Найдите значение выражения: а) 6/7 * 7/12 * 5/3

**Задание 5.470** а) $$\frac{6}{7} \cdot \frac{7}{12} \cdot \frac{5}{3} = \frac{6 \cdot 7 \cdot 5}{7 \cdot 12 \cdot 3} = \frac{1 \cdot 1 \cdot 5}{1 \cdot 2 \cdot 3} = \frac{5}{6}$$ б) $$\frac{3}{4} \cdot \frac{10}{13} \cdot \frac{39}{40} = \frac{3 \cdot 10 \cdot 39}{4 \cdot 13 \cdot 40} = \frac{3 \cdot 1 \cdot 3}{4 \cdot 1 \cdot 4} = \frac{9}{16}$$ в) $$11 \cdot \frac{5}{33} \cdot \frac{3}{10} = \frac{11 \cdot 5 \cdot 3}{33 \cdot 10} = \frac{1 \cdot 1 \cdot 3}{3 \cdot 2} = \frac{3}{6} = \frac{1}{2}$$ г) $$\frac{3}{4} \cdot \frac{4}{5} \cdot \frac{5}{6} \cdot 12 = \frac{3 \cdot 4 \cdot 5 \cdot 12}{4 \cdot 5 \cdot 6} = \frac{3 \cdot 12}{6} = 3 \cdot 2 = 6$$ д) $$\left(\frac{2}{3}\right)^2 + \frac{13}{21} \cdot \frac{7}{26} - \frac{5}{18} = \frac{4}{9} + \frac{13 \cdot 7}{21 \cdot 26} - \frac{5}{18} = \frac{4}{9} + \frac{1 \cdot 1}{3 \cdot 2} - \frac{5}{18} = \frac{4}{9} + \frac{1}{6} - \frac{5}{18}$$ Приводим к общему знаменателю 18: $$\frac{8}{18} + \frac{3}{18} - \frac{5}{18} = \frac{6}{18} = \frac{1}{3}$$ е) $$\left(\frac{3}{7} - \frac{1}{7}\right)^2 \cdot \frac{49}{16} + \left(\frac{1}{2}\right)^3 = \left(\frac{2}{7}\right)^2 \cdot \frac{49}{16} + \frac{1}{8} = \frac{4}{49} \cdot \frac{49}{16} + \frac{1}{8} = \frac{4}{16} + \frac{1}{8} = \frac{1}{4} + \frac{1}{8} = \frac{2}{8} + \frac{1}{8} = \frac{3}{8}$$ **Задание 5.471** а) $$\left(\frac{4}{9} + \frac{2}{9}\right) \cdot \frac{9}{13} = \frac{6}{9} \cdot \frac{9}{13} = \frac{6}{13}$$ б) $$\frac{2}{3} \cdot \left(\frac{9}{8} - \frac{3}{4}\right) = \frac{2}{3} \cdot \left(\frac{9}{8} - \frac{6}{8}\right) = \frac{2}{3} \cdot \frac{3}{8} = \frac{2}{8} = \frac{1}{4}$$ в) $$\left(\frac{9}{11} - \frac{4}{11}\right) \cdot \frac{11}{5} = \frac{5}{11} \cdot \frac{11}{5} = 1$$ г) $$2 \cdot \frac{1}{8} + \frac{7}{12} \cdot \frac{3}{7} = \frac{2}{8} + \frac{7 \cdot 3}{12 \cdot 7} = \frac{1}{4} + \frac{3}{12} = \frac{1}{4} + \frac{1}{4} = \frac{2}{4} = \frac{1}{2}$$ д) $$\left(\frac{2}{3}\right)^2 + \frac{13}{21} \cdot \frac{7}{26} - \frac{5}{18} = \frac{4}{9} + \frac{1}{6} - \frac{5}{18} = \frac{8+3-5}{18} = \frac{6}{18} = \frac{1}{3}$$ е) $$\left(\frac{3}{7} - \frac{1}{7}\right)^2 \cdot \frac{49}{16} + \left(\frac{1}{2}\right)^3 = \left(\frac{2}{7}\right)^2 \cdot \frac{49}{16} + \frac{1}{8} = \frac{4}{49} \cdot \frac{49}{16} + \frac{1}{8} = \frac{1}{4} + \frac{1}{8} = \frac{3}{8}$$