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

Разбираемся:

• а) \(\frac{3}{7} \cdot \frac{5}{11} = \frac{3 \cdot 5}{7 \cdot 11} = \frac{15}{77}\)
• б) \(\frac{6}{25} \cdot \frac{5}{18} = \frac{6 \cdot 5}{25 \cdot 18} = \frac{1 \cdot 1}{5 \cdot 3} = \frac{1}{15}\)
• в) \(\frac{4}{7} \cdot 2 = \frac{4 \cdot 2}{7} = \frac{8}{7} = 1\frac{1}{7}\)
• г) \(\frac{5}{9} : \frac{10}{27} = \frac{5}{9} \cdot \frac{27}{10} = \frac{5 \cdot 27}{9 \cdot 10} = \frac{1 \cdot 3}{1 \cdot 2} = \frac{3}{2} = 1\frac{1}{2}\)
• д) \(\frac{12}{13} : 6 = \frac{12}{13} \cdot \frac{1}{6} = \frac{12 \cdot 1}{13 \cdot 6} = \frac{2 \cdot 1}{13 \cdot 1} = \frac{2}{13}\)
• e) \(4 : \frac{6}{13} = 4 \cdot \frac{13}{6} = \frac{4 \cdot 13}{6} = \frac{2 \cdot 13}{3} = \frac{26}{3} = 8\frac{2}{3}\)