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.