5.471 Выполните действия: a) (4/9 + 2/9) * 9/13; б) 2/3 * (9/8 - 3/4); в) (9/11 - 4/11) * 11/5; г) 2 * 1/8 + 7/12 * 3/7; д) (2/3)^2 + 13/21 * 7/26 - 5/18; e) (3/7 - 1/7) * 49/16 + (1/2)^3.

a) $$\left(\frac{4}{9} + \frac{2}{9}\right) \cdot \frac{9}{13} = \frac{4+2}{9} \cdot \frac{9}{13} = \frac{6}{9} \cdot \frac{9}{13} = \frac{2}{3} \cdot \frac{9}{13} = \frac{2 \cdot 3}{13} = \frac{6}{13}$$

Ответ: 6/13

б) $$\frac{2}{3} \cdot \left(\frac{9}{8} - \frac{3}{4}\right) = \frac{2}{3} \cdot \left(\frac{9}{8} - \frac{3 \cdot 2}{4 \cdot 2}\right) = \frac{2}{3} \cdot \left(\frac{9}{8} - \frac{6}{8}\right) = \frac{2}{3} \cdot \frac{9-6}{8} = \frac{2}{3} \cdot \frac{3}{8} = \frac{2}{8} = \frac{1}{4}$$

Ответ: 1/4

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

Ответ: 1

г) $$2 \cdot \frac{1}{8} + \frac{7}{12} \cdot \frac{3}{7} = \frac{2}{8} + \frac{7 \cdot 3}{12 \cdot 7} = \frac{1}{4} + \frac{3}{12} = \frac{1}{4} + \frac{1}{4} = \frac{1+1}{4} = \frac{2}{4} = \frac{1}{2}$$

Ответ: 1/2

д) $$\left(\frac{2}{3}\right)^2 + \frac{13}{21} \cdot \frac{7}{26} - \frac{5}{18} = \frac{4}{9} + \frac{13 \cdot 7}{21 \cdot 26} - \frac{5}{18} = \frac{4}{9} + \frac{1 \cdot 1}{3 \cdot 2} - \frac{5}{18} = \frac{4}{9} + \frac{1}{6} - \frac{5}{18} = \frac{4 \cdot 2}{9 \cdot 2} + \frac{1 \cdot 3}{6 \cdot 3} - \frac{5}{18} = \frac{8}{18} + \frac{3}{18} - \frac{5}{18} = \frac{8+3-5}{18} = \frac{6}{18} = \frac{1}{3}$$

Ответ: 1/3

e) $$\left(\frac{3}{7} - \frac{1}{7}\right) \cdot \frac{49}{16} + \left(\frac{1}{2}\right)^3 = \frac{3-1}{7} \cdot \frac{49}{16} + \frac{1}{8} = \frac{2}{7} \cdot \frac{49}{16} + \frac{1}{8} = \frac{1 \cdot 7}{1 \cdot 8} + \frac{1}{8} = \frac{7}{8} + \frac{1}{8} = \frac{7+1}{8} = \frac{8}{8} = 1$$

Ответ: 1