{5}{11} = \frac{5}{11}$$
6. $$16\frac{3}{13}-6\frac{8}{13} = 15\frac{16}{13} - 6\frac{8}{13} = (15-6) + (\frac{16}{13} - \frac{8}{13}) = 9 + \frac{8}{13} = 9\frac{8}{13}$$
7. $$13\frac{4}{9}-2\frac{8}{9} = 12\frac{13}{9} - 2\frac{8}{9} = (12-2) + (\frac{13}{9} - \frac{8}{9}) = 10 + \frac{5}{9} = 10\frac{5}{9}$$
8. $$10\frac{7}{16}-4\frac{12}{16} = 9\frac{23}{16} - 4\frac{12}{16} = (9-4) + (\frac{23}{16} - \frac{12}{16}) = 5 + \frac{11}{16} = 5\frac{11}{16}$$
9. $$29\frac{49}{53}-8\frac{49}{53} = (29-8) + (\frac{49}{53} - \frac{49}{53}) = 21 + 0 = 21$$
10. $$\left(20\frac{16}{25}+13\frac{9}{25}\right)-\left(23\frac{4}{14}+7\frac{13}{14}\right) = (20+13) + (\frac{16}{25}+\frac{9}{25}) - \left((23+7) + (\frac{4}{14}+\frac{13}{14})\right) = 33 + \frac{25}{25} - \left(30 + \frac{17}{14}\right) = 33+1 - (30 + 1\frac{3}{14}) = 34 - 31\frac{3}{14} = 33\frac{14}{14} - 31\frac{3}{14} = (33-31) + (\frac{14}{14} - \frac{3}{14}) = 2 + \frac{11}{14} = 2\frac{11}{14}$$

Ответы:

1. 10
2. $$22\frac{10}{27}$$
3. $$\frac{7}{19}$$
4. $$4\frac{3}{5}$$
5. $$\frac{5}{11}$$
6. $$9\frac{8}{13}$$
7. $$10\frac{5}{9}$$
8. $$5\frac{11}{16}$$
9. 21
10. $$2\frac{11}{14}$$