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Ответ:
2. Вычислите:
- A) \( 3\frac{19}{24} + 5\frac{1}{9} + 1\frac{5}{24} \) = \( (3+5+1) + (\frac{19}{24} + \frac{5}{24}) + \frac{1}{9} \) = \( 9 + \frac{24}{24} + \frac{1}{9} \) = \( 9 + 1 + \frac{1}{9} = 10\frac{1}{9} \)
- Б) \( 1\frac{5}{8} + 4\frac{8}{17} + 2\frac{3}{8} \) = \( (1+4+2) + (\frac{5}{8} + \frac{3}{8}) + \frac{8}{17} \) = \( 7 + \frac{8}{8} + \frac{8}{17} \) = \( 7 + 1 + \frac{8}{17} = 8\frac{8}{17} \)
- В) \( 5\frac{16}{39} + 1\frac{6}{11} - 2\frac{16}{39} \) = \( (5-2) + (\frac{16}{39} - \frac{16}{39}) + \frac{6}{11} \) = \( 3 + 0 + \frac{6}{11} = 3\frac{6}{11} \)
- Г) \( 2\frac{9}{49} + 7\frac{3}{85} + 3\frac{40}{49} \) = \( (2+7+3) + (\frac{9}{49} + \frac{40}{49}) + \frac{3}{85} \) = \( 12 + \frac{49}{49} + \frac{3}{85} \) = \( 12 + 1 + \frac{3}{85} = 13\frac{3}{85} \)
- Д) \( 7\frac{13}{14} - 4\frac{17}{25} - 2\frac{13}{14} \) = \( (7-4-2) + (\frac{13}{14} - \frac{13}{14}) - \frac{17}{25} \) = \( 1 + 0 - \frac{17}{25} = \frac{25}{25} - \frac{17}{25} = \frac{8}{25} \)
- Е) \( 5\frac{16}{39} + 1\frac{6}{11} - 2\frac{16}{39} \) = \( (5-2) + (\frac{16}{39} - \frac{16}{39}) + \frac{6}{11} \) = \( 3 + 0 + \frac{6}{11} = 3\frac{6}{11} \)
- Ж) \( 4\frac{7}{45} + 11\frac{4}{13} + 8\frac{5}{26} \) = \( 4\frac{7}{45} + 11\frac{4}{13} + 8\frac{5}{26} \) = \( \frac{187}{45} + \frac{147}{13} + \frac{213}{26} \). Найдем общий знаменатель для 45, 13, 26. \( 45 = 3^2 \times 5 \), \( 13 = 13 \), \( 26 = 2 \times 13 \). НОК = \( 2 \times 3^2 \times 5 \times 13 = 1170 \). = \( \frac{187 \times 26}{1170} + \frac{147 \times 90}{1170} + \frac{213 \times 45}{1170} \) = \( \frac{4862 + 13230 + 9585}{1170} = \frac{27677}{1170} \) = \( 23\frac{777}{1170} \) = \( 23\frac{259}{390} \)
- З) \( 8\frac{7}{60} + 1\frac{3}{50} + 2 + 4\frac{4}{25} + 7\frac{7}{12} + 2\frac{2}{15} + 4\frac{11}{100} \) = \( (8+1+2+4+7+2+4) + (\frac{7}{60} + \frac{3}{50} + \frac{4}{25} + \frac{7}{12} + \frac{2}{15} + \frac{11}{100}) \) = \( 28 + \frac{7}{60} + \frac{3}{50} + \frac{8}{50} + \frac{7}{12} + \frac{2}{15} + \frac{11}{100} \) = \( 28 + \frac{7}{60} + \frac{11}{50} + \frac{7}{12} + \frac{2}{15} + \frac{11}{100} \). НОК для 60, 50, 12, 15, 100 = 300. \( 28 + \frac{35}{300} + \frac{66}{300} + \frac{175}{300} + \frac{40}{300} + \frac{33}{300} \) = \( 28 + \frac{349}{300} = 28 + 1\frac{49}{300} = 29\frac{49}{300} \)
- И) \( 4\frac{1}{7} + 5\frac{4}{9} + 12\frac{6}{7} + 3\frac{5}{11} + 10\frac{5}{9} + 11\frac{6}{11} + 4\frac{4}{7} \) = \( (4+12+10+11) + (\frac{1}{7} + \frac{6}{7} + \frac{4}{7}) + (\frac{4}{9} + \frac{5}{9}) + (\frac{5}{11} + \frac{6}{11}) \) = \( 37 + \frac{11}{7} + \frac{9}{9} + \frac{11}{11} \) = \( 37 + 1\frac{4}{7} + 1 + 1 \) = \( 40\frac{4}{7} \)
- И) \( 6\frac{49}{75} + \frac{5}{84} + 3\frac{1}{5} + \frac{14}{15} + 10\frac{9}{14} \) = \( (6+3+10) + (\frac{49}{75} + \frac{5}{84} + \frac{1}{5} + \frac{14}{15} + \frac{9}{14}) \) = \( 19 + \frac{49}{75} + \frac{5}{84} + \frac{1}{5} + \frac{14}{15} + \frac{9}{14} \). НОК для 75, 84, 5, 15, 14 = 2100. \( 19 + \frac{49 \times 28}{2100} + \frac{5 \times 25}{2100} + \frac{1 \times 420}{2100} + \frac{14 \times 140}{2100} + \frac{9 \times 150}{2100} \) = \( 19 + \frac{1372 + 125 + 420 + 1960 + 1350}{2100} \) = \( 19 + \frac{5227}{2100} = 19 + 2\frac{1027}{2100} = 21\frac{1027}{2100} \)
Ответ: Результаты вычислений приведены в каждом пункте.
