Решите примеры с дробями.

1) $$\frac{8}{35} \cdot \left(\frac{5}{6} + \frac{11}{12}\right) = \frac{8}{35} \cdot \left(\frac{10}{12} + \frac{11}{12}\right) = \frac{8}{35} \cdot \frac{21}{12} = \frac{8 \cdot 21}{35 \cdot 12} = \frac{(2 \cdot 4) \cdot (3 \cdot 7)}{(5 \cdot 7) \cdot (3 \cdot 4)} = \frac{2}{5}$$ **Ответ:** $\frac{2}{5}$ 2) $$\frac{9}{10} \cdot \left(\frac{11}{12} - \frac{2}{9}\right) = \frac{9}{10} \cdot \left(\frac{33}{36} - \frac{8}{36}\right) = \frac{9}{10} \cdot \frac{25}{36} = \frac{9 \cdot 25}{10 \cdot 36} = \frac{9 \cdot (5 \cdot 5)}{(2 \cdot 5) \cdot (4 \cdot 9)} = \frac{5}{2 \cdot 4} = \frac{5}{8}$$ **Ответ:** $\frac{5}{8}$ 3) $$\frac{24}{49} : \frac{6}{7} + \frac{1}{14} = \frac{24}{49} \cdot \frac{7}{6} + \frac{1}{14} = \frac{24 \cdot 7}{49 \cdot 6} + \frac{1}{14} = \frac{(4 \cdot 6) \cdot 7}{(7 \cdot 7) \cdot 6} + \frac{1}{14} = \frac{4}{7} + \frac{1}{14} = \frac{8}{14} + \frac{1}{14} = \frac{9}{14}$$ **Ответ:** $\frac{9}{14}$ 4) $$\frac{35}{24} : \frac{15}{32} - 3 = \frac{35}{24} \cdot \frac{32}{15} - 3 = \frac{35 \cdot 32}{24 \cdot 15} - 3 = \frac{(7 \cdot 5) \cdot (4 \cdot 8)}{(3 \cdot 8) \cdot (3 \cdot 5)} - 3 = \frac{7 \cdot 4}{3 \cdot 3} - 3 = \frac{28}{9} - 3 = \frac{28}{9} - \frac{27}{9} = \frac{1}{9}$$ **Ответ:** $\frac{1}{9}$ 5) $$\frac{11}{20} - \frac{12}{25} \cdot \frac{15}{16} = \frac{11}{20} - \frac{12 \cdot 15}{25 \cdot 16} = \frac{11}{20} - \frac{(3 \cdot 4) \cdot (3 \cdot 5)}{(5 \cdot 5) \cdot (4 \cdot 4)} = \frac{11}{20} - \frac{3 \cdot 3}{5 \cdot 4} = \frac{11}{20} - \frac{9}{20} = \frac{2}{20} = \frac{1}{10}$$ **Ответ:** $\frac{1}{10}$ 6) $$18 \cdot \frac{5}{81} - \frac{2}{3} = \frac{18 \cdot 5}{81} - \frac{2}{3} = \frac{(2 \cdot 9) \cdot 5}{(9 \cdot 9)} - \frac{2}{3} = \frac{10}{9} - \frac{2}{3} = \frac{10}{9} - \frac{6}{9} = \frac{4}{9}$$ **Ответ:** $\frac{4}{9}$ 7) $$\frac{2}{7} : \left(\frac{5}{7} + \frac{11}{21}\right) = \frac{2}{7} : \left(\frac{15}{21} + \frac{11}{21}\right) = \frac{2}{7} : \frac{26}{21} = \frac{2}{7} \cdot \frac{21}{26} = \frac{2 \cdot 21}{7 \cdot 26} = \frac{2 \cdot (3 \cdot 7)}{7 \cdot (2 \cdot 13)} = \frac{3}{13}$$ **Ответ:** $\frac{3}{13}$ 8) $$\frac{3}{10} - \frac{9}{25} : \left(4 - 1\frac{9}{10}\right) + \frac{4}{7} = \frac{3}{10} - \frac{9}{25} : \left(4 - \frac{19}{10}\right) + \frac{4}{7} = \frac{3}{10} - \frac{9}{25} : \left(\frac{40}{10} - \frac{19}{10}\right) + \frac{4}{7} = \frac{3}{10} - \frac{9}{25} : \frac{21}{10} + \frac{4}{7} = \frac{3}{10} - \frac{9}{25} \cdot \frac{10}{21} + \frac{4}{7} = \frac{3}{10} - \frac{9 \cdot 10}{25 \cdot 21} + \frac{4}{7} = \frac{3}{10} - \frac{(3 \cdot 3) \cdot (2 \cdot 5)}{(5 \cdot 5) \cdot (3 \cdot 7)} + \frac{4}{7} = \frac{3}{10} - \frac{3 \cdot 2}{5 \cdot 7} + \frac{4}{7} = \frac{3}{10} - \frac{6}{35} + \frac{4}{7}$$ Приводим к общему знаменателю 70: $ = \frac{3 \cdot 7}{10 \cdot 7} - \frac{6 \cdot 2}{35 \cdot 2} + \frac{4 \cdot 10}{7 \cdot 10} = \frac{21}{70} - \frac{12}{70} + \frac{40}{70} = \frac{21 - 12 + 40}{70} = \frac{9 + 40}{70} = \frac{49}{70} = \frac{7}{10}$ **Ответ:** $\frac{7}{10}$