5471 Выполните действия: а) (4/9 + 2/9) * 9/13 ; в) (9/11 - 4/11) * 11/5 ; д) (2/3)^2 + 13/21 * 7/26 - 5/18 ; е) (3/7 - 1/7)^2 * 49/16 + (1/2)^3 ; б) 2/3 * (9/8 - 3/4) ; г) 2 * 1/8 + 7/12 * 3/7 ;

Выполним действия:

а) $$ (\frac{4}{9} + \frac{2}{9}) \cdot \frac{9}{13} = \frac{4+2}{9} \cdot \frac{9}{13} = \frac{6}{9} \cdot \frac{9}{13} = \frac{6 \cdot 9}{9 \cdot 13} = \frac{6}{13} $$

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

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

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

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

е) $$ (\frac{3}{7} - \frac{1}{7})^2 \cdot \frac{49}{16} + (\frac{1}{2})^3 = (\frac{3-1}{7})^2 \cdot \frac{49}{16} + \frac{1}{8} = (\frac{2}{7})^2 \cdot \frac{49}{16} + \frac{1}{8} = \frac{4}{49} \cdot \frac{49}{16} + \frac{1}{8} = \frac{4 \cdot 49}{49 \cdot 16} + \frac{1}{8} = \frac{4}{16} + \frac{1}{8} = \frac{1}{4} + \frac{1}{8} = \frac{1 \cdot 2}{4 \cdot 2} + \frac{1}{8} = \frac{2}{8} + \frac{1}{8} = \frac{2+1}{8} = \frac{3}{8} $$

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