Задание 2. Найдите значение выражения 1) \(\left(2\frac{3}{17} + \frac{1}{34}\right) \cdot 17\) 2) \(\left(1\frac{1}{4} - \frac{3}{19}\right) \cdot 19\) 3) \(4\frac{3}{8} \cdot \left(\frac{3}{8} + 1\frac{4}{13}\right)\) 4) \(5\frac{2}{5} : \left(3\frac{1}{4}\right)\)

Решение:

1. \(\left(2\frac{3}{17} + \frac{1}{34}\right) \cdot 17\)
   \(\left(\frac{2 \cdot 17 + 3}{17} + \frac{1}{34}\right) \cdot 17 = \left(\frac{37}{17} + \frac{1}{34}\right) \cdot 17 = \left(\frac{37 \cdot 2}{34} + \frac{1}{34}\right) \cdot 17 = \frac{74 + 1}{34} \cdot 17 = \frac{75}{34} \cdot 17 = \frac{75 \cdot 17}{34} = \frac{75}{2}\)
2. \(\left(1\frac{1}{4} - \frac{3}{19}\right) \cdot 19\)
   \(\left(\frac{1 \cdot 4 + 1}{4} - \frac{3}{19}\right) \cdot 19 = \left(\frac{5}{4} - \frac{3}{19}\right) \cdot 19 = \left(\frac{5 \cdot 19}{76} - \frac{3 \cdot 4}{76}\right) \cdot 19 = \frac{95 - 12}{76} \cdot 19 = \frac{83}{76} \cdot 19 = \frac{83 \cdot 19}{76} = \frac{83}{4}\)
3. \(4\frac{3}{8} \cdot \left(\frac{3}{8} + 1\frac{4}{13}\right)\)
   \(\frac{35}{8} \cdot \left(\frac{3}{8} + \frac{17}{13}\right) = \frac{35}{8} \cdot \left(\frac{3 \cdot 13 + 17 \cdot 8}{104}\right) = \frac{35}{8} \cdot \left(\frac{39 + 136}{104}\right) = \frac{35}{8} \cdot \frac{175}{104} = \frac{35 \cdot 175}{8 \cdot 104} = \frac{6125}{832}\)
4. \(5\frac{2}{5} : \left(3\frac{1}{4}\right)\)
   \(\frac{27}{5} : \frac{13}{4} = \frac{27}{5} \cdot \frac{4}{13} = \frac{27 \cdot 4}{5 \cdot 13} = \frac{108}{65}\)

Ответ: 1) \(\frac{75}{2}\); 2) \(\frac{83}{4}\); 3) \(\frac{6125}{832}\); 4) \(\frac{108}{65}\).