Вариант 2 1. Выполните действие: a) \frac{5}{6}\cdot\frac{7}{9}; б) \frac{11}{28}\cdot\frac{7}{33}; в) 3\frac{5}{7}\cdot1\frac{1}{13}; г) 2\frac{2}{3}:6; д) \frac{3}{8}:\frac{9}{16}; е) \frac{15}{16}:5.

a) $$ \frac{5}{6} \cdot \frac{7}{9} = \frac{5 \cdot 7}{6 \cdot 9} = \frac{35}{54} $$

б) $$ \frac{11}{28} \cdot \frac{7}{33} = \frac{11 \cdot 7}{28 \cdot 33} = \frac{1 \cdot 1}{4 \cdot 3} = \frac{1}{12} $$

в) $$ 3\frac{5}{7} \cdot 1\frac{1}{13} = \frac{3 \cdot 7 + 5}{7} \cdot \frac{1 \cdot 13 + 1}{13} = \frac{26}{7} \cdot \frac{14}{13} = \frac{26 \cdot 14}{7 \cdot 13} = \frac{2 \cdot 2}{1 \cdot 1} = 4 $$

г) $$ 2\frac{2}{3} : 6 = \frac{2 \cdot 3 + 2}{3} : \frac{6}{1} = \frac{8}{3} \cdot \frac{1}{6} = \frac{8 \cdot 1}{3 \cdot 6} = \frac{4 \cdot 1}{3 \cdot 3} = \frac{4}{9} $$

д) $$ \frac{3}{8} : \frac{9}{16} = \frac{3}{8} \cdot \frac{16}{9} = \frac{3 \cdot 16}{8 \cdot 9} = \frac{1 \cdot 2}{1 \cdot 3} = \frac{2}{3} $$

е) $$ \frac{15}{16} : 5 = \frac{15}{16} : \frac{5}{1} = \frac{15}{16} \cdot \frac{1}{5} = \frac{15 \cdot 1}{16 \cdot 5} = \frac{3 \cdot 1}{16 \cdot 1} = \frac{3}{16} $$

Ответ:

a) $$ \frac{35}{54} $$

б) $$ \frac{1}{12} $$

в) 4

г) $$ \frac{4}{9} $$

д) $$ \frac{2}{3} $$

е) $$ \frac{3}{16} $$