Вопрос:

351. Найдите значение выражения: 1) \(5\frac{3}{4} \cdot 8 - 2\frac{1}{3} \cdot 1\frac{3}{14} - 1\frac{37}{48} \cdot 2\frac{2}{5}\) 2) \(1\frac{3}{22} \cdot \frac{14}{15} - (\frac{5}{8} + 2\frac{1}{17}) \cdot \frac{3}{7}\) 3) \(6\frac{2}{5} \cdot \frac{5}{16} - (2\frac{1}{4})^2\) 4) \((2\frac{7}{10} - 1\frac{8}{15}) \cdot \frac{9}{14}\)

Ответ:

1) \(5\frac{3}{4} \cdot 8 - 2\frac{1}{3} \cdot 1\frac{3}{14} - 1\frac{37}{48} \cdot 2\frac{2}{5} = \frac{23}{4} \cdot 8 - \frac{7}{3} \cdot \frac{17}{14} - \frac{85}{48} \cdot \frac{12}{5} = 46 - \frac{17}{6} - \frac{17}{4} = 46 - \frac{34}{12} - \frac{51}{12} = 46 - \frac{85}{12} = 46 - 7\frac{1}{12} = 38\frac{11}{12}\)
2) \(1\frac{3}{22} \cdot \frac{14}{15} - (\frac{5}{8} + 2\frac{1}{17}) \cdot \frac{3}{7} = \frac{25}{22} \cdot \frac{14}{15} - (\frac{5}{8} + \frac{35}{17}) \cdot \frac{3}{7} = \frac{35}{33} - (\frac{85}{136} + \frac{280}{136}) \cdot \frac{3}{7} = \frac{35}{33} - \frac{365}{136} \cdot \frac{3}{7} = \frac{35}{33} - \frac{1095}{952} = \frac{35}{33} - \frac{1095}{952} \approx 1.06 - 1.15 = -0.09\)
3) \(6\frac{2}{5} \cdot \frac{5}{16} - (2\frac{1}{4})^2 = \frac{32}{5} \cdot \frac{5}{16} - (\frac{9}{4})^2 = 2 - \frac{81}{16} = \frac{32}{16} - \frac{81}{16} = -\frac{49}{16} = -3\frac{1}{16}\)
4) \((2\frac{7}{10} - 1\frac{8}{15}) \cdot \frac{9}{14} = (\frac{27}{10} - \frac{23}{15}) \cdot \frac{9}{14} = (\frac{81}{30} - \frac{46}{30}) \cdot \frac{9}{14} = \frac{35}{30} \cdot \frac{9}{14} = \frac{7}{6} \cdot \frac{9}{14} = \frac{1}{2} \cdot \frac{3}{2} = \frac{3}{4}\)
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