Solve the following fraction multiplication and division problems. Show your work.

Решение:

1. \( \frac{3}{8} \cdot \frac{3}{4} = \frac{3 \cdot 3}{8 \cdot 4} = \frac{9}{32} \)
2. \( \frac{5}{12} \cdot \frac{8}{9} = \frac{5 \cdot 8}{12 \cdot 9} = \frac{40}{108} = \frac{10}{27} \)
3. \( \frac{3}{10} \cdot \frac{20}{33} = \frac{3 \cdot 20}{10 \cdot 33} = \frac{60}{330} = \frac{6}{33} = \frac{2}{11} \)
4. \( \frac{2}{3} \cdot \frac{3}{8} = \frac{2 \cdot 3}{3 \cdot 8} = \frac{6}{24} = \frac{1}{4} \)
5. \( \frac{15}{16} \cdot \frac{8}{25} = \frac{15 \cdot 8}{16 \cdot 25} = \frac{120}{400} = \frac{12}{40} = \frac{3}{10} \)
6. \( \frac{3}{7} \cdot \frac{2}{6} = \frac{3 \cdot 2}{7 \cdot 6} = \frac{6}{42} = \frac{1}{7} \)
7. \( \frac{2}{7} \cdot \frac{6}{25} = \frac{2 \cdot 6}{7 \cdot 25} = \frac{12}{175} \)
8. \( \frac{4}{3} \cdot \frac{3}{7} = \frac{4 \cdot 3}{3 \cdot 7} = \frac{12}{21} = \frac{4}{7} \)
9. \( \frac{5}{6} \cdot \frac{5}{7} = \frac{5 \cdot 5}{6 \cdot 7} = \frac{25}{42} \)
10. \( \frac{17}{40} \cdot \frac{4}{51} = \frac{17 \cdot 4}{40 \cdot 51} = \frac{68}{2040} = \frac{1}{30} \)
11. \( \frac{8}{15} \cdot \frac{11}{13} = \frac{8 \cdot 11}{15 \cdot 13} = \frac{88}{195} \)
12. \( \frac{3}{7} \cdot \frac{2}{6} = \frac{3 \cdot 2}{7 \cdot 6} = \frac{6}{42} = \frac{1}{7} \)
13. \( \frac{3}{8} \cdot \frac{7}{15} = \frac{3 \cdot 7}{8 \cdot 15} = \frac{21}{120} = \frac{7}{40} \)
14. \( \frac{11}{26} \cdot \frac{13}{55} = \frac{11 \cdot 13}{26 \cdot 55} = \frac{143}{1430} = \frac{1}{10} \)
15. \( \frac{2}{10} \cdot \frac{3}{9} = \frac{2 \cdot 3}{10 \cdot 9} = \frac{6}{90} = \frac{1}{15} \)
16. \( \frac{6}{25} \cdot \frac{7}{18} = \frac{6 \cdot 7}{25 \cdot 18} = \frac{42}{450} = \frac{7}{75} \)
17. \( \frac{45}{57} \cdot \frac{23}{19} = \frac{45 \cdot 23}{57 \cdot 19} = \frac{1035}{1083} = \frac{35}{37} \)
18. \( \frac{20}{21} \cdot \frac{42}{73} = \frac{20 \cdot 42}{21 \cdot 73} = \frac{840}{1533} = \frac{840}{1533} = \frac{280}{511} \)
19. \( \frac{8}{16} \cdot \frac{13}{26} = \frac{8 \cdot 13}{16 \cdot 26} = \frac{104}{416} = \frac{1}{4} \)

Ответ: решения приведены в порядке выполнения.