Вычислите (3/4-1/2) * 5 (5/7+1/21) : 2 (7/10-1/5) : 3 (1/4-1/12) * 5 (1/4+1/6) : 10 (5/6-1/4) : 7

Question

Дмитрий Сергеев

Математика

7 июня, 11:58

Вычислите (3/4-1/2) * 5 (5/7+1/21) : 2 (7/10-1/5) : 3 (1/4-1/12) * 5 (1/4+1/6) : 10 (5/6-1/4) : 7

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Пётр Верещагин · Answer 1

(3/4 - 1/2) * 5 = 1/4.

1). 3/4 - 1/2 = 3/4 - (1 * 2) / (2 * 2) = 3/4 - 2/4 = 1/4;

2) 1/4 * 5 = (1 * 5) / (4 * 5) = 5/20 = 1/4.

(5/7 + 1/21) : 2 = 8/21.

1). 5/7 + 1/21 = (5 * 3) / (7 * 3) + 1/21 = 15/21 + 1/21 = 16/21;

2). 16/21 : 2 = 16/21 : 2/1 = 16/21 * 1/2 = (16 * 1) / (21 * 2) = 16/42 = 8/21.

(7/10 - 1/5) : 3 = 1/6.

1). 7/10 - 1/5 = 7/10 - (1 * 2) / (5 * 2) = 7/10 - 2/10 = 5/10 = 1/2;

2). 1/2 : 3 = 1/2 * 1/3 = 1/6.

(1/4 - 1/12) * 5 = 5/6.

1). 1/4 - 1/12 = (1 * 3) / (4 * 3) - 1/12 = 3/12 - 1/12 = 2/12 = 1/6;

2). 1/6 * 5 = 5/6.

(1/4 + 1/6) : 10 = 1/24.

1). 1/4 + 1/6 = (1 * 3) / (4 * 3) + (1 * 2) / (6 * 2) = 3/12 + 2/12 = 5/12;

2). 5/12 : 10 = 5/12 * 1/10 = 5/120 = 1/24.

(5/6 - 1/4) : 7 = 12.

1). 5/6 - 1/4 = (5 * 2) / (6 * 2) - (1 * 3) / (4 * 3) = 10/12 - 3/12 = 7/12;

2). 7/12 : 7 = 7/12 * 1/7 = 12/1 = 12.