Вариант 1 1. Выполните действие: a) \frac{3}{7}\cdot\frac{5}{11}; б) \frac{6}{25}:\frac{5}{18}; в) 3\frac{3}{5}\cdot1\frac{1}{9}; г) 1\frac{1}{7}\cdot14; д) \frac{5}{9}:\frac{10}{27}; е) \frac{12}{13}:6.

a) $$ \frac{3}{7} \cdot \frac{5}{11} = \frac{3 \cdot 5}{7 \cdot 11} = \frac{15}{77} $$

б) $$ \frac{6}{25} : \frac{5}{18} = \frac{6}{25} \cdot \frac{18}{5} = \frac{6 \cdot 18}{25 \cdot 5} = \frac{108}{125} $$

в) $$ 3\frac{3}{5} \cdot 1\frac{1}{9} = \frac{3 \cdot 5 + 3}{5} \cdot \frac{1 \cdot 9 + 1}{9} = \frac{18}{5} \cdot \frac{10}{9} = \frac{18 \cdot 10}{5 \cdot 9} = \frac{2 \cdot 2}{1 \cdot 1} = 4 $$

г) $$ 1\frac{1}{7} \cdot 14 = \frac{1 \cdot 7 + 1}{7} \cdot 14 = \frac{8}{7} \cdot 14 = \frac{8 \cdot 14}{7} = 8 \cdot 2 = 16 $$

д) $$ \frac{5}{9} : \frac{10}{27} = \frac{5}{9} \cdot \frac{27}{10} = \frac{5 \cdot 27}{9 \cdot 10} = \frac{1 \cdot 3}{1 \cdot 2} = \frac{3}{2} = 1\frac{1}{2} $$

е) $$ \frac{12}{13} : 6 = \frac{12}{13} : \frac{6}{1} = \frac{12}{13} \cdot \frac{1}{6} = \frac{12 \cdot 1}{13 \cdot 6} = \frac{2 \cdot 1}{13 \cdot 1} = \frac{2}{13} $$

Ответ:

a) $$ \frac{15}{77} $$

б) $$ \frac{108}{125} $$

в) 4

г) 16

д) $$ 1\frac{1}{2} $$

е) $$ \frac{2}{13} $$