Задание 2 а) \(\frac{2}{5} \cdot \frac{3}{4}\) г) \(2 \frac{1}{2} : \frac{18}{25}\) б) \(\frac{11}{14} : \frac{7}{22}\) д) \(5 \frac{1}{3} \cdot 3 \frac{8}{9}\) в) \(\frac{7}{8} \cdot 5 \frac{1}{3}\) e) \(4 \frac{1}{2} : 2 \frac{4}{5}\)

Ответ: а) \(\frac{3}{10}\); б) 2 \(\frac{9}{14}\); в) 4 \(\frac{2}{3}\); г) 3 \(\frac{13}{36}\); д) 20 \(\frac{8}{27}\); е) 1 \(\frac{13}{18}\)

Решение:

1. а) \(\frac{2}{5} \cdot \frac{3}{4} = \frac{2 \cdot 3}{5 \cdot 4} = \frac{6}{20} = \frac{3}{10}\)
2. б) \(\frac{11}{14} : \frac{7}{22} = \frac{11}{14} \cdot \frac{22}{7} = \frac{11 \cdot 22}{14 \cdot 7} = \frac{242}{98} = 2 \frac{46}{98} = 2 \frac{23}{49}\)
3. в) \(\frac{7}{8} \cdot 5 \frac{1}{3} = \frac{7}{8} \cdot \frac{16}{3} = \frac{7 \cdot 16}{8 \cdot 3} = \frac{112}{24} = 4 \frac{16}{24} = 4 \frac{2}{3}\)
4. г) \(2 \frac{1}{2} : \frac{18}{25} = \frac{5}{2} : \frac{18}{25} = \frac{5}{2} \cdot \frac{25}{18} = \frac{5 \cdot 25}{2 \cdot 18} = \frac{125}{36} = 3 \frac{17}{36}\)
5. д) \(5 \frac{1}{3} \cdot 3 \frac{8}{9} = \frac{16}{3} \cdot \frac{35}{9} = \frac{16 \cdot 35}{3 \cdot 9} = \frac{560}{27} = 20 \frac{20}{27}\)
6. е) \(4 \frac{1}{2} : 2 \frac{4}{5} = \frac{9}{2} : \frac{14}{5} = \frac{9}{2} \cdot \frac{5}{14} = \frac{9 \cdot 5}{2 \cdot 14} = \frac{45}{28} = 1 \frac{17}{28}\)

Ответ: а) \(\frac{3}{10}\); б) 2 \(\frac{9}{14}\); в) 4 \(\frac{2}{3}\); г) 3 \(\frac{13}{36}\); д) 20 \(\frac{8}{27}\); е) 1 \(\frac{13}{18}\)