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

Решение:

1. \(2 \frac{3}{17} = \frac{2 \cdot 17 + 3}{17} = \frac{34+3}{17} = \frac{37}{17}\)
2. \(\frac{37}{17} + \frac{1}{34} = \frac{37 \cdot 2}{17 \cdot 2} + \frac{1}{34} = \frac{74}{34} + \frac{1}{34} = \frac{75}{34}\)
3. \(\frac{75}{34} \cdot 17 = \frac{75 \cdot 17}{34} = \frac{75}{2} = 37,5\)
4. \(1 \frac{1}{4} = \frac{1 \cdot 4 + 1}{4} = \frac{5}{4}\)
5. \(\frac{5}{4} - \frac{3}{19} = \frac{5 \cdot 19}{4 \cdot 19} - \frac{3 \cdot 4}{19 \cdot 4} = \frac{95}{76} - \frac{12}{76} = \frac{83}{76}\)
6. \(\frac{83}{76} \cdot 19 = \frac{83 \cdot 19}{76} = \frac{83}{4} = 20,75\)
7. \(4 \frac{3}{8} = \frac{4 \cdot 8 + 3}{8} = \frac{32+3}{8} = \frac{35}{8}\)
8. \(\frac{3}{8} + 1 \frac{4}{13} = \frac{3}{8} + \frac{1 \cdot 13 + 4}{13} = \frac{3}{8} + \frac{17}{13} = \frac{3 \cdot 13 + 17 \cdot 8}{8 \cdot 13} = \frac{39+136}{104} = \frac{175}{104}\)
9. \(\frac{35}{8} : \frac{175}{104} = \frac{35}{8} \cdot \frac{104}{175} = \frac{35 \cdot 104}{8 \cdot 175} = \frac{1 \cdot 13}{1 \cdot 5} = \frac{13}{5} = 2,6\)
10. \(5 \frac{2}{5} = \frac{5 \cdot 5 + 2}{5} = \frac{25+2}{5} = \frac{27}{5}\)
11. \(3 \frac{1}{4} - \frac{3}{4} = \frac{3 \cdot 4 + 1}{4} - \frac{3}{4} = \frac{13}{4} - \frac{3}{4} = \frac{10}{4} = \frac{5}{2}\)
12. \(\frac{27}{5} : \frac{5}{2} = \frac{27}{5} \cdot \frac{2}{5} = \frac{54}{25} = 2,16\)

Ответ: 1) 37,5; 2) 20,75; 3) 2,6; 4) 2,16.