1 целая 4/11 разделять 3 целых 1/7 разделять 3 целых 4/7

1 4/11 : 3 1/7 : 3 4/7 = 147/1210.

1) 1 4/11 : 3 1/7 = (1 * 11 + 4)/11 : (3 * 7 + 1)/7 = (11 + 4)/11 : (21 + 1)/7 = 15/11 : 22/7 = 15/11 * 7/22 = (15 * 7)/(11 * 22) = 105/242;

2) 105/242 : 3 4/7 = 105/242 : (3 * 7 + 4)/7 = 105/242 : (21 + 4)/7 = 105/242 : 25/7 = 105/242 * 7/25 = (105 * 7)/(242 * 25) = (5 * 21 * 7)/(242 * 5 * 5) = (21 * 7)/(242 * 5) = 147/1210.

Решим сходственный пример:

3 2/7 : 1 3/5 : 3/4 = 2 31/42.

1) 3 2/7 : 1 3/5 = (3 * 7 + 2)/7 : (1 * 5 + 3)/5 = 23/7 : 8/5 = 23/7 * 5/8 = 115/56;

2) 115/56 : 3/4 = 115/56 * 4/3 = (115 * 4)/(4 * 14 * 3) = 115/(14 * 3) = 115/42 = 2 31/42.