1. (6 баллов) Выполните действия: a) \(\frac{5}{7}\) \(\cdot\) \(\frac{6}{5}\); б) \(\frac{6}{25}\) \(\cdot\) \(\frac{5}{18}\); в) \(\frac{4}{7}\) \(\cdot\) 2; г) \(\frac{5}{9}\) \(\cdot\) \(\frac{10}{27}\); д) \(\frac{12}{13}\) : 6; е) 4 : \(\frac{6}{13}\)

Решим примеры на умножение и деление дробей.

1. а) \(\frac{5}{7}\) \(\cdot\) \(\frac{6}{5}\) = \(\frac{5 \cdot 6}{7 \cdot 5}\) = \(\frac{30}{35}\) = \(\frac{6}{7}\)

   Сократили дробь на 5.

2. б) \(\frac{6}{25}\) \(\cdot\) \(\frac{5}{18}\) = \(\frac{6 \cdot 5}{25 \cdot 18}\) = \(\frac{30}{450}\) = \(\frac{1}{15}\)

   Сократили дробь на 30.

3. в) \(\frac{4}{7}\) \(\cdot\) 2 = \(\frac{4 \cdot 2}{7}\) = \(\frac{8}{7}\) = 1\(\frac{1}{7}\)

4. г) \(\frac{5}{9}\) \(\cdot\) \(\frac{10}{27}\) = \(\frac{5 \cdot 10}{9 \cdot 27}\) = \(\frac{50}{243}\)

5. д) \(\frac{12}{13}\) : 6 = \(\frac{12}{13}\) : \(\frac{6}{1}\) = \(\frac{12 \cdot 1}{13 \cdot 6}\) = \(\frac{12}{78}\) = \(\frac{2}{13}\)

   Сократили дробь на 6.

6. е) 4 : \(\frac{6}{13}\) = \(\frac{4}{1}\) : \(\frac{6}{13}\) = \(\frac{4 \cdot 13}{1 \cdot 6}\) = \(\frac{52}{6}\) = \(\frac{26}{3}\) = 8\(\frac{2}{3}\)

   Сократили дробь на 2.

Ответ: а) \(\frac{6}{7}\); б) \(\frac{1}{15}\); в) 1\(\frac{1}{7}\); г) \(\frac{50}{243}\); д) \(\frac{2}{13}\); е) 8\(\frac{2}{3}\)