4.46 Вычислите. a) 1-\(\frac{4}{7}\)-\(\frac{2}{7}\)-\(\frac{3}{7}\)-\(\frac{1}{7}\)-\(\frac{3}{7}\) = ? б) 2-\(\frac{5}{9}\) + \(\frac{9}{13}\)+\(\frac{9}{9}\)+\(\frac{13}{13}\) = ? в) \(\frac{16}{17}\):8-\(\frac{1}{17}\)-\(\frac{7}{17}\):2 = ? г) 4,5 + 3,5 : 5 + 1,4 - 2,2 - 0,01 = ?

Решим данное задание: a) 1-\(\frac{4}{7}\)-\(\frac{2}{7}\)-\(\frac{3}{7}\)-\(\frac{1}{7}\)-\(\frac{3}{7}\) = \(\frac{7}{7}\)-\(\frac{4}{7}\)-\(\frac{2}{7}\)-\(\frac{3}{7}\)-\(\frac{1}{7}\)-\(\frac{3}{7}\) = \(\frac{7-4-2-3-1-3}{7}\) = \(\frac{-6}{7}\) = -\(\frac{6}{7}\) б) 2-\(\frac{5}{9}\) + \(\frac{9}{13}\)+\(\frac{9}{9}\)+\(\frac{13}{13}\) = 2 - \(\frac{5}{9}\) + \(\frac{9}{13}\) + 1 + 1 = 4 - \(\frac{5}{9}\) + \(\frac{9}{13}\) = \(\frac{4 \cdot 9 \cdot 13 - 5 \cdot 13 + 9 \cdot 9}{9 \cdot 13}\) = \(\frac{468 - 65 + 81}{117}\) = \(\frac{484}{117}\) = \(4\frac{16}{117}\) в) \(\frac{16}{17}\):8-\(\frac{1}{17}\)-\(\frac{7}{17}\):2 = \(\frac{16}{17}\) : \(\frac{8}{1}\) - \(\frac{1}{17}\) - \(\frac{7}{17}\) : \(\frac{2}{1}\) = \(\frac{16}{17 \cdot 8}\) - \(\frac{1}{17}\) - \(\frac{7}{17 \cdot 2}\) = \(\frac{2}{17}\) - \(\frac{1}{17}\) - \(\frac{7}{34}\) = \(\frac{2 \cdot 2 - 1 \cdot 2 - 7}{34}\) = \(\frac{4-2-7}{34}\) = \(\frac{-5}{34}\) = -\(\frac{5}{34}\) г) 4,5 + 3,5 : 5 + 1,4 - 2,2 - 0,01 = 4,5 + 0,7 + 1,4 - 2,2 - 0,01 = 6,6 - 2,2 - 0,01 = 4,4 - 0,01 = 4,39

Ответ: а) -\(\frac{6}{7}\); б) \(4\frac{16}{117}\); в) -\(\frac{5}{34}\); г) 4,39

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