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

Решение:

1. \( \left( 2\frac{3}{17} + \frac{1}{34} \right) \cdot 17 = \left( \frac{34+3}{17} + \frac{1}{34} \right) \cdot 17 = \left( \frac{37 \cdot 2}{17 \cdot 2} + \frac{1}{34} \right) \cdot 17 = \left( \frac{74}{34} + \frac{1}{34} \right) \cdot 17 = \frac{75}{34} \cdot 17 = \frac{75}{2} = 37.5 \)
2. \( \left( 1\frac{1}{4} - \frac{3}{19} \right) \cdot 19 = \left( \frac{5}{4} - \frac{3}{19} \right) \cdot 19 = \left( \frac{95}{76} - \frac{12}{76} \right) \cdot 19 = \frac{83}{76} \cdot 19 = \frac{83}{4} = 20.75 \)
3. \( 4\frac{3}{8} : \left( \frac{3}{8} + \frac{4}{13} \right) = \frac{35}{8} : \left( \frac{39+32}{104} \right) = \frac{35}{8} : \frac{71}{104} = \frac{35}{8} \cdot \frac{104}{71} = \frac{35 \cdot 13}{71} = \frac{455}{71} \)
4. \( 5\frac{2}{5} : \left( 3\frac{1}{4} - 2\frac{4}{5} \right) = \frac{27}{5} : \left( \frac{13}{4} - \frac{14}{5} \right) = \frac{27}{5} : \left( \frac{65-56}{20} \right) = \frac{27}{5} : \frac{9}{20} = \frac{27}{5} \cdot \frac{20}{9} = 3 \cdot 4 = 12 \)

Ответ: 1) 37.5; 2) 20.75; 3) 455/71; 4) 12.