Вопрос:

65. Найдите значение выражения: 1) 9 \(\frac{1}{4}\) * 8 - 1 \(\frac{5}{12}\) * 5 \(\frac{1}{2}\) - 2 \(\frac{4}{5}\) * 2 \(\frac{11}{12}\) 2) 1 \(\frac{1}{22}\) * 3 \(\frac{2}{3}\) - (2 \(\frac{5}{6}\) + 3 \(\frac{5}{6}\) * \(\frac{7}{23}\)) * \(\frac{3}{5}\)

Ответ:

Решение:
1) 9 \(\frac{1}{4}\) * 8 - 1 \(\frac{5}{12}\) * 5 \(\frac{1}{2}\) - 2 \(\frac{4}{5}\) * 2 \(\frac{11}{12}\) = \(\frac{37}{4}\) * 8 - \(\frac{17}{12}\) * \(\frac{11}{2}\) - \(\frac{14}{5}\) * \(\frac{35}{12}\) = 74 - \(\frac{187}{24}\) - \(\frac{490}{60}\) = 74 - \(\frac{187}{24}\) - \(\frac{245}{30}\) = \(\frac{74*120 - 187*5 - 245*4}{120}\) = \(\frac{8880 - 935 - 980}{120}\) = \(\frac{6965}{120}\) = \(\frac{1393}{24}\) = 58 \(\frac{1}{24}\)
2) 1 \(\frac{1}{22}\) * 3 \(\frac{2}{3}\) - (2 \(\frac{5}{6}\) + 3 \(\frac{5}{6}\) * \(\frac{7}{23}\)) * \(\frac{3}{5}\) = \(\frac{23}{22}\) * \(\frac{11}{3}\) - (\(\frac{17}{6}\) + \(\frac{23}{6}\) * \(\frac{7}{23}\)) * \(\frac{3}{5}\) = \(\frac{253}{66}\) - (\(\frac{17}{6}\) + \(\frac{7}{6}\)) * \(\frac{3}{5}\) = \(\frac{253}{66}\) - \(\frac{24}{6}\) * \(\frac{3}{5}\) = \(\frac{253}{66}\) - 4 * \(\frac{3}{5}\) = \(\frac{253}{66}\) - \(\frac{12}{5}\) = \(\frac{1265}{330}\) - \(\frac{792}{330}\) = \(\frac{473}{330}\) = 1 \(\frac{143}{330}\)

Ответ:
1) 58 \(\frac{1}{24}\)
2) 1 \(\frac{143}{330}\)
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