Вычислите:(-6 1/7+5 3/4): 11/14-(-3 3/4+1 5/6):1/6

Произведем вычисления по действиям:

1. - 6 1/7 + 5 3/4 = -(6 · 7 + 1)/7 + (5 · 4 + 3)/4 =

-43/7 + 23/4 = -43 · 4/7 · 4 + 23 · 7/4 · 7 = -172/28 + 161/28 = -11/28;

2. -11/28 : 11/14 = -11/28 · 14/11 = -1/2;

3. -3 3/4 + 1 5/6 = -(3 · 4 + 3)/4 + (1 · 6 + 5)/6 = -15/4 + 11/6 =

-15 · 3/4 · 3 + 11 · 2/6 · 2 = -45/12 + 22/12 = -23/12;

4. -23/12 : 1/6 = -23/12 · 6/1 = -23/2;

5. -1/2 - (-23/2) = -1/2 + 23/2 = 22/2 = 11.