1) \(\frac{11}{15} - \frac{4}{10} + \frac{1}{45}\) 2) \(4 - 4\frac{5}{9}\) 3) \(4\frac{3}{10} + 1\frac{5}{12}\) 4) \(6\frac{15}{21} + 2\frac{9}{14}\) 5) \(5\frac{1}{6} - 3\frac{3}{4}\)

Решим примеры:

1. \(\frac{11}{15} - \frac{4}{10} + \frac{1}{45}\)
2. Приведем дроби к общему знаменателю. Наименьший общий знаменатель для 15, 10 и 45 будет 90.
3. \(\frac{11}{15} = \frac{11 \cdot 6}{15 \cdot 6} = \frac{66}{90}\)
4. \(\frac{4}{10} = \frac{4 \cdot 9}{10 \cdot 9} = \frac{36}{90}\)
5. \(\frac{1}{45} = \frac{1 \cdot 2}{45 \cdot 2} = \frac{2}{90}\)
6. \(\frac{66}{90} - \frac{36}{90} + \frac{2}{90} = \frac{66 - 36 + 2}{90} = \frac{32}{90} = \frac{16}{45}\)
7. \(4 - 4\frac{5}{9}\)
8. \(4 - 4\frac{5}{9} = 4 - \frac{4 \cdot 9 + 5}{9} = 4 - \frac{36 + 5}{9} = 4 - \frac{41}{9} = \frac{4 \cdot 9}{9} - \frac{41}{9} = \frac{36}{9} - \frac{41}{9} = \frac{36 - 41}{9} = \frac{-5}{9} = -\frac{5}{9}\)
9. \(4\frac{3}{10} + 1\frac{5}{12}\)
10. \(4\frac{3}{10} = \frac{4 \cdot 10 + 3}{10} = \frac{40 + 3}{10} = \frac{43}{10}\)
11. \(1\frac{5}{12} = \frac{1 \cdot 12 + 5}{12} = \frac{12 + 5}{12} = \frac{17}{12}\)
12. Приведем к общему знаменателю 60.
13. \(\frac{43}{10} = \frac{43 \cdot 6}{10 \cdot 6} = \frac{258}{60}\)
14. \(\frac{17}{12} = \frac{17 \cdot 5}{12 \cdot 5} = \frac{85}{60}\)
15. \(\frac{258}{60} + \frac{85}{60} = \frac{258 + 85}{60} = \frac{343}{60} = 5\frac{43}{60}\)
16. \(6\frac{15}{21} + 2\frac{9}{14}\)
17. \(6\frac{15}{21} = 6\frac{5}{7} = \frac{6 \cdot 7 + 5}{7} = \frac{42 + 5}{7} = \frac{47}{7}\)
18. \(2\frac{9}{14} = \frac{2 \cdot 14 + 9}{14} = \frac{28 + 9}{14} = \frac{37}{14}\)
19. Приведем к общему знаменателю 14.
20. \(\frac{47}{7} = \frac{47 \cdot 2}{7 \cdot 2} = \frac{94}{14}\)
21. \(\frac{94}{14} + \frac{37}{14} = \frac{94 + 37}{14} = \frac{131}{14} = 9\frac{5}{14}\)
22. \(5\frac{1}{6} - 3\frac{3}{4}\)
23. \(5\frac{1}{6} = \frac{5 \cdot 6 + 1}{6} = \frac{30 + 1}{6} = \frac{31}{6}\)
24. \(3\frac{3}{4} = \frac{3 \cdot 4 + 3}{4} = \frac{12 + 3}{4} = \frac{15}{4}\)
25. Приведем к общему знаменателю 12.
26. \(\frac{31}{6} = \frac{31 \cdot 2}{6 \cdot 2} = \frac{62}{12}\)
27. \(\frac{15}{4} = \frac{15 \cdot 3}{4 \cdot 3} = \frac{45}{12}\)
28. \(\frac{62}{12} - \frac{45}{12} = \frac{62 - 45}{12} = \frac{17}{12} = 1\frac{5}{12}\)

Ответ: 1) \(\frac{16}{45}\); 2) \(-\frac{5}{9}\); 3) \(5\frac{43}{60}\); 4) \(9\frac{5}{14}\); 5) \(1\frac{5}{12}\)