выполните действия: 1) 5 целых 1/6 : 31 + (3 целых 1/4 + 2 целых 1/6) : 2 целых 3/5 - 2/3 : 4/9

Выполним действия:

5 1/6 : 31 + (3 1/4 + 2 1/6) : 2 3/5 - 2/3 : 4/9 = 3/4.

1) 5 1/6 : 31 = (5 * 6 + 1)/6 : 31 = 31/6 : 31 = 31/6 * 1/31 = 31/(6 * 31) = 1/6;

2) 3 1/4 + 2 1/6 = 3 + 2 + 1/4 + 1/6 = 5 + (1 * 3)/12 + (1 * 2)/12 = 5 + 3/12 + 2/12 = 5 + (3 + 2)/12 = 5 5/12;

3) 5 5/12 : 2 3/5 = (5 * 12 + 5)/12 : (2 * 5 + 3)/5 = 65/12 : 13/5 = 65/12 * 5/13 = (13 * 5 * 5)/(12 * 13) = (5 * 5)/12 = 25/12 = 2 1/12;

4) 2/3 : 4/9 = 2/3 * 9/4 = (2 * 3 * 3)/(3 * 2 * 2) = 3/2 = 1 1/2;

5) 1/6 + 2 1/12 = 2 + 1/12 + 1/6 = 2 + 1/12 + 2/12 = 2 + 3/12 = 2 + 1/4 = 2 1/4;

6) 2 1/4 - 1 1/2 = 2 - 1 + 1/4 - 1/2 = 1 + 1/4 - 2/4 = 1 - 1/4 = 4/4 - 1/4 = 3/4.