4,221 Выполните сложение: а) - + ; б) - + ; в) + (-); г) -1 + ; д) -4 + 2; e) 10 + (-8); ж) 8+(-7); (з) -9+8,5.

Выполним сложение:

a) $$-\frac{3}{7} + \frac{6}{7} = \frac{6}{7} - \frac{3}{7} = \frac{6-3}{7} = \frac{3}{7}$$

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

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

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

ж) $$8\frac{2}{7} + (-7\frac{5}{14}) = \frac{8 \cdot 7 + 2}{7} - \frac{7 \cdot 14 + 5}{14} = \frac{56 + 2}{7} - \frac{98 + 5}{14} = \frac{58}{7} - \frac{103}{14} = \frac{58 \cdot 2}{7 \cdot 2} - \frac{103}{14} = \frac{116}{14} - \frac{103}{14} = \frac{116 - 103}{14} = \frac{13}{14}$$

з) $$-9\frac{1}{7} + 8.5 = - \frac{9 \cdot 7 + 1}{7} + 8.5 = -\frac{63 + 1}{7} + 8.5 = -\frac{64}{7} + 8.5 = -9.14 + 8.5 = -0.64$$

Ответ: a) $$\frac{3}{7}$$, б) $$\frac{-2}{11}$$, в) $$\frac{7}{12}$$, г) $$\frac{-3}{7}$$, д) $$-1\frac{1}{8}$$, e) $$1\frac{8}{13}$$, ж) $$\frac{13}{14}$$, з) -0.64.