Решите пример : (9 - 2 ЦЕЛЫХ 2 / 15 * 3 целых1/8) * 9/14=

Question

Кира Тихонова

Математика

29 марта, 08:38

Решите пример : (9 - 2 ЦЕЛЫХ 2 / 15 * 3 целых1/8) * 9/14=

+1

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Polli · Answer 1

(9 - 2 2/15 * 3 1/8) * 9/14 = 1 1/2.

1) 2 2/15 * 3 1/8 = (2 * 15 + 2) / 15 * (3 * 8 + 1) / 8 = (30 + 2) / 15 * (24 + 1) / 8 = 32/15 * 25/8 = (32 * 25) / (15 * 8) = (8 * 4 * 5 * 5) / (5 * 3 * 8) = (4 * 5) / 3 = 20/3 = 6 (20 - 6 * 3) / 3 = 6 (20 - 18) / 3 = 6 2/3;

2) 9 - 6 2/3 = 9 - 6 - 2/3 = 3 - 2/3 = 2 + 1 - 2/3 = 2 + 3/3 - 2/3 = 2 + (3 - 2) / 3 = 2 + 1/3 = 2 1/3;

3) 2 1/3 * 9/14 = (2 * 3 + 1) / 3 * 9/14 = (6 + 1) / 3 * 9/14 = 7/3 * 9/14 = (7 * 9) / (3 * 14) = (7 * 3 * 3) / (3 * 7 * 2) = 3/2 = 1 (3 - 1 * 2) / 2 = 1 (3 - 2) / 2 = 1 1/2.