5.471 Выполните действия:

Решение:

1. \(\left(\frac{4}{9} + \frac{2}{9}\right) \cdot \frac{9}{13} = \left(\frac{4+2}{9}\right) \cdot \frac{9}{13} = \frac{6}{9} \cdot \frac{9}{13} = \frac{6 \cdot 9}{9 \cdot 13} = \frac{6}{13}\)
2. \(\left(\frac{9}{11} - \frac{4}{11}\right) \cdot \frac{11}{5} = \left(\frac{9-4}{11}\right) \cdot \frac{11}{5} = \frac{5}{11} \cdot \frac{11}{5} = \frac{5 \cdot 11}{11 \cdot 5} = 1\)
3. \(\frac{2}{3} \cdot \left(\frac{9}{8} - \frac{3}{4}\right) = \frac{2}{3} \cdot \left(\frac{9}{8} - \frac{6}{8}\right) = \frac{2}{3} \cdot \frac{3}{8} = \frac{2 \cdot 3}{3 \cdot 8} = \frac{2}{8} = \frac{1}{4}\)
4. \(2 \cdot \frac{1}{8} + \frac{7}{12} \cdot \frac{3}{7} = \frac{2}{8} + \frac{7 \cdot 3}{12 \cdot 7} = \frac{1}{4} + \frac{3}{12} = \frac{1}{4} + \frac{1}{4} = \frac{1+1}{4} = \frac{2}{4} = \frac{1}{2}\)
5. \(\left(\frac{2}{3}\right)^2 + \frac{13}{21} \cdot \frac{7}{26} - \frac{5}{18} = \frac{4}{9} + \frac{13 \cdot 7}{21 \cdot 26} - \frac{5}{18} = \frac{4}{9} + \frac{1}{2 \cdot 3} - \frac{5}{18} = \frac{4}{9} + \frac{1}{6} - \frac{5}{18} = \frac{8}{18} + \frac{3}{18} - \frac{5}{18} = \frac{6}{18} = \frac{1}{3}\)
6. \(\left(\frac{3}{7} - \frac{1}{7}\right)^2 \cdot \frac{49}{16} + \left(\frac{1}{2}\right)^3 = \left(\frac{2}{7}\right)^2 \cdot \frac{49}{16} + \frac{1}{8} = \frac{4}{49} \cdot \frac{49}{16} + \frac{1}{8} = \frac{4}{16} + \frac{1}{8} = \frac{1}{4} + \frac{1}{8} = \frac{2}{8} + \frac{1}{8} = \frac{3}{8}\)

Ответ: а) 6/13; б) 1; в) 1/4; г) 1/2; д) 1/3; е) 3/8.