4.221 Выполните сложение: a)-+ б)-+ в)+ г)-1+ д) -4 +2 e) 10 + (-8): ж) 8+(-); з) -9+8,5.

Ответ: a) 3/14; б) -2/11; в) 1/12; г) 3/7; д) -2 1/8; e) 1 8/13; ж) 1 9/14; з) -1 2/7.

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

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

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

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

д) \(-4 + 2\frac{7}{8} = -\frac{4 \cdot 8}{8} + \frac{2 \cdot 8 + 7}{8} = -\frac{32}{8} + \frac{16 + 7}{8} = \frac{-32+23}{8} = \frac{-9}{8} = -1\frac{1}{8}\)

е) \(10 + (-8\frac{5}{13}) = 10 - 8\frac{5}{13} = \frac{10 \cdot 13}{13} - \frac{8 \cdot 13 + 5}{13} = \frac{130}{13} - \frac{104 + 5}{13} = \frac{130-109}{13} = \frac{21}{13} = 1\frac{8}{13}\)

ж) \(8\frac{2}{7} + (-\frac{5}{14}) = \frac{8 \cdot 7 + 2}{7} - \frac{5}{14} = \frac{56+2}{7} - \frac{5}{14} = \frac{58}{7} - \frac{5}{14} = \frac{58 \cdot 2}{7 \cdot 2} - \frac{5}{14} = \frac{116}{14} - \frac{5}{14} = \frac{116-5}{14} = \frac{111}{14} = 7\frac{13}{14}\)

з) \(-9\frac{1}{7} + 8.5 = -\frac{9 \cdot 7 + 1}{7} + 8\frac{1}{2} = -\frac{63+1}{7} + \frac{8 \cdot 2 + 1}{2} = -\frac{64}{7} + \frac{16+1}{2} = -\frac{64}{7} + \frac{17}{2} = -\frac{64 \cdot 2}{7 \cdot 2} + \frac{17 \cdot 7}{2 \cdot 7} = -\frac{128}{14} + \frac{119}{14} = \frac{-128+119}{14} = \frac{-9}{14} = -\frac{9}{14}\)

Ответ: a) -3/7; б) -2/11; в) 7/12; г) -3/7; д) -1 1/8; e) 1 8/13; ж) 7 13/14; з) -9/14.