433. Выполните действие: a) \(\frac{3}{4}\cdot \frac{5}{7}\); б) \(\frac{1}{8}\cdot \frac{3}{4}\); в) \(\frac{4}{7}\cdot \frac{5}{6}\); г) \(\frac{2}{5}\cdot \frac{7}{11}\); д) \(\frac{1}{2}\cdot \frac{4}{9}\); е) \(\frac{11}{12}\cdot \frac{8}{9}\); ж) \(\frac{2}{5}\cdot \frac{3}{2}\); з) \(\frac{11}{15}\cdot \frac{3}{5}\); и) \(\frac{15}{16}\cdot \frac{5}{9}\); к) \(\frac{12}{25}\cdot \frac{9}{16}\); л) \(\frac{14}{17}\cdot \frac{34}{63}\); м) \(\frac{17}{26}\cdot \frac{13}{18}\); н) \((\frac{4}{5})^2\); о) \((\frac{2}{3})^2\); п) \((\frac{1}{7})^2\).

Ответ: а) \(\frac{15}{28}\); б) \(\frac{3}{32}\); в) \(\frac{10}{21}\); г) \(\frac{14}{55}\); д) \(\frac{2}{9}\); е) \(\frac{22}{27}\); ж) \(\frac{3}{5}\); з) \(\frac{11}{25}\); и) \(\frac{25}{48}\); к) \(\frac{27}{100}\); л) \(\frac{4}{9}\); м) \(\frac{1}{36}\); н) \(\frac{16}{25}\); о) \(\frac{4}{9}\); п) \(\frac{1}{49}\)

Решение:

1. а) \(\frac{3}{4}\cdot \frac{5}{7} = \frac{3\cdot 5}{4\cdot 7} = \frac{15}{28}\)
2. б) \(\frac{1}{8}\cdot \frac{3}{4} = \frac{1\cdot 3}{8\cdot 4} = \(\frac{3}{32}\)
3. в) \(\frac{4}{7}\cdot \frac{5}{6} = \frac{4\cdot 5}{7\cdot 6} = \frac{20}{42} = \frac{10}{21}\)
4. г) \(\frac{2}{5}\cdot \frac{7}{11} = \frac{2\cdot 7}{5\cdot 11} = \frac{14}{55}\)
5. д) \(\frac{1}{2}\cdot \frac{4}{9} = \frac{1\cdot 4}{2\cdot 9} = \frac{4}{18} = \frac{2}{9}\)
6. е) \(\frac{11}{12}\cdot \frac{8}{9} = \frac{11\cdot 8}{12\cdot 9} = \frac{88}{108} = \frac{22}{27}\)
7. ж) \(\frac{2}{5}\cdot \frac{3}{2} = \frac{2\cdot 3}{5\cdot 2} = \frac{6}{10} = \frac{3}{5}\)
8. з) \(\frac{11}{15}\cdot \frac{3}{5} = \frac{11\cdot 3}{15\cdot 5} = \frac{33}{75} = \frac{11}{25}\)
9. и) \(\frac{15}{16}\cdot \frac{5}{9} = \frac{15\cdot 5}{16\cdot 9} = \frac{75}{144} = \frac{25}{48}\)
10. к) \(\frac{12}{25}\cdot \frac{9}{16} = \frac{12\cdot 9}{25\cdot 16} = \frac{108}{400} = \frac{27}{100}\)
11. л) \(\frac{14}{17}\cdot \frac{34}{63} = \frac{14\cdot 34}{17\cdot 63} = \frac{476}{1071} = \frac{4}{9}\)
12. м) \(\frac{17}{26}\cdot \frac{13}{18} = \frac{17\cdot 13}{26\cdot 18} = \frac{221}{468} = \frac{17}{36}\)
13. н) \((\frac{4}{5})^2 = \frac{4^2}{5^2} = \frac{16}{25}\)
14. о) \((\frac{2}{3})^2 = \frac{2^2}{3^2} = \frac{4}{9}\)
15. п) \((\frac{1}{7})^2 = \frac{1^2}{7^2} = \frac{1}{49}\)

Ответ: а) \(\frac{15}{28}\); б) \(\frac{3}{32}\); в) \(\frac{10}{21}\); г) \(\frac{14}{55}\); д) \(\frac{2}{9}\); е) \(\frac{22}{27}\); ж) \(\frac{3}{5}\); з) \(\frac{11}{25}\); и) \(\frac{25}{48}\); к) \(\frac{27}{100}\); л) \(\frac{4}{9}\); м) \(\frac{1}{36}\); н) \(\frac{16}{25}\); о) \(\frac{4}{9}\); п) \(\frac{1}{49}\)