Вычислите.а) (-2 5/6+3 5/24):4 1/2; б)(1 2/3+2 5/9):(-21 3/4+7 1/2).

Вычислим:

1. (-2 5/6 + 3 5/24) : 4 1/2 = 1/12;

1) -2 5/6 + 3 5/24 = 3 5/24 - 2 5/6 = 3 - 2 + 5/24 - 5/6 = 1 + 5/24 - (5 * 4)/24 = 1 + 5/24 - 20/24 = 1 + (5 - 20)/24 = 1 - 15/24 = 24/24 - 15/24 = (24 - 15)/24 = 9/24 = 3/8;

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

2. (1 2/3 + 2 5/9) : (-21 3/4 + 7 1/2) = -56/153;

1) 1 2/3 + 2 5/9 = 1 + 2 + 6/9 + 5/9 = 3 + 11/9 = 3 + 1 2/3 = 4 2/3;

2) -21 3/4 + 7 1/2 = -21 + 7 - 3/4 + 1/2 = -14 - 3/4 + 2/4 = -14 - 1/4 = -14 1/4;

3) 4 2/3 : (-14 1/4) = 14/3 : (-57/4) = -14/3 * 4/51 = -56/153.