Вопрос:

Выполните действия: a) 7 3/17 + 8 5/17 - 1 6/17 б) 10 7/15 - 3 1/15 + 4 4/15 в) 5 7/10 - (4 3/10 - 2 1/10) г) 9 9/11 - (3 2/11 - 2 3/11)

Ответ:

a) \(7\frac{3}{17} + 8\frac{5}{17} - 1\frac{6}{17}\) = \((7 + 8 - 1) + (\frac{3}{17} + \frac{5}{17} - \frac{6}{17})\) = \(14 + \frac{3+5-6}{17}\) = \(14 + \frac{2}{17}\) = \(14\frac{2}{17}\) б) \(10\frac{7}{15} - 3\frac{1}{15} + 4\frac{4}{15}\) = \((10 - 3 + 4) + (\frac{7}{15} - \frac{1}{15} + \frac{4}{15})\) = \(11 + \frac{7-1+4}{15}\) = \(11 + \frac{10}{15}\) = \(11\frac{10}{15}\) = \(11\frac{2}{3}\) в) \(5\frac{7}{10} - (4\frac{3}{10} - 2\frac{1}{10})\) = \(5\frac{7}{10} - ((4 - 2) + (\frac{3}{10} - \frac{1}{10}))\) = \(5\frac{7}{10} - (2 + \frac{2}{10})\) = \(5\frac{7}{10} - 2\frac{2}{10}\) = \((5 - 2) + (\frac{7}{10} - \frac{2}{10})\) = \(3 + \frac{5}{10}\) = \(3\frac{5}{10}\) = \(3\frac{1}{2}\) г) \(9\frac{9}{11} - (3\frac{2}{11} - 2\frac{3}{11})\) = \(9\frac{9}{11} - ((3 - 2) + (\frac{2}{11} - \frac{3}{11}))\) = \(9\frac{9}{11} - (1 - \frac{1}{11})\) = \(9\frac{9}{11} - \frac{10}{11}\) = \(9 + \frac{9}{11} - \frac{10}{11}\) = \(9 - \frac{1}{11}\) = \(8\frac{11}{11} - \frac{1}{11}\) = \(8\frac{10}{11}\)
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