06. Дроби и степени Блок 1. ФИПИ Задание 1. Найдите значение выражения

Решение:

1. \( \frac{3}{4} \cdot \frac{6}{5} = \frac{3 \cdot 6}{4 \cdot 5} = \frac{18}{20} = \frac{9}{10} \)
2. \( \frac{21}{5} : \frac{3}{7} = \frac{21}{5} \cdot \frac{7}{3} = \frac{21 \cdot 7}{5 \cdot 3} = \frac{7 \cdot 7}{5 \cdot 1} = \frac{49}{5} = 9 \frac{4}{5} \)
3. \( \frac{3}{5} \cdot \frac{25}{4} = \frac{3 \cdot 25}{5 \cdot 4} = \frac{3 \cdot 5}{1 \cdot 4} = \frac{15}{4} = 3 \frac{3}{4} \)
4. \( \frac{9}{5} : \frac{2}{3} = \frac{9}{5} \cdot \frac{3}{2} = \frac{9 \cdot 3}{5 \cdot 2} = \frac{27}{10} = 2 \frac{7}{10} \)
5. \( \frac{5}{3} \cdot \frac{9}{2} = \frac{5 \cdot 9}{3 \cdot 2} = \frac{5 \cdot 3}{1 \cdot 2} = \frac{15}{2} = 7 \frac{1}{2} \)
6. \( \frac{7}{5} : \frac{12}{35} = \frac{7}{5} \cdot \frac{35}{12} = \frac{7 \cdot 35}{5 \cdot 12} = \frac{7 \cdot 7}{1 \cdot 12} = \frac{49}{12} = 4 \frac{1}{12} \)
7. \( \frac{12}{5} \cdot \frac{15}{2} = \frac{12 \cdot 15}{5 \cdot 2} = \frac{6 \cdot 3}{1 \cdot 1} = 18 \)
8. \( \frac{6}{5} : \frac{4}{11} = \frac{6}{5} \cdot \frac{11}{4} = \frac{6 \cdot 11}{5 \cdot 4} = \frac{3 \cdot 11}{5 \cdot 2} = \frac{33}{10} = 3 \frac{3}{10} \)
9. \( \frac{3}{5} \cdot \frac{4}{35} = \frac{3 \cdot 4}{5 \cdot 35} = \frac{12}{175} \)
10. \( \frac{15}{4} : \frac{3}{7} = \frac{15}{4} \cdot \frac{7}{3} = \frac{15 \cdot 7}{4 \cdot 3} = \frac{5 \cdot 7}{4 \cdot 1} = \frac{35}{4} = 8 \frac{3}{4} \)
11. \( \frac{21}{2} : \frac{3}{5} = \frac{21}{2} \cdot \frac{5}{3} = \frac{21 \cdot 5}{2 \cdot 3} = \frac{7 \cdot 5}{2 \cdot 1} = \frac{35}{2} = 17 \frac{1}{2} \)
12. \( \frac{14}{5} \cdot \frac{7}{2} = \frac{14 \cdot 7}{5 \cdot 2} = \frac{7 \cdot 7}{5 \cdot 1} = \frac{49}{5} = 9 \frac{4}{5} \)
13. \( \frac{1}{4} \cdot \frac{3}{25} = \frac{1 \cdot 3}{4 \cdot 25} = \frac{3}{100} \)
14. \( \frac{1}{5} \cdot \frac{27}{50} = \frac{1 \cdot 27}{5 \cdot 50} = \frac{27}{250} \)
15. \( \frac{1}{2} \cdot \frac{9}{25} = \frac{1 \cdot 9}{2 \cdot 25} = \frac{9}{50} \)
16. \( \frac{1}{5} \cdot \frac{3}{4} = \frac{1 \cdot 3}{5 \cdot 4} = \frac{3}{20} \)
17. \( \frac{1}{2} \cdot \frac{13}{50} = \frac{1 \cdot 13}{2 \cdot 50} = \frac{13}{100} \)
18. \( \frac{1}{10} \cdot \frac{23}{20} = \frac{1 \cdot 23}{10 \cdot 20} = \frac{23}{200} \)
19. \( \frac{9}{4} \cdot \frac{8}{5} = \frac{9 \cdot 8}{4 \cdot 5} = \frac{9 \cdot 2}{1 \cdot 5} = \frac{18}{5} = 3 \frac{3}{5} \)
20. \( \frac{11}{5} + \frac{13}{4} = \frac{11 \cdot 4}{5 \cdot 4} + \frac{13 \cdot 5}{4 \cdot 5} = \frac{44}{20} + \frac{65}{20} = \frac{109}{20} = 5 \frac{9}{20} \)
21. \( \frac{1}{10} + \frac{21}{50} = \frac{1 \cdot 5}{10 \cdot 5} + \frac{21}{50} = \frac{5}{50} + \frac{21}{50} = \frac{26}{50} = \frac{13}{25} \)
22. \( \frac{3}{4} + \frac{7}{25} = \frac{3 \cdot 25}{4 \cdot 25} + \frac{7 \cdot 4}{25 \cdot 4} = \frac{75}{100} + \frac{28}{100} = \frac{103}{100} = 1 \frac{3}{100} \)
23. \( \frac{4}{25} + \frac{15}{4} = \frac{4 \cdot 4}{25 \cdot 4} + \frac{15 \cdot 25}{4 \cdot 25} = \frac{16}{100} + \frac{375}{100} = \frac{391}{100} = 3 \frac{91}{100} \)

Ответ: 1) \( \frac{9}{10} \) ; 2) \( 9 \frac{4}{5} \) ; 3) \( 3 \frac{3}{4} \) ; 4) \( 2 \frac{7}{10} \) ; 5) \( 7 \frac{1}{2} \) ; 6) \( 4 \frac{1}{12} \) ; 7) 18 ; 8) \( 3 \frac{3}{10} \) ; 9) \( \frac{12}{175} \) ; 10) \( 8 \frac{3}{4} \) ; 11) \( 17 \frac{1}{2} \) ; 12) \( 9 \frac{4}{5} \) ; 13) \( \frac{3}{100} \) ; 14) \( \frac{27}{250} \) ; 15) \( \frac{9}{50} \) ; 16) \( \frac{3}{20} \) ; 17) \( \frac{13}{100} \) ; 18) \( \frac{23}{200} \) ; 19) \( 3 \frac{3}{5} \) ; 20) \( 5 \frac{9}{20} \) ; 21) \( \frac{13}{25} \) ; 22) \( 1 \frac{3}{100} \) ; 23) \( 3 \frac{91}{100} \) .