4. Найдите значение выражения: 1) 4 1/7 × 14 - 2 1/4 × 3/8 - 1 1/9 × 3/8; 2) 1 31/32 × 3 1/5 - (8 5/9 + 6/35 + 2 2/15) × 5/12; 3) (4 5/12 - 3 13/24) : (1 1/4 + 5/6 - 5/7); 4) (2,06 : 1/60 - 14,84 : 7/60) - 0,084 × 1/12; 5) (-2,3 - 3,91 : (-2,3)) : (-0,01) × (-0,7); 6) (-11/18 + 29/45) : (19/27 - 35/54).

1. Решение:

1. \[ 4\frac{1}{7} \times 14 - 2\frac{1}{4} \times \frac{3}{8} - 1\frac{1}{9} \times \frac{3}{8} = \frac{29}{7} \times 14 - \frac{9}{4} \times \frac{3}{8} - \frac{10}{9} \times \frac{3}{8} \]
2. \[ = 29 \times 2 - \frac{27}{32} - \frac{10}{9} \times \frac{3}{8} = 58 - \frac{27}{32} - \frac{10}{24} = 58 - \frac{27}{32} - \frac{5}{12} \]
3. \[ = 58 - (\frac{27 \times 3}{32 \times 3} + \frac{5 \times 8}{12 \times 8}) = 58 - (\frac{81}{96} + \frac{40}{96}) = 58 - \frac{121}{96} \]
4. \[ = \frac{58 \times 96}{96} - \frac{121}{96} = \frac{5568 - 121}{96} = \frac{5447}{96} \]
5. Ответ: 5447⁄₉₆
6. 2. Решение:
7. \[ 1\frac{31}{32} \times 3\frac{1}{5} - \left(8\frac{5}{9} + \frac{6}{35} + 2\frac{2}{15}\right) \times \frac{5}{12} \]
8. \[ = \frac{63}{32} \times \frac{16}{5} - \left(\frac{77}{9} + \frac{6}{35} + \frac{32}{15}\right) \times \frac{5}{12} \]
9. \[ = \frac{63}{2 \times 5} - \left(\frac{77 \times 35 + 6 \times 9 + 32 \times 7}{315}\right) \times \frac{5}{12} \]
10. \[ = \frac{63}{10} - \left(\frac{2695 + 54 + 224}{315}\right) \times \frac{5}{12} = \frac{63}{10} - \frac{2973}{315} \times \frac{5}{12} \]
11. \[ = \frac{63}{10} - \frac{2973 \times 5}{315 \times 12} = \frac{63}{10} - \frac{14865}{3780} = \frac{63}{10} - \frac{329}{84} \]
12. \[ = \frac{63 \times 84 - 329 \times 10}{840} = \frac{5292 - 3290}{840} = \frac{2002}{840} = \frac{1001}{420} \]
13. Ответ: 1001⁄₄₂₀
14. 3. Решение:
15. \[ \left(4\frac{5}{12} - 3\frac{13}{24}\right) : \left(1\frac{1}{4} + \frac{5}{6} - \frac{5}{7}\right) \]
16. \[ = \left(\frac{53}{12} - \frac{85}{24}\right) : \left(\frac{5}{4} + \frac{5}{6} - \frac{5}{7}\right) \]
17. \[ = \left(\frac{106}{24} - \frac{85}{24}\right) : \left(\frac{5 \times 21 + 5 \times 14 - 5 \times 12}{84}\right) \]
18. \[ = \frac{21}{24} : \left(\frac{105 + 70 - 60}{84}\right) = \frac{7}{8} : \frac{115}{84} \]
19. \[ = \frac{7}{8} \times \frac{84}{115} = \frac{7 \times 21}{2 \times 115} = \frac{147}{230} \]
20. Ответ: 147⁄23⁃
21. 4. Решение:
22. \[ (2.06 : \frac{1}{60} - 14.84 : \frac{7}{60}) - 0.084 \times \frac{1}{12} \]
23. \[ = (2.06 \times 60 - 14.84 \times \frac{60}{7}) - 0.007 \]
24. \[ = (123.6 - \frac{890.4}{7}) - 0.007 \]
25. \[ = (123.6 - 127.2) - 0.007 \]
26. \[ = -3.6 - 0.007 = -3.607 \]
27. Ответ: -3.607
28. 5. Решение:
29. \[ (-2.3 - 3.91 : (-2.3)) : (-0.01) \times (-0.7) \]
30. \[ = (-2.3 - (-1.7)) : (-0.01) \times (-0.7) \]
31. \[ = (-2.3 + 1.7) : (-0.01) \times (-0.7) \]
32. \[ = (-0.6) : (-0.01) \times (-0.7) \]
33. \[ = 60 \times (-0.7) = -42 \]
34. Ответ: -42
35. 6. Решение:
36. \[ \left(-\frac{11}{18} + \frac{29}{45}\right) : \left(\frac{19}{27} - \frac{35}{54}\right) \]
37. \[ = \left(-\frac{11 \times 5}{18 \times 5} + \frac{29 \times 2}{45 \times 2}\right) : \left(\frac{19 \times 2}{27 \times 2} - \frac{35}{54}\right) \]
38. \[ = \left(-\frac{55}{90} + \frac{58}{90}\right) : \left(\frac{38}{54} - \frac{35}{54}\right) \]
39. \[ = \frac{3}{90} : \frac{3}{54} = \frac{1}{30} : \frac{3}{54} \]
40. \[ = \frac{1}{30} \times \frac{54}{3} = \frac{1}{30} \times 18 = \frac{18}{30} = \frac{3}{5} \]
41. Ответ: 3⁄₅