Вычислите : а)55\48 : (11\16 + 3\32 ) - 14\15

а)

1) 11/16 + 3/32 = (11 * 2 + 3 * 1)/32 = (22 + 3)/32 = 25/32;

2) 55/48 : 25/32 = 55/48 * 32/25 = 11/3 * 2/5 = 22/15 = 1 7/15;

3) 14/15 * 5/7 = 2/3;

4) 1 7/15 - 2/3 = 22/15 - 2/3 = (22 * 1 - 2 * 5)/15 = (22 - 10)/15 = 12/15 = 4/5.

Ответ: 4/5.

б)

1) 1/12 + 1/13 = (1 * 13 + 1 * 12)/156 = (13 + 12)/156 = 25/156;

2) (25/156) ^ 2 = 625/24336;

3) 1/12 - 1/13 = (1 * 13 - 1 * 12)/156 = (13 - 12)/156 = 1/156;

4) (1/156)^2 = 1/24336;

5) (1/10)^3 = 1/1000;

6) 625/24336 : 1/24336 = 625/24336 * 24336/1 = 625;

7) 625 * 1/1000 = 625/1000 = 0,625.

Ответ: 0,625.