\(\left\)\(6\frac{7}{20} - 15\frac{2}{5} \cdot \frac{1}{4} \right\) \(\cdot\) \(\frac{1}{10}\) + \(\frac{7}{20}\)

Решение:

Выполним действия по порядку:

1. 
   \[ 15\frac{2}{5} \cdot \frac{1}{4} = \frac{77}{5} \cdot \frac{1}{4} = \frac{77}{20} \]
   
2. 
   \[ 6\frac{7}{20} - \frac{77}{20} = \frac{127}{20} - \frac{77}{20} = \frac{50}{20} = \frac{5}{2} \]
   
3. 
   \[ \frac{5}{2} \cdot \frac{1}{10} = \frac{5}{20} = \frac{1}{4} \]
   
4. 
   \[ \frac{1}{4} + \frac{7}{20} = \frac{5}{20} + \frac{7}{20} = \frac{12}{20} = \frac{3}{5} \]
   

Ответ: \(\frac{3}{5}\)