К) $$6\frac{1}{10}·2,391-0,109·1\frac{5}{6}-1\frac{5}{6}·2,391+0,109·6\frac{1}{10}$$

К) Выполним действия:

1) $$6\frac{1}{10} = \frac{6 \cdot 10 + 1}{10} = \frac{61}{10}$$

2) $$\frac{61}{10} \cdot 2,391 = \frac{61}{10} \cdot \frac{2391}{1000} = \frac{145851}{10000}$$

3) $$1\frac{5}{6} = \frac{1 \cdot 6 + 5}{6} = \frac{11}{6}$$

4) $$0,109 \cdot \frac{11}{6} = \frac{109}{1000} \cdot \frac{11}{6} = \frac{1199}{6000}$$

5) $$\frac{11}{6} \cdot 2,391 = \frac{11}{6} \cdot \frac{2391}{1000} = \frac{26301}{6000}$$

6) $$0,109 \cdot \frac{61}{10} = \frac{109}{1000} \cdot \frac{61}{10} = \frac{6649}{10000}$$

7) $$\frac{145851}{10000} - \frac{1199}{6000} - \frac{26301}{6000} + \frac{6649}{10000} = \frac{145851 \cdot 6}{10000 \cdot 6} - \frac{1199 \cdot 10}{6000 \cdot 10} - \frac{26301 \cdot 10}{6000 \cdot 10} + \frac{6649 \cdot 6}{10000 \cdot 6} = \frac{875106}{60000} - \frac{11990}{60000} - \frac{263010}{60000} + \frac{39894}{60000} = \frac{875106 - 11990 - 263010 + 39894}{60000} = \frac{640000}{60000} = \frac{64}{6} = \frac{32}{3} = 10\frac{2}{3}$$

Ответ: $$10\frac{2}{3}$$