Задание 41. Выполните умножение. A.

Решение:

Для умножения обыкновенных дробей нужно:

1. Числитель умножить на числитель.
2. Знаменатель умножить на знаменатель.
3. Если возможно, сократить полученную дробь.

Вычисления:

1) \(\frac{3}{7} \cdot \frac{2}{5} = \frac{3 \cdot 2}{7 \cdot 5} = \frac{6}{35}\)

2) \(\frac{2}{11} \cdot \frac{4}{5} = \frac{2 \cdot 4}{11 \cdot 5} = \frac{8}{55}\)

3) \(\frac{3}{5} \cdot \frac{6}{7} = \frac{3 \cdot 6}{5 \cdot 7} = \frac{18}{35}\)

4) \(\frac{1}{9} \cdot \frac{4}{7} = \frac{1 \cdot 4}{9 \cdot 7} = \frac{4}{63}\)

5) \(\frac{5}{6} \cdot \frac{1}{11} = \frac{5 \cdot 1}{6 \cdot 11} = \frac{5}{66}\)

6) \(\frac{3}{4} \cdot \frac{1}{8} = \frac{3 \cdot 1}{4 \cdot 8} = \frac{3}{32}\)

7) \(\frac{5}{7} \cdot \frac{5}{6} = \frac{5 \cdot 5}{7 \cdot 6} = \frac{25}{42}\)

8) \(\frac{3}{13} \cdot \frac{1}{2} = \frac{3 \cdot 1}{13 \cdot 2} = \frac{3}{26}\)

9) \(\frac{4}{5} \cdot \frac{8}{25} = \frac{4 \cdot 8}{5 \cdot 25} = \frac{32}{125}\)

10) \(\frac{2}{7} \cdot \frac{2}{5} = \frac{2 \cdot 2}{7 \cdot 5} = \frac{4}{35}\)

11) \(\frac{1}{4} \cdot \frac{3}{1} = \frac{1 \cdot 3}{4 \cdot 1} = \frac{3}{4}\)

12) \(\frac{2}{7} \cdot \frac{4}{7} = \frac{2 \cdot 4}{7 \cdot 7} = \frac{8}{49}\)

13) \(\frac{3}{14} \cdot \frac{3}{1} = \frac{3 \cdot 3}{14 \cdot 1} = \frac{9}{14}\)

14) \(\frac{2}{17} \cdot \frac{8}{1} = \frac{2 \cdot 8}{17 \cdot 1} = \frac{16}{17}\)

15) \(\frac{5}{14} \cdot \frac{3}{1} = \frac{5 \cdot 3}{14 \cdot 1} = \frac{15}{14}\)

16) \(\frac{4}{27} \cdot \frac{3}{1} = \frac{4 \cdot 3}{27 \cdot 1} = \frac{12}{27} = \frac{4}{9}\)

17) \(\frac{6}{7} \cdot 7 = \frac{6 \cdot 7}{7} = 6\)

18) \(\frac{3}{11} \cdot 22 = \frac{3 \cdot 22}{11} = 3 \cdot 2 = 6\)

19) \(15 \cdot \frac{4}{5} = \frac{15 \cdot 4}{5} = 3 \cdot 4 = 12\)

20) \(28 \cdot \frac{3}{7} = \frac{28 \cdot 3}{7} = 4 \cdot 3 = 12\)

21) \(\frac{2}{5} \cdot \frac{2}{9} = \frac{2 \cdot 2}{5 \cdot 9} = \frac{4}{45}\)

22) \(\frac{6}{7} \cdot \frac{2}{9} = \frac{6 \cdot 2}{7 \cdot 9} = \frac{12}{63} = \frac{4}{21}\)

23) \(\frac{8}{11} \cdot \frac{3}{4} = \frac{8 \cdot 3}{11 \cdot 4} = \frac{24}{44} = \frac{6}{11}\)

24) \(\frac{10}{8} \cdot \frac{9}{20} = \frac{10 \cdot 9}{8 \cdot 20} = \frac{90}{160} = \frac{9}{16}\)

25) \(\frac{14}{25} \cdot \frac{5}{7} = \frac{14 \cdot 5}{25 \cdot 7} = \frac{70}{175} = \frac{2}{5}\)

26) \(\frac{12}{55} \cdot \frac{5}{9} = \frac{12 \cdot 5}{55 \cdot 9} = \frac{60}{495} = \frac{4}{33}\)

27) \(\frac{1}{12} \cdot \frac{4}{5} = \frac{1 \cdot 4}{12 \cdot 5} = \frac{4}{60} = \frac{1}{15}\)

28) \(\frac{1}{6} \cdot \frac{3}{8} = \frac{1 \cdot 3}{6 \cdot 8} = \frac{3}{48} = \frac{1}{16}\)

Ответ: 6/35, 8/55, 18/35, 4/63, 5/66, 3/32, 25/42, 3/26, 32/125, 4/35, 3/4, 8/49, 9/14, 16/17, 15/14, 4/9, 6, 6, 12, 12, 4/45, 4/21, 6/11, 9/16, 2/5, 4/33, 1/15, 1/16.