1.105. Вычислите:

Решение:

1. A) \(2\frac{3}{4} - 0,6 = 2,75 - 0,6 = 2,15\)
2. Б) \(121,2 : \frac{6}{25} = 121,2 \cdot \frac{25}{6} = 20,2 \cdot 25 = 505\)
3. B) \(5,18 \cdot \frac{5}{7} = \frac{518}{100} \cdot \frac{5}{7} = \frac{259}{50} \cdot \frac{5}{7} = \frac{259}{70} = 3,7\)
4. Г) \(0,36 + \frac{1}{2} = 0,36 + 0,5 = 0,86\)
5. Д) \(5,8 - \frac{3}{4} = 5,8 - 0,75 = 5,05\)
6. E) \(\frac{2}{5} : 0,001 = 0,4 : 0,001 = 400\)
7. Ë) \(\frac{2}{3} + 0,6 = \frac{2}{3} + \frac{3}{5} = \frac{10+9}{15} = \frac{19}{15} = 1\frac{4}{15}\)
8. Ж) \(0,75^3 = (\frac{3}{4})^3 = \frac{27}{64}\)
9. 3) \(1\frac{1}{6} - 0,5 = \frac{7}{6} - \frac{1}{2} = \frac{7-3}{6} = \frac{4}{6} = \frac{2}{3}\)
10. И) \(0,3 - \frac{5}{9} = \frac{3}{10} - \frac{5}{9} = \frac{27-50}{90} = -\frac{23}{90}\)
11. Й) \(\frac{8}{11} : 0,4 = \frac{8}{11} : \frac{2}{5} = \frac{8}{11} \cdot \frac{5}{2} = \frac{40}{22} = \frac{20}{11} = 1\frac{9}{11}\)
12. K) \(3\frac{4}{5} - 1,8 = 3,8 - 1,8 = 2\)
13. Л) \(0,84 \cdot \frac{3}{4} = \frac{84}{100} \cdot \frac{3}{4} = \frac{21}{25} \cdot \frac{3}{4} = \frac{63}{100} = 0,63\)
14. M) \(2,2 : \frac{11}{15} = \frac{22}{10} \cdot \frac{15}{11} = \frac{11}{5} \cdot \frac{15}{11} = 3\)
15. H) \(3\frac{9}{10} + 1,68 = 3,9 + 1,68 = 5,58\)
16. O) \(4,2 : 3\frac{1}{2} = 4,2 : 3,5 = \frac{42}{10} : \frac{35}{10} = \frac{42}{35} = \frac{6}{5} = 1,2\)
17. П) \(1\frac{1}{5} - 20,08 = 1,2 - 20,08 = -18,88\)
18. P) \(5,384 - \frac{4}{20} = 5,384 - 0,2 = 5,184\)
19. C) \(1\frac{2}{3} + 2,5 = \frac{5}{3} + 2,5 = \frac{5}{3} + \frac{5}{2} = \frac{10+15}{6} = \frac{25}{6} = 4\frac{1}{6}\)
20. T) \(7\frac{3}{8} - 2,35 = 7,375 - 2,35 = 5,025\)
21. У) \(5,7 : 6\frac{1}{3} = 5,7 : \frac{19}{3} = \frac{57}{10} \cdot \frac{3}{19} = \frac{3}{10} \cdot 3 = \frac{9}{10} = 0,9\)
22. Ф) \(42,14 - 1\frac{7}{10} = 42,14 - 1,7 = 40,44\)
23. X) \(1\frac{1}{5} + 3,2 = 1,2 + 3,2 = 4,4\)
24. Ц) \(3,6 : \frac{2}{9} = \frac{36}{10} \cdot \frac{9}{2} = \frac{18}{5} \cdot 9 = \frac{162}{5} = 32,4\)
25. Ч) \(7\frac{3}{5} - 3,059 = 7,6 - 3,059 = 4,541\)
26. Ш) \(\frac{1}{8} : 12,5 = 0,125 : 12,5 = 0,01\)
27. Щ) \(2\frac{3}{11} - 0,22 = \frac{25}{11} - \frac{22}{100} = \frac{25}{11} - \frac{11}{50} = \frac{1250 - 121}{550} = \frac{1129}{550} \approx 2,05\)
28. Ъ) \(2,5 + 8\frac{4}{11} = 2,5 + \frac{92}{11} = \frac{5}{2} + \frac{92}{11} = \frac{55 + 184}{22} = \frac{239}{22} = 10\frac{19}{22}\)
29. Ы) \(9\frac{7}{11} : 1,06 = \frac{106}{11} : \frac{106}{100} = \frac{106}{11} \cdot \frac{100}{106} = \frac{100}{11} = 9\frac{1}{11}\)
30. Ь) \(8,02 - 3\frac{1}{3} = 8,02 - \frac{10}{3} = \frac{802}{100} - \frac{10}{3} = \frac{401}{50} - \frac{10}{3} = \frac{1203 - 500}{150} = \frac{703}{150} = 4\frac{103}{150}\)

Ответ: приведены результаты вычислений для каждого пункта.