8. Найдите значение выражения, используя свойства сложения или свойства вычитания:

Решение:

1. \( \frac{1}{8} + \frac{4}{18} + \frac{7}{8} + \frac{5}{18} = (\frac{1}{8} + \frac{7}{8}) + (\frac{4}{18} + \frac{5}{18}) = \frac{8}{8} + \frac{9}{18} = 1 + \frac{1}{2} = 1\frac{1}{2} \)
2. \( \frac{4}{7} + \frac{2}{9} + \frac{4}{11} + \frac{3}{7} = (\frac{4}{7} + \frac{3}{7}) + \frac{2}{9} + \frac{4}{11} = \frac{7}{7} + \frac{2}{9} + \frac{4}{11} = 1 + \frac{2 \cdot 11 + 4 \cdot 9}{9 \cdot 11} = 1 + \frac{22 + 36}{99} = 1 + \frac{58}{99} = 1\frac{58}{99} \)
3. \( (\frac{11}{48} + \frac{47}{69}) - \frac{24}{69} = \frac{11}{48} + (\frac{47}{69} - \frac{24}{69}) = \frac{11}{48} + \frac{23}{69} \). \( \frac{23}{69} = \frac{23}{3 \cdot 23} = \frac{1}{3} \). \( \frac{11}{48} + \frac{1}{3} = \frac{11}{48} + \frac{1 \cdot 16}{3 \cdot 16} = \frac{11}{48} + \frac{16}{48} = \frac{11+16}{48} = \frac{27}{48} = \frac{9}{16} \)
4. \( \frac{19}{28} - (\frac{1}{17} + \frac{5}{28}) = \frac{19}{28} - \frac{5}{28} - \frac{1}{17} = (\frac{19}{28} - \frac{5}{28}) - \frac{1}{17} = \frac{14}{28} - \frac{1}{17} = \frac{1}{2} - \frac{1}{17} = \frac{1 \cdot 17 - 1 \cdot 2}{2 \cdot 17} = \frac{17 - 2}{34} = \frac{15}{34} \)

Ответ: 1) \( 1\frac{1}{2} \); 2) \( 1\frac{58}{99} \); 3) \( \frac{9}{16} \); 4) \( \frac{15}{34} \).