Упростите \(4\,\frac{3}{5}\) m + \(9\,\frac{6}{7}\) n − \(3\,\frac{1}{5}\) m − \(5\,\frac{2}{7}\) n; найдите значение при m = \(1\,\frac{11}{14}\), n = \(2\,\frac{5}{8}\).
Ответ
(\(4\,\frac{3}{5}\) − \(3\,\frac{1}{5}\))m + (\(9\,\frac{6}{7}\) − \(5\,\frac{2}{7}\))n = \(1\,\frac{2}{5}\) m + \(4\,\frac{4}{7}\) n.
\(\frac{7}{5}\) · \(\frac{25}{14}\) = (7 · 25)/(5 · 14) = \(\frac{5}{2}\).
\(\frac{32}{7}\) · \(\frac{21}{8}\) = (32 · 21)/(7 · 8) = 12.
\(\frac{5}{2}\) + 12 = \(\frac{5}{2}\) + \(\frac{24}{2}\) = \(\frac{29}{2}\).
Ответ: \(14\,\frac{1}{2}\).