5/6 - (7/15 - 17/20) : 1 1/45 = 1 целая 5/24
1) 7/15 - 17/20 = 28/60 - 51/60 = - 23/60
2) - 23/60 : 1 1/45 = - 23/60 : 46/45 = - 23/60 * 45/46 = - (1*3)/(4*2) =
= - 3/8
3) 5/6 - (- 3/8) = 20/24 + 9/24 = 29/24 = 1 целая 5/24
Пояснения:
7/15 = 28/60 - доп.множ. 4
17/20 = 51/60 - доп.множ. 3
5/6 = 20/24 - доп.множ. 4
3/8 = 9/24 - доп.множ. 3
- 5/9 - 1 43/72 : (7/24 + 3/16) = - 3 целых 8/9
1) 7/24 + 3/16 = 14/48 + 9/48 = 23/48
2) 1 43/72 : 23/48 = 115/72 * 48/23 = (115*2)/(3*23) = 230/69 = 3 целых 23/69 = 3 целых 1/3
3) - 5/9 - 3 1/3 = - 5/9 - 3 3/9 = - 3 целых 8/9
Пояснения:
7/24 = 14/48 - доп.множ. 2
3/16 = 9/48 - доп.множ. 3
1 целая 43/72 = (1*72+43)/72 = 115/72
1/3 = 3/9 - доп.множ. 3