Задание 2. Найдите значение выражения (2 3/17 + 1/34) * 17; 2) (1 1/4 - 3/19) * 19; 3) 4 3/8 * (3/8 + 1 1/13); 4) 5 2/5 * (3 1/4 - 1/4)

Решение:

1. 
   \( \left(2\frac{3}{17} + \frac{1}{34}\right) \cdot 17 = \left(\frac{34+3}{34} + \frac{1}{34}\right) \cdot 17 = \left(\frac{37}{34} + \frac{1}{34}\right) \cdot 17 = \frac{38}{34} \cdot 17 = \frac{19}{17} \cdot 17 = 19 \)
   
2. 
   \( \left(1\frac{1}{4} - \frac{3}{19}\right) \cdot 19 = \left(\frac{5}{4} - \frac{3}{19}\right) \cdot 19 = \left(\frac{5 \cdot 19 - 3 \cdot 4}{4 \cdot 19}\right) \cdot 19 = \left(\frac{95 - 12}{76}\right) \cdot 19 = \frac{83}{76} \cdot 19 = \frac{83}{4} = 20.75 \)
   
3. 
   \( 4\frac{3}{8} \cdot \left(\frac{3}{8} + 1\frac{1}{13}\right) = \frac{35}{8} \cdot \left(\frac{3}{8} + \frac{14}{13}\right) = \frac{35}{8} \cdot \left(\frac{3 \cdot 13 + 14 \cdot 8}{8 \cdot 13}\right) = \frac{35}{8} \cdot \left(\frac{39 + 112}{104}\right) = \frac{35}{8} \cdot \frac{151}{104} = \frac{5285}{832} \approx 6.35 \)
   
4. 
   \( 5\frac{2}{5} \cdot \left(3\frac{1}{4} - \frac{1}{4}\right) = \frac{27}{5} \cdot \left(\frac{13}{4} - \frac{1}{4}\right) = \frac{27}{5} \cdot \frac{12}{4} = \frac{27}{5} \cdot 3 = \frac{81}{5} = 16.2 \)
   

Ответ: 1) 19; 2) 20.75; 3) 5285/832; 4) 16.2.