Вопрос по математике:

Выполнить действие) 5) (3 1/4+1 1/6: 1 5/9) :2 2/7+5 1/9:7 2/3= 6) (1/6 (7/18+2/27):5/9)+3/11×21/5=

Выполним действия:

1. (3 1/4 + 1 1/6 : 1 5/9) : 2 2/7 + 5 1/9 : 7 2/3 = 4 2/3;

1) 1 1/6 : 1 5/9 = 7/6 : 14/9 = 7/6 * 9/14 = (7 * 3 * 3)/(3 * 2 * 7 * 2) = 3/4;

2) 3 1/4 + 3/4 = 13/4 + 3/4 = 16/4 = 4;

3) 4 : 2 2/7 = 4 : 16/7 = 4 * 7/16 = 7/4 = 1 3/4;

4) 5 1/9 : 7 2/3 = 46/9 : 23/3 = 46/9 * 3/23 = 2/3;

5) 4 + 2/3 = 4 2/3.

2. (1/6 * (7/18 + 2/27) : 5/9) + 3/11 * 21/5 = 1 563/1980.

1) 7/18 + 2/27 = (3 * 7 + 2 * 2)/54 = (21 + 4)/54 = 25/54;

2) 1/6 * 25/54 = 25/324;

3) 25/324 : 5/9 = 25/324 * 9/5 = 5/36;

4) 3/11 * 21/5 = (3 * 21)/(11 * 5) = 63/55;

5) 5/36 + 63/55 = (55 * 5 + 36 * 63)/(36 * 55) = (275 + 2268)/(36 * 55) = 2543/1980 = 1 563/1980.