Вычислить (10 3/4-12:1 1/5)*4/9+2 1/6+3 1/4:5 1/5

Вычислим значение выражения:

(10 3/4 - 12 : 1 1/5) * 4/9 + 2 1/6 + 3 1/4 : 5 1/5 = 3 13/24;

1) 12 : 1 1/5 = 12 : (1 * 5 + 1)/5 = 12 : 6/5 = 12 * 5/6 = (12 * 5)/6 = (6 * 2 * 5)/6 = 2 * 5 = 10;

2) 10 3/4 - 10 = 10 - 10 + 3/4 = 3/4;

3) 3 1/4 : 5 1/5 = (3 * 4 + 1)/4 : (5 * 5 + 1)/5 = 13/4 : 26/5 = 13/4 * 5/26 = (13 * 5)/(4 * 26) = (13 * 5)/(4 * 13 * 2) = 5/(4 * 2) = 5/8;

4) 3/4 + 2 1/6 = 2 + 3/4 + 1/6 = 2 + (3 * 3)/12 + (1 * 2)/12 = 2 + 9/12 + 2/12 = 2 + 11/12 = 2 11/12;

5) 2 11/12 + 5/8 = 2 + 11/12 + 5/8 = 2 + (11 * 2)/24 + (5 * 3)/24 = 2 + 22/24 + 15/24 = 2 + 37/24 = 2 + 1 13/24 = 3 13/24.