выполните действие: 1) ( 3 целых 1/4 + 1 целая 1/6 : 1 целая 5/9) : 2 целых 2/7 + 5 целых 1/9 : 7 целых 2/3

Выполним действия:

(3 1/4 + 1 1/6 : 1 5/9) : 2 2/7 + 5 1/9 : 7 2/3 = 2 5/12;

1) 1 1/6 : 1 5/9 = (1 * 6 + 1)/6 : (1 * 9 + 5)/9 = 7/6 : 14/9 = 7/6 * 9/14 = (7 * 9)/(6 * 14) = (7 * 3 * 3)/(3 * 2 * 7 * 2) = 3/(2 * 2) = 3/4;

2) 3 1/4 + 3/4 = 3 + (1 + 3)/4 = 3 + 4/4 = 3 + 1 = 4;

3) 4 : 2 2/7 = 4 : (2 * 7 + 2)/7 = 4 : 16/7 = 4 * 7/16 = (4 * 7)/(4 * 4) = 7/4 = 1 3/4;

4) 5 1/9 : 7 2/3 = (5 * 9 + 1)/9 : (7 * 3 + 2)/3 = 46/9 : 23/3 = 46/9 * 3/23 = (2 * 23 * 3)/(3 * 3 * 23) = 2/3;

5) 1 3/4 + 2/3 = 1 + 3/4 + 2/3 = 1 + (3 * 3)/12 + (2 * 4)/12 = 1 + 9/12 + 8/12 = 1 + 17/12 = 1 + 1 5/12 = 2 5/12.