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

Привет! Давай выполним сложение дробей и смешанных чисел.

1. a) \(\frac{3}{7} + \frac{6}{7} = \frac{3+6}{7} = \frac{9}{7} = 1\frac{2}{7}\)

2. б) \(\frac{3}{4} + (-\frac{1}{6}) = \frac{3}{4} - \frac{1}{6} = \frac{3\cdot3}{4\cdot3} - \frac{1\cdot2}{6\cdot2} = \frac{9}{12} - \frac{2}{12} = \frac{9-2}{12} = \frac{7}{12}\)

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

4. г) \(\frac{5}{11} + \frac{3}{11} = \frac{5+3}{11} = \frac{8}{11}\)

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

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

7. ж) \(8\frac{2}{7} + (-\frac{5}{14}) = \frac{8\cdot7+2}{7} - \frac{5}{14} = \frac{58}{7} - \frac{5}{14} = \frac{58\cdot2}{7\cdot2} - \frac{5}{14} = \frac{116}{14} - \frac{5}{14} = \frac{116-5}{14} = \frac{111}{14} = 7\frac{13}{14}\)

8. з) \(-9\frac{1}{7} + 8,5 = -\frac{9\cdot7+1}{7} + 8,5 = -\frac{64}{7} + 8,5 = -9,1428 + 8,5 = -0,6428 \approx -0,64\)

Ответ: a) 1\frac{2}{7}; б) \frac{7}{12}; в) -\frac{3}{7}; г) \frac{8}{11}; д) -1\frac{1}{8}; e) 1\frac{8}{13}; ж) 7\frac{13}{14}; з) -0,64

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