1. (6 баллов) Выполните действия: a) 3/7 * 5/11; б) 6/25 * 5/18; в) 4/7 : 2; г) 5/9 : 10/27; д) 12/13 : 6; e) 4 : 6/13

Решение:

1. a) \(\frac{3}{7} \times \frac{5}{11} = \frac{3 \times 5}{7 \times 11} = \frac{15}{77}\)
2. б) \(\frac{6}{25} \times \frac{5}{18} = \frac{6 \times 5}{25 \times 18} = \frac{30}{450} = \frac{1}{15}\)
3. в) \(\frac{4}{7} : 2 = \frac{4}{7} : \frac{2}{1} = \frac{4}{7} \times \frac{1}{2} = \frac{4 \times 1}{7 \times 2} = \frac{4}{14} = \frac{2}{7}\)
4. г) \(\frac{5}{9} : \frac{10}{27} = \frac{5}{9} \times \frac{27}{10} = \frac{5 \times 27}{9 \times 10} = \frac{135}{90} = \frac{3}{2}\)
5. д) \(\frac{12}{13} : 6 = \frac{12}{13} : \frac{6}{1} = \frac{12}{13} \times \frac{1}{6} = \frac{12 \times 1}{13 \times 6} = \frac{12}{78} = \frac{2}{13}\)
6. е) \(4 : \frac{6}{13} = \frac{4}{1} : \frac{6}{13} = \frac{4}{1} \times \frac{13}{6} = \frac{4 \times 13}{1 \times 6} = \frac{52}{6} = \frac{26}{3}\)