14. 1) \(\left(1+\frac{1}{4}\right)\cdot 2\) 2) \(\left(5+\frac{3}{14}\right)\cdot 7\) 3) \(\left(100+\frac{3}{20}\right)\cdot 4\) 4) \(\left(4+\frac{3}{4}\right)\cdot 4\) 5) \(\left(17+\frac{3}{5}\right)\cdot 10\) 6) \(\left(12+\frac{7}{18}\right)\cdot 9\)

1) \(\left(1+\frac{1}{4}\right)\cdot 2 = \left(\frac{4}{4}+\frac{1}{4}\right)\cdot 2 = \frac{5}{4}\cdot 2 = \frac{5}{2} = 2\frac{1}{2}\)
2) \(\left(5+\frac{3}{14}\right)\cdot 7 = 5\cdot 7 + \frac{3}{14}\cdot 7 = 35 + \frac{3}{2} = 35 + 1\frac{1}{2} = 36\frac{1}{2}\)
3) \(\left(100+\frac{3}{20}\right)\cdot 4 = 100\cdot 4 + \frac{3}{20}\cdot 4 = 400 + \frac{3}{5} = 400\frac{3}{5}\)
4) \(\left(4+\frac{3}{4}\right)\cdot 4 = 4\cdot 4 + \frac{3}{4}\cdot 4 = 16 + 3 = 19\)
5) \(\left(17+\frac{3}{5}\right)\cdot 10 = 17\cdot 10 + \frac{3}{5}\cdot 10 = 170 + 6 = 176\)
6) \(\left(12+\frac{7}{18}\right)\cdot 9 = 12\cdot 9 + \frac{7}{18}\cdot 9 = 108 + \frac{7}{2} = 108 + 3\frac{1}{2} = 111\frac{1}{2}\)