е) \(\frac{19}{20}\) \(\cdot\) \(\frac{2}{19}\) + \(\frac{3}{7}\) \(\cdot\) \(\frac{19}{20}\) \(\cdot\) \(\frac{3}{7}\) = ...

1. Вынесем общий множитель \(\frac{19}{20}\) за скобки: \[\frac{19}{20} \cdot \frac{2}{19} + \frac{19}{20} \cdot \frac{3}{7} = \frac{19}{20} \cdot \left(\frac{2}{19} + \frac{3}{7}\right).\]
2. Приведем дроби к общему знаменателю: \[\frac{19}{20} \cdot \left(\frac{2 \cdot 7}{19 \cdot 7} + \frac{3 \cdot 19}{7 \cdot 19}\right) = \frac{19}{20} \cdot \left(\frac{14}{133} + \frac{57}{133}\right).\]
3. Сложим дроби: \[\frac{19}{20} \cdot \left(\frac{14 + 57}{133}\right) = \frac{19}{20} \cdot \frac{71}{133}.\]
4. Сократим дроби: \[\frac{19}{20} \cdot \frac{71}{133} = \frac{1}{20} \cdot \frac{71}{7} = \frac{71}{140}.\]

Ответ: \(\frac{71}{140}\)