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

Ответ:

а) \(-\frac{3}{7} + \frac{6}{7} = \frac{6-3}{7} = \frac{3}{7}\)

б) \(-\frac{5}{11} + \frac{3}{11} = \frac{3-5}{11} = -\frac{2}{11}\)

в) \(\frac{3}{4} + (-\frac{1}{6}) = \frac{3}{4} - \frac{1}{6} = \frac{9}{12} - \frac{2}{12} = \frac{7}{12}\)

г) \(-1 + \frac{4}{7} = -\frac{7}{7} + \frac{4}{7} = \frac{4-7}{7} = -\frac{3}{7}\)

д) \(-4 + 2\frac{7}{8} = -4 + \frac{2\cdot8+7}{8} = -4 + \frac{23}{8} = -\frac{32}{8} + \frac{23}{8} = -\frac{9}{8} = -1\frac{1}{8}\)

ж) \(8\frac{2}{7} + (-7\frac{5}{14}) = \frac{8\cdot7+2}{7} - \frac{7\cdot14+5}{14} = \frac{58}{7} - \frac{103}{14} = \frac{116}{14} - \frac{103}{14} = \frac{13}{14}\)

e) \(10+(-8\frac{5}{13}) = 10 - 8\frac{5}{13} = 10 - \frac{8\cdot13+5}{13} = 10 - \frac{109}{13} = \frac{130}{13} - \frac{109}{13} = \frac{21}{13} = 1\frac{8}{13}\)

з) \(-9\frac{1}{7} + 8,5 = -\frac{9\cdot7+1}{7} + \frac{85}{10} = -\frac{64}{7} + \frac{17}{2} = -\frac{128}{14} + \frac{119}{14} = -\frac{9}{14}\)

Ответ: