Решите образцы по действиям :а) 1/4 * 4 3/4 * 16/57

а) 1) 4 3/4 + 1 2/3 = 4 + 1 + 3/4 + 2/3 = 5 + (3 * 3)/12 + (2 * 4)/12 = 5 + 9/12 + 8/12 = 5 + 17/12 = 5 + 1 5/12 = 6 5/12;

2) 1/4 * 4 3/4 = 1/4 * 19/4 = 19/16 = 1 3/16;

3) 19/16 * 16/57 = (19 * 16)/(16 * 19 * 3) = 1/3;

4) 6 5/12 * 16/21 = 77/12 * 16/21 = (7 * 11 * 4 * 4)/(4 * 3 * 7 * 3) = 44/9 = 4 8/9;

5) 1/3 + 4 8/9 = 3/9 + 4 + 8/9 = 4 + 12/9 = 4 + 3/9 = 4 1/3;

6) 4 1/3 + 2/27 = 4 + 9/27 + 2/27 = 4 11/27;

7) 4 11/27 + 4 1/2 = 8 + (11 * 2)/54 + (1 * 27)/54 = 8 + 22/54 + 27/54 = 8 49/54.

б) 1) 4/5 + 1/6 = 24/30 + 5/30 = 29/30;

2) 23 2/3 - 15 5/9 = 8 + 6/9 - 5/9 = 8 1/9;

3) 29/30 * 8 1/9 = 29/30 * 73/9 = (29 * 73)/(30 * 9) = 2117/270 = 7 227/270;

4) 2117/270 * 45/58 = (29 * 73 * 45)/(45 * 6 * 29 * 2) = 73/12 = 6 1/12;

5) 6 1/12 - 1/2 = 6 1/12 - 6/12 = 6 - 5/12 = 5 7/12.