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

Решение:

1. \[ \left( \frac{2}{3} + \frac{1}{17} \right) \times 17 = \frac{2}{3} \times 17 + \frac{1}{17} \times 17 = \frac{34}{3} + 1 = 11 \frac{1}{3} + 1 = 12 \frac{1}{3} \]
2. \[ \left( \frac{1}{4} + \frac{3}{19} \right) \times 19 = \frac{1}{4} \times 19 + \frac{3}{19} \times 19 = \frac{19}{4} + 3 = 4 \frac{3}{4} + 3 = 7 \frac{3}{4} \]
3. \[ 4 \frac{3}{8} : \left( 3 \frac{1}{4} + 1 \frac{1}{13} \right) = \frac{35}{8} : \left( \frac{13}{4} + \frac{14}{13} \right) = \frac{35}{8} : \left( \frac{13 \times 13}{4 \times 13} + \frac{14 \times 4}{13 \times 4} \right) = \frac{35}{8} : \left( \frac{169}{52} + \frac{56}{52} \right) = \frac{35}{8} : \frac{225}{52} = \frac{35}{8} \times \frac{52}{225} = \frac{7}{2} \times \frac{13}{45} = \frac{91}{90} = 1 \frac{1}{90} \]
4. \[ 5 \frac{2}{5} : \left( 3 \frac{1}{4} - 2 \frac{4}{5} \right) = \frac{27}{5} : \left( \frac{13}{4} - \frac{14}{5} \right) = \frac{27}{5} : \left( \frac{13 \times 5}{4 \times 5} - \frac{14 \times 4}{5 \times 4} \right) = \frac{27}{5} : \left( \frac{65}{20} - \frac{56}{20} \right) = \frac{27}{5} : \frac{9}{20} = \frac{27}{5} \times \frac{20}{9} = 3 \times 4 = 12 \]

Ответ: 1) 12 1/3; 2) 7 3/4; 3) 1 1/90; 4) 12