Задание 2. Найдите значение выражения 1) \( (2 \frac{3}{17} + \frac{1}{34}) : 17 \); 2) \( (1 \frac{4}{19} - \frac{1}{19}) : 17 \); 3) \( 40 : (1 + \frac{1}{3}) \); 4) \( 5 \frac{1}{2} : (3 - \frac{2}{4}) \).

Решение:

1. \( (2 \frac{3}{17} + \frac{1}{34}) : 17 \)
1. \( 2 \frac{3}{17} = \frac{2 × 17 + 3}{17} = \frac{34 + 3}{17} = \frac{37}{17} \)
2. \( \frac{37}{17} + \frac{1}{34} = \frac{37 × 2}{17 × 2} + \frac{1}{34} = \frac{74}{34} + \frac{1}{34} = \frac{75}{34} \)
3. \( \frac{75}{34} : 17 = \frac{75}{34 × 17} = \frac{75}{578} \)
2. \( (1 \frac{4}{19} - \frac{1}{19}) : 17 \)
1. \( 1 \frac{4}{19} = \frac{1 × 19 + 4}{19} = \frac{19 + 4}{19} = \frac{23}{19} \)
2. \( \frac{23}{19} - \frac{1}{19} = \frac{22}{19} \)
3. \( \frac{22}{19} : 17 = \frac{22}{19 × 17} = \frac{22}{323} \)
3. \( 40 : (1 + \frac{1}{3}) \)
1. \( 1 + \frac{1}{3} = \frac{3}{3} + \frac{1}{3} = \frac{4}{3} \)
2. \( 40 : \frac{4}{3} = 40 × \frac{3}{4} = \frac{40 × 3}{4} = 10 × 3 = 30 \)
4. \( 5 \frac{1}{2} : (3 - \frac{2}{4}) \)
1. \( 5 \frac{1}{2} = \frac{5 × 2 + 1}{2} = \frac{11}{2} \)
2. \( 3 - \frac{2}{4} = 3 - \frac{1}{2} = \frac{6}{2} - \frac{1}{2} = \frac{5}{2} \)
3. \( \frac{11}{2} : \frac{5}{2} = \frac{11}{2} × \frac{2}{5} = \frac{11}{5} \)

Ответ: 1) \( \frac{75}{578} \); 2) \( \frac{22}{323} \); 3) 30; 4) \( \frac{11}{5} \).