1 Вычислите: 1)7\frac{14}{15}+2\frac{1}{15}; 2)9\frac{24}{27}+12\frac{13}{27}; 3) 1-\frac{12}{19}; 4)8-3\frac{6}{15}; 5) 12-11\frac{6}{11}; 6) 16\frac{3}{13}-6\frac{8}{13}; 7) 13\frac{4}{9}-2\frac{8}{9}; 8) 10\frac{7}{16}-4\frac{12}{16}; 9) 29\frac{49}{53}-8\frac{49}{53}; 10) (20\frac{16}{25}+13\frac{9}{25})-(23\frac{4}{14}+7\frac{13}{14}).

Решение:

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

Ответ: 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) 3\frac{11}{14}.