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

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

Ответ: $$\frac{3}{7}$$

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

Ответ: $$\frac{7}{12}$$

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

Ответ: $$-1\frac{1}{8}$$

ж) $$8\frac{2}{7}+(-7\frac{5}{14}) = 8\frac{4}{14}-7\frac{5}{14} = \frac{8 \cdot 14 + 4}{14} - \frac{7 \cdot 14 + 5}{14} = \frac{116}{14} - \frac{103}{14} = \frac{116 - 103}{14} = \frac{13}{14}$$

Ответ: $$\frac{13}{14}$$

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

Ответ: $$\frac{-2}{11}$$

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

Ответ: $$\frac{-3}{7}$$

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

Ответ: $$1\frac{8}{13}$$

з) $$-9\frac{1}{7}+ 8,5 = -9\frac{1}{7}+ 8\frac{1}{2} = -\frac{9 \cdot 7 + 1}{7} + \frac{8 \cdot 2 + 1}{2} = -\frac{64}{7} + \frac{17}{2} = -\frac{64 \cdot 2}{7 \cdot 2} + \frac{17 \cdot 7}{2 \cdot 7} = -\frac{128}{14} + \frac{119}{14} = \frac{119 - 128}{14} = -\frac{9}{14}$$

Ответ: $$-\frac{9}{14}$$