\( \left( \frac{6}{20} - 15 \frac{1}{5} \right) \cdot \frac{1}{7} + \frac{1}{10} - \frac{7}{20} \)

Решение:

Выполним действия по порядку:

1. \( 15 \frac{1}{5} = \frac{76}{5} \)
2. \( \frac{6}{20} - \frac{76}{5} = \frac{3}{10} - \frac{76}{5} = \frac{3}{10} - \frac{152}{10} = -\frac{149}{10} \)
3. \( -\frac{149}{10} \cdot \frac{1}{7} = -\frac{149}{70} \)
4. \( -\frac{149}{70} + \frac{1}{10} = -\frac{149}{70} + \frac{7}{70} = -\frac{142}{70} = -\frac{71}{35} \)
5. \( -\frac{71}{35} - \frac{7}{20} = \frac{-71 \cdot 4 - 7 \cdot 7}{140} = \frac{-284 - 49}{140} = -\frac{333}{140} \)

Ответ: \( -\frac{333}{140} \).