462. Найдите значение выражения: 1) (2 5/9 - 1 20/21) : 1 8/49 + 1 8/9 : 6; 2) (1 17/18 - 1 13/14) - 2 5/1 * 19/20 : (2 25/78 - 1 1/26).

Решение:

1. \( (2 \frac{5}{9} - 1 \frac{20}{21}) : 1 \frac{8}{49} + 1 \frac{8}{9} : 6 = (\frac{23}{9} - \frac{41}{21}) : \frac{57}{49} + \frac{17}{9} : 6 = (\frac{161 - 123}{63}) : \frac{57}{49} + \frac{17}{54} = \frac{38}{63} \times \frac{49}{57} + \frac{17}{54} = \frac{38 \times 7}{9 \times 57} + \frac{17}{54} = \frac{266}{513} + \frac{17}{54} = \frac{266 \times 2 + 17 \times 19}{1026} = \frac{532 + 323}{1026} = \frac{855}{1026} = \frac{95}{114} \)
2. \( (1 \frac{17}{18} - 1 \frac{13}{14}) - 2 \frac{5}{1} \times \frac{19}{20} : (2 \frac{25}{78} - 1 \frac{1}{26}) = (\frac{35}{18} - \frac{27}{14}) - 2 \times \frac{19}{20} : (\frac{201}{78} - \frac{27}{26}) = (\frac{245 - 270}{126}) - \frac{19}{10} : (\frac{201}{78} - \frac{81}{78}) = -\frac{25}{126} - \frac{19}{10} : \frac{120}{78} = -\frac{25}{126} - \frac{19}{10} \times \frac{78}{120} = -\frac{25}{126} - \frac{1482}{1200} = -0.198 - 1.235 = -1.433 \)

Ответ: 1) \(\frac{95}{114}\); 2) \(-1.433\).