Задание 1. Найдите значение выражения

Решение:

Выполним действия с дробями согласно указанным операциям.

1.

\( \frac{3}{4} \cdot \frac{6}{5} = \frac{3 \cdot 6}{4 \cdot 5} = \frac{18}{20} = \frac{9}{10} \)

2.

\( \frac{21}{5} \cdot \frac{3}{7} = \frac{21 \cdot 3}{5 \cdot 7} = \frac{3 \cdot 3}{5} = \frac{9}{5} \)

3.

\( \frac{3}{5} \cdot \frac{25}{4} = \frac{3 \cdot 25}{5 \cdot 4} = \frac{3 \cdot 5}{4} = \frac{15}{4} \)

4.

\( \frac{9}{5} \cdot \frac{2}{3} = \frac{9 \cdot 2}{5 \cdot 3} = \frac{3 \cdot 2}{5} = \frac{6}{5} \)

5.

\( \frac{5}{3} \cdot \frac{9}{2} = \frac{5 \cdot 9}{3 \cdot 2} = \frac{5 \cdot 3}{2} = \frac{15}{2} \)

6.

\( \frac{7}{5} \cdot \frac{12}{35} = \frac{7 \cdot 12}{5 \cdot 35} = \frac{12}{5 \cdot 5} = \frac{12}{25} \)

7.

\( \frac{12}{5} : \frac{15}{2} = \frac{12}{5} \cdot \frac{2}{15} = \frac{12 \cdot 2}{5 \cdot 15} = \frac{4 \cdot 2}{5 \cdot 5} = \frac{8}{25} \)

8.

\( \frac{6}{5} \cdot \frac{4}{11} = \frac{6 \cdot 4}{5 \cdot 11} = \frac{24}{55} \)

9.

\( \frac{3}{5} \cdot \frac{4}{35} = \frac{3 \cdot 4}{5 \cdot 35} = \frac{12}{175} \)

10.

\( \frac{15}{4} \cdot \frac{3}{7} = \frac{15 \cdot 3}{4 \cdot 7} = \frac{45}{28} \)

11.

\( \frac{21}{2} \cdot \frac{3}{5} = \frac{21 \cdot 3}{2 \cdot 5} = \frac{63}{10} \)

12.

\( \frac{14}{5} \cdot \frac{7}{2} = \frac{14 \cdot 7}{5 \cdot 2} = \frac{7 \cdot 7}{5} = \frac{49}{5} \)

13.

\( \frac{1}{4} - \frac{3}{25} = \frac{1 \cdot 25}{4 \cdot 25} - \frac{3 \cdot 4}{25 \cdot 4} = \frac{25 - 12}{100} = \frac{13}{100} \)

14.

\( \frac{1}{5} - \frac{27}{50} = \frac{1 \cdot 10}{5 \cdot 10} - \frac{27}{50} = \frac{10 - 27}{50} = \frac{-17}{50} \)

15.

\( \frac{1}{2} - \frac{9}{25} = \frac{1 \cdot 25}{2 \cdot 25} - \frac{9 \cdot 2}{25 \cdot 2} = \frac{25 - 18}{50} = \frac{7}{50} \)

16.

\( \frac{1}{5} - \frac{3}{4} = \frac{1 \cdot 4}{5 \cdot 4} - \frac{3 \cdot 5}{4 \cdot 5} = \frac{4 - 15}{20} = \frac{-11}{20} \)

17.

\( \frac{1}{2} - \frac{13}{50} = \frac{1 \cdot 25}{2 \cdot 25} - \frac{13}{50} = \frac{25 - 13}{50} = \frac{12}{50} = \frac{6}{25} \)

18.

\( \frac{1}{10} - \frac{23}{20} = \frac{1 \cdot 2}{10 \cdot 2} - \frac{23}{20} = \frac{2 - 23}{20} = \frac{-21}{20} \)

19.

\( \frac{14}{25} + \frac{3}{2} = \frac{14 \cdot 2}{25 \cdot 2} + \frac{3 \cdot 25}{2 \cdot 25} = \frac{28 + 75}{50} = \frac{103}{50} \)

20.

\( \frac{9}{4} + \frac{8}{5} = \frac{9 \cdot 5}{4 \cdot 5} + \frac{8 \cdot 4}{5 \cdot 4} = \frac{45 + 32}{20} = \frac{77}{20} \)

21.

\( \frac{11}{5} + \frac{13}{4} = \frac{11 \cdot 4}{5 \cdot 4} + \frac{13 \cdot 5}{4 \cdot 5} = \frac{44 + 65}{20} = \frac{109}{20} \)

22.

\( \frac{1}{10} + \frac{21}{50} = \frac{1 \cdot 5}{10 \cdot 5} + \frac{21}{50} = \frac{5 + 21}{50} = \frac{26}{50} = \frac{13}{25} \)

23.

\( \frac{3}{4} + \frac{7}{25} = \frac{3 \cdot 25}{4 \cdot 25} + \frac{7 \cdot 4}{25 \cdot 4} = \frac{75 + 28}{100} = \frac{103}{100} \)

24.

\( \frac{4}{25} + \frac{15}{4} = \frac{4 \cdot 4}{25 \cdot 4} + \frac{15 \cdot 25}{4 \cdot 25} = \frac{16 + 375}{100} = \frac{391}{100} \)

Ответ: 1. \( \frac{9}{10} \) 2. \( \frac{9}{5} \) 3. \( \frac{15}{4} \) 4. \( \frac{6}{5} \) 5. \( \frac{15}{2} \) 6. \( \frac{12}{25} \) 7. \( \frac{8}{25} \) 8. \( \frac{24}{55} \) 9. \( \frac{12}{175} \) 10. \( \frac{45}{28} \) 11. \( \frac{63}{10} \) 12. \( \frac{49}{5} \) 13. \( \frac{13}{100} \) 14. \( -\frac{17}{50} \) 15. \( \frac{7}{50} \) 16. \( -\frac{11}{20} \) 17. \( \frac{6}{25} \) 18. \( -\frac{21}{20} \) 19. \( \frac{103}{50} \) 20. \( \frac{77}{20} \) 21. \( \frac{109}{20} \) 22. \( \frac{13}{25} \) 23. \( \frac{103}{100} \) 24. \( \frac{391}{100} \)