5.471 Выполните действия: 2 2 9 3 г) a) 11 4 11 5' д) +2126 18' + 4 9 9 13' 11 7 3 ; 2 49 2 13 7 5 e) +(); 8 12 16

а) \((\frac{4}{9} + \frac{2}{9}) : \frac{9}{13} = \frac{6}{9} : \frac{9}{13} = \frac{2}{3} \cdot \frac{13}{9} = \frac{2 \cdot 13}{3 \cdot 9} = \frac{26}{27}\)

б) \(2 \cdot (\frac{9}{3} - \frac{3}{4}) = 2 \cdot (\frac{36}{12} - \frac{9}{12}) = 2 \cdot \frac{27}{12} = 2 \cdot \frac{9}{4} = \frac{18}{4} = \frac{9}{2} = 4\frac{1}{2}\)

в) \((\frac{9}{11} - \frac{4}{11}) \cdot \frac{11}{5} = \frac{5}{11} \cdot \frac{11}{5} = 1\)

г) \(2 \cdot \frac{1}{8} + \frac{7}{12} = \frac{2}{8} + \frac{7}{12} = \frac{1}{4} + \frac{7}{12} = \frac{3}{12} + \frac{7}{12} = \frac{10}{12} = \frac{5}{6}\)

д) \((\frac{2}{3})^2 + \frac{13}{21} + \frac{7}{26} = \frac{4}{9} + \frac{13}{21} + \frac{7}{26} = \frac{4 \cdot 21 \cdot 26 + 13 \cdot 9 \cdot 26 + 7 \cdot 9 \cdot 21}{9 \cdot 21 \cdot 26} = \frac{2184 + 3042 + 1323}{4914} = \frac{6549}{4914} = 1\frac{1635}{4914} = 1\frac{545}{1638}\)

е) \((\frac{3}{7} - \frac{1}{7})^2 + \frac{49}{16} = (\frac{2}{7})^2 + \frac{49}{16} = \frac{4}{49} + \frac{49}{16} = \frac{4 \cdot 16 + 49 \cdot 49}{49 \cdot 16} = \frac{64 + 2401}{784} = \frac{2465}{784} = 3\frac{113}{784}\)

Ответ: а) \(\frac{26}{27}\); б) \(4\frac{1}{2}\); в) 1; г) \(\frac{5}{6}\); д) \(1\frac{545}{1638}\); е) \(3\frac{113}{784}\)