4.221 Выполните сложение: a) \(\frac{3}{7} + \frac{6}{7}\); в) \(\frac{3}{4} + (-\frac{1}{6})\); б) \(-\frac{5}{11} + \frac{3}{11}\); г) -1 + \(\frac{4}{7}\); д) -4 + 2\(\frac{7}{8}\); e) 10 + (-8\(\frac{5}{13}\)); ж) 8\(\frac{2}{7}\) + (-\(\frac{7}{14}\)); з) -9\(\frac{1}{7}\) + 8,5.

Ответ: a) \(\frac{9}{7}\); б) -\(\frac{2}{11}\); в) \(\frac{7}{12}\); г) -\(\frac{3}{7}\); д) -1\(\frac{1}{8}\); е) 1\(\frac{8}{13}\); ж) 7\(\frac{6}{7}\); з) -\(\frac{6}{7}\)

Приступим к решению каждого выражения:

1. a) \(\frac{3}{7} + \frac{6}{7} = \frac{3+6}{7} = \frac{9}{7}\)
2. б) \(-\frac{5}{11} + \frac{3}{11} = \frac{-5+3}{11} = -\frac{2}{11}\)
3. в) \(\frac{3}{4} + (-\frac{1}{6}) = \frac{3}{4} - \frac{1}{6} = \frac{9}{12} - \frac{2}{12} = \frac{7}{12}\)
4. г) \(-1 + \frac{4}{7} = -\frac{7}{7} + \frac{4}{7} = \frac{-7+4}{7} = -\frac{3}{7}\)
5. д) \(-4 + 2\frac{7}{8} = -4 + \frac{2 \cdot 8 + 7}{8} = -4 + \frac{23}{8} = -\frac{32}{8} + \frac{23}{8} = \frac{-32+23}{8} = -\frac{9}{8} = -1\frac{1}{8}\)
6. е) \(10 + (-8\frac{5}{13}) = 10 - 8\frac{5}{13} = \frac{130}{13} - \frac{109}{13} = \frac{21}{13} = 1\frac{8}{13}\)
7. ж) \(8\frac{2}{7} + (-\frac{7}{14}) = 8\frac{4}{14} - \frac{7}{14} = 7 + \frac{14+4-7}{14} = 7\frac{11}{14} =\frac{109}{14}\)
8. з) \(-9\frac{1}{7} + 8,5 = -9\frac{1}{7} + 8\frac{1}{2} = -\frac{64}{7} + \frac{17}{2} = \frac{-128+119}{14} = -\frac{9}{14}\)

Ответ: a) \(\frac{9}{7}\); б) -\(\frac{2}{11}\); в) \(\frac{7}{12}\); г) -\(\frac{3}{7}\); д) -1\(\frac{1}{8}\); е) 1\(\frac{8}{13}\); ж) 7\(\frac{6}{7}\); з) -\(\frac{6}{7}\)