А) 2 4/15+1 5/6 б) 4 7/10-1 8/15 в) 8 3/8 - (5 5/6+1 3/4)

Question

Иван Грачев

Математика

28 июня, 18:21

А) 2 4/15+1 5/6 б) 4 7/10-1 8/15 в) 8 3/8 - (5 5/6+1 3/4)

+4

Ответы (1)

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Варвара Орехова · Answer 1

Первый пример.

2 4/15 + 1 5/6 = 4 1/10;

2 4/15 + 1 5/6 = 2 * 15 + 4/15 + 1 * 6 + 5/6 = 34/15 + 11/6 = 34 * 6/15 * 6 + 11 * 15/6 * 15 = 204/90 + 165/90 = 204 + 165/90 = 369/90 = 41 * 9/10 * 9 = 41/10 = 1 + 4 * 10/10 = 4 1/10.

Второй пример.

4 7/10 - 1 8/15 = 3 1/6;

4 7/10 - 1 8/15 = 4 * 10 + 7/10 - 1 * 15 + 8/15 = 47/10 - 23/15 = 47 * 15/10 * 15 - 23 * 10/15 * 10 = 705/150 - 230/150 = 705 - 230/150 = 475/150 = 19 * 25/6 * 25 = 19/6 = 1 + 3 * 6/6 = 3 1/6.

Третий пример.

8 3/8 - (5 5/6 + 1 3/4) = 19/24;

5 5/6 + 1 3/4 = 5 * 6 + 5/6 + 1 * 4 + 3/4 = 35/6 + 7/4 = 35 * 4/6 * 4 + 7 * 6/4 * 6 = 140/24 + 42/24 = 140 + 42/24 = 182/24 = 91 * 2/12 * 2 = 91/12 = 7 + 7*12/12 = 7 7/12;

8 3/8 - 7 7/12 = 8 * 8 + 3/8 - 7 * 12 + 7/12 = 67/8 - 91/12 = 67 * 12/8 * 12 - 91 * 8/12 * 8 = 804/96 - 728/96 = 804 - 728/96 = 76/96 = 19 * 4/24 * 4 = 19/24.