Вычислите: 1) \((2\frac{5}{9}-1\frac{20}{21}):1\frac{8}{49}+1\frac{8}{9}:6\); 2) \((1\frac{17}{18}\cdot1\frac{13}{14}-2\frac{5}{8}:1\frac{19}{20}):(2\frac{25}{78}-1\frac{1}{26})\).

1)

\(2\frac{5}{9}=\frac{23}{9}\), \(1\frac{20}{21}=\frac{41}{21}\), \(1\frac{8}{49}=\frac{57}{49}\), \(1\frac{8}{9}=\frac{17}{9}\).

\[\left(\frac{23}{9}-\frac{41}{21}\right):\frac{57}{49}+\frac{17}{9}:6\]

\[\frac{23}{9}-\frac{41}{21}=\frac{161-123}{63}=\frac{38}{63}.\]

\[\frac{38}{63}:\frac{57}{49}=\frac{38}{63}\cdot\frac{49}{57}=\frac{266}{513}.\]

\[\frac{17}{9}:6=\frac{17}{54}.\]

\[\frac{266}{513}+\frac{17}{54}=\frac{532}{1026}+\frac{323}{1026}=\frac{855}{1026}=\frac{95}{114}.\]

2)

\(1\frac{17}{18}=\frac{35}{18}\), \(1\frac{13}{14}=\frac{27}{14}\), \(2\frac{5}{8}=\frac{21}{8}\), \(1\frac{19}{20}=\frac{39}{20}\), \(2\frac{25}{78}=\frac{181}{78}\), \(1\frac{1}{26}=\frac{27}{26}\).

\[\frac{35}{18}\cdot\frac{27}{14}=\frac{15}{4},\qquad \frac{21}{8}:\frac{39}{20}=\frac{35}{26}.\]

\[\frac{15}{4}-\frac{35}{26}=\frac{195-70}{52}=\frac{125}{52}.\]

\[\frac{181}{78}-\frac{27}{26}=\frac{181}{78}-\frac{81}{78}=\frac{50}{39}.\]

\[\frac{125}{52}:\frac{50}{39}=\frac{125}{52}\cdot\frac{39}{50}=\frac{15}{8}=1\frac{7}{8}.\]

Ответ: 1) \(\frac{95}{114}\); 2) \(1\frac{7}{8}\).