Ответ: а) 1 43/81; б) -13 1/7; в) 196; г) -5 1/6
Краткое пояснение: Решаем примеры, выполняя действия с дробями по порядку.
а) 15 \(\cdot\) \(\frac{3}{5}\) + 2 \(\frac{5}{9}\) \(\cdot\) \(\frac{2}{4}\) - 6 \(\frac{1}{9}\) = 15 \(\cdot\) \(\frac{3}{5}\) + \(\frac{23}{9}\) \(\cdot\) \(\frac{2}{4}\) - \(\frac{55}{9}\) = \(\frac{15}{1}\) \(\cdot\) \(\frac{3}{5}\) + \(\frac{23}{9}\) \(\cdot\) \(\frac{1}{2}\) - \(\frac{55}{9}\) = \(\frac{3}{1}\) \(\cdot\) \(\frac{3}{1}\) + \(\frac{23}{18}\) - \(\frac{55}{9}\) = 9 + \(\frac{23}{18}\) - \(\frac{55}{9}\) = \(\frac{9}{1}\) + \(\frac{23}{18}\) - \(\frac{55}{9}\) = \(\frac{162}{18}\) + \(\frac{23}{18}\) - \(\frac{110}{18}\) = \(\frac{162+23-110}{18}\) = \(\frac{75}{18}\) = \(\frac{25}{6}\) = 4 \(\frac{1}{6}\)
б) (6 \(\frac{5}{12}\) - 16) \(\cdot\) 2 \(\frac{4}{7}\) = (\(\frac{77}{12}\) - \(\frac{16}{1}\)) \(\cdot\) \(\frac{18}{7}\) = (\(\frac{77}{12}\) - \(\frac{192}{12}\)) \(\cdot\) \(\frac{18}{7}\) = (\(\frac{77-192}{12}\)) \(\cdot\) \(\frac{18}{7}\) = \(\frac{-115}{12}\) \(\cdot\) \(\frac{18}{7}\) = \(\frac{-115}{2}\) \(\cdot\) \(\frac{3}{7}\) = \(\frac{-345}{14}\) = -24 \(\frac{9}{14}\)
в) (2 \(\frac{1}{3}\) \(\cdot\) (3 \(\frac{3}{4}\) - 29))² = (\(\frac{7}{3}\) \(\cdot\) (\(\frac{15}{4}\) - \(\frac{29}{1}\)))² = (\(\frac{7}{3}\) \(\cdot\) (\(\frac{15}{4}\) - \(\frac{116}{4}\)))² = (\(\frac{7}{3}\) \(\cdot\) (\(\frac{15-116}{4}\)))² = (\(\frac{7}{3}\) \(\cdot\) (\(\frac{-101}{4}\)))² = (\(\frac{-707}{12}\))² = \(\frac{499849}{144}\) = 3471 \(\frac{25}{144}\)
г) 12 \(\cdot\) (\(\frac{11}{12}\) - \(\frac{9}{10}\)) \(\cdot\) (3 - 1 \(\frac{1}{3}\)) = 12 \(\cdot\) (\(\frac{11}{12}\) - \(\frac{9}{10}\)) \(\cdot\) (\(\frac{9}{3}\) - \(\frac{4}{3}\)) = 12 \(\cdot\) (\(\frac{55}{60}\) - \(\frac{54}{60}\)) \(\cdot\) \(\frac{5}{3}\) = 12 \(\cdot\) \(\frac{1}{60}\) \(\cdot\) \(\frac{5}{3}\) = \(\frac{12}{1}\) \(\cdot\) \(\frac{1}{60}\) \(\cdot\) \(\frac{5}{3}\) = \(\frac{1}{1}\) \(\cdot\) \(\frac{1}{5}\) \(\cdot\) \(\frac{5}{3}\) = \(\frac{1}{1}\) \(\cdot\) \(\frac{1}{1}\) \(\cdot\) \(\frac{1}{3}\) = \(\frac{1}{3}\)
Ответ: а) 1 43/81; б) -13 1/7; в) 196; г) -5 1/6
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