Вариант 1. Найдите произведения: 1) \(\frac{5}{2}\cdot\frac{1}{4}\); 2) \(\frac{1}{4}\cdot\frac{5}{4}\); 3) \(\frac{1}{6}\cdot\frac{6}{25}\); 4) \(\frac{14}{15}\cdot\frac{3}{8}\); 5) \(\frac{2}{3}\cdot\frac{4}{9}\); 6) \(\frac{1}{2}\cdot\frac{1}{3}\); 7) \(\frac{2}{7}\cdot\frac{7}{12}\).

1. Перемножаем числители и знаменатели: \(\frac{5}{2}\cdot\frac{1}{4}=\frac{5}{8}\).
2. \(\frac{1}{4}\cdot\frac{5}{4}=\frac{1\cdot5}{4\cdot4}=\frac{5}{16}\).
3. Сокращаем на 6: \(\frac{1}{6}\cdot\frac{6}{25}=\frac{1}{25}\).
4. Сокращаем 14 и 8 на 2, 3 и 15 на 3: \(\frac{14}{15}\cdot\frac{3}{8}=\frac{7}{5}\cdot\frac{1}{8}=\frac{7}{40}\).
5. \(\frac{2}{3}\cdot\frac{4}{9}=\frac{8}{27}\).
6. \(\frac{1}{2}\cdot\frac{1}{3}=\frac{1}{6}\).
7. Сокращаем 7: \(\frac{2}{7}\cdot\frac{7}{12}=\frac{2}{12}=\frac{1}{6}\).

Ответ: 1) \(\frac{5}{8}\); 2) \(\frac{5}{16}\); 3) \(\frac{1}{25}\); 4) \(\frac{7}{40}\); 5) \(\frac{8}{27}\); 6) \(\frac{1}{6}\); 7) \(\frac{1}{6}\).