Solve the following multiplication and division problems with fractions.

Решение:

1. \( \frac{2}{5} \cdot \frac{3}{4} = \frac{2 \cdot 3}{5 \cdot 4} = \frac{6}{20} = \frac{3}{10} \)


2. \( \frac{1}{7} \cdot \frac{2}{3} = \frac{1 \cdot 2}{7 \cdot 3} = \frac{2}{21} \)


3. \( \frac{4}{5} \cdot \frac{6}{5} = \frac{4 \cdot 6}{5 \cdot 5} = \frac{24}{25} \)


4. \( \frac{1}{8} \cdot \frac{9}{9} = \frac{1 \cdot 9}{8 \cdot 9} = \frac{9}{72} = \frac{1}{8} \)


5. \( \frac{2}{3} \cdot \frac{6}{7} = \frac{2 \cdot 6}{3 \cdot 7} = \frac{12}{21} = \frac{4}{7} \)


6. \( \frac{5}{6} \cdot \frac{4}{10} = \frac{5 \cdot 4}{6 \cdot 10} = \frac{20}{60} = \frac{1}{3} \)


7. \( \frac{11}{14} \cdot \frac{7}{22} = \frac{11 \cdot 7}{14 \cdot 22} = \frac{77}{308} = \frac{1}{4} \)


8. \( \frac{4}{5} : \frac{5}{8} = \frac{4}{5} \cdot \frac{8}{5} = \frac{32}{25} \)


9. \( \frac{15}{10} : \frac{8}{3} = \frac{15}{10} \cdot \frac{3}{8} = \frac{45}{80} = \frac{9}{16} \)


10. \( \frac{3}{10} \cdot \frac{2}{6} = \frac{3 \cdot 2}{10 \cdot 6} = \frac{6}{60} = \frac{1}{10} \)


11. \( \frac{17}{33} \cdot \frac{11}{34} = \frac{17 \cdot 11}{33 \cdot 34} = \frac{187}{1122} = \frac{1}{6} \)


12. \( \frac{4}{5} : \frac{2}{5} = \frac{4}{5} \cdot \frac{5}{2} = \frac{20}{10} = 2 \)


13. \( \frac{1}{5} : \frac{3}{7} = \frac{1}{5} \cdot \frac{7}{3} = \frac{7}{15} \)


14. \( \frac{5}{7} : \frac{5}{7} = \frac{5}{7} \cdot \frac{7}{5} = \frac{35}{35} = 1 \)


15. \( \frac{2}{4} : \frac{3}{5} = \frac{2}{4} \cdot \frac{5}{3} = \frac{10}{12} = \frac{5}{6} \)


16. \( \frac{11}{77} : \frac{8}{16} = \frac{11}{77} \cdot \frac{16}{8} = \frac{176}{616} = \frac{4}{14} = \frac{2}{7} \)


17. \( \frac{23}{46} : \frac{5}{15} = \frac{23}{46} \cdot \frac{15}{5} = \frac{345}{230} = \frac{3}{2} \)


18. \( \frac{14}{21} : \frac{14}{22} = \frac{14}{21} \cdot \frac{22}{14} = \frac{308}{294} = \frac{22}{21} \)


19. \( \frac{25}{50} : \frac{18}{27} = \frac{25}{50} \cdot \frac{27}{18} = \frac{675}{900} = \frac{3}{4} \)


20. \( \frac{20}{40} : \frac{27}{18} = \frac{20}{40} \cdot \frac{18}{27} = \frac{360}{1080} = \frac{1}{3} \)


21. \( \frac{70}{270} : \frac{63}{81} = \frac{70}{270} \cdot \frac{81}{63} = \frac{5670}{17010} = \frac{1}{3} \)


22. \( \frac{2}{33} : \frac{24}{30} = \frac{2}{33} \cdot \frac{30}{24} = \frac{60}{792} = \frac{5}{66} \)


23. \( \frac{5}{7} : \frac{21}{15} : \frac{9}{24} = \frac{5}{7} \cdot \frac{15}{21} \cdot \frac{24}{9} = \frac{1800}{1323} = \frac{200}{147} \)


24. \( \frac{4}{5} : \frac{8}{10} : \frac{20}{2} = \frac{4}{5} \cdot \frac{10}{8} \cdot \frac{2}{20} = \frac{80}{800} = \frac{1}{10} \)


25. \( \frac{6}{7} : \frac{3}{9} : \frac{28}{30} = \frac{6}{7} \cdot \frac{9}{3} \cdot \frac{30}{28} = \frac{1620}{588} = \frac{135}{49} \)


26. \( \frac{40}{50} : \frac{20}{5} : \frac{3}{4} = \frac{40}{50} \cdot \frac{5}{20} \cdot \frac{4}{3} = \frac{800}{3000} = \frac{4}{15} \)


27. \( \frac{17}{20} : \frac{10}{34} : \frac{5}{2} = \frac{17}{20} \cdot \frac{34}{10} \cdot \frac{2}{5} = \frac{1156}{1000} = \frac{289}{250} \)


28. \( \frac{15}{20} : \frac{150}{200} : \frac{2}{3} = \frac{15}{20} \cdot \frac{200}{150} \cdot \frac{3}{2} = \frac{9000}{6000} = \frac{3}{2} \)


29. \( \frac{14}{63} : \frac{18}{28} : \frac{2}{6} = \frac{14}{63} \cdot \frac{28}{18} \cdot \frac{6}{2} = \frac{2352}{2268} = \frac{28}{27} \)


30. \( \frac{77}{25} : \frac{11}{13} : \frac{65}{7} = \frac{77}{25} \cdot \frac{13}{11} \cdot \frac{7}{65} = \frac{7007}{3575} = \frac{637}{325} \)


31. \( \frac{81}{90} : \frac{2}{3} : \frac{18}{20} = \frac{81}{90} \cdot \frac{3}{2} \cdot \frac{20}{18} = \frac{4860}{3240} = \frac{3}{2} \)


32. \( \frac{42}{60} : \frac{7}{12} : \frac{3}{21} = \frac{42}{60} \cdot \frac{12}{7} \cdot \frac{21}{3} = \frac{10584}{1260} = \frac{84}{10} = \frac{42}{5} \)

Ответ: Результаты вычислений представлены в решениях выше.