Задача 1. Найдите значение выражения 1) \(\frac{2}{7} \cdot \frac{42}{5}\) 2) \(\frac{3}{16} : \frac{5}{8}\) 3) \(\frac{1}{10} \cdot \frac{39}{50}\) 4) \(\frac{1}{5} + \frac{3}{20}\)

Решение:

1. \(\frac{2}{7} \cdot \frac{42}{5} = \frac{2 \cdot 42}{7 \cdot 5} = \frac{2 \cdot 6}{5} = \frac{12}{5}\)
2. \(\frac{3}{16} : \frac{5}{8} = \frac{3}{16} \cdot \frac{8}{5} = \frac{3 \cdot 8}{16 \cdot 5} = \frac{3}{2 \cdot 5} = \frac{3}{10}\)
3. \(\frac{1}{10} \cdot \frac{39}{50} = \frac{1 \cdot 39}{10 \cdot 50} = \frac{39}{500}\)
4. \(\frac{1}{5} + \frac{3}{20} = \frac{1 \cdot 4}{5 \cdot 4} + \frac{3}{20} = \frac{4}{20} + \frac{3}{20} = \frac{7}{20}\)

Ответ: 1) \(\frac{12}{5}\), 2) \(\frac{3}{10}\), 3) \(\frac{39}{500}\), 4) \(\frac{7}{20}\).