Вычеслите 1) 1/2-1/3-1/42) 2/3-1/4-1/63) 1/8-1/4-1/2

Question

Дмитрий Степанов

Математика

16 октября, 07:56

Вычеслите 1) 1/2-1/3-1/42) 2/3-1/4-1/63) 1/8-1/4-1/2

+3

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Оливия Дьяконова · Answer 1

№1.

1/2 - 1/3 - 1/4 = 3/6 - 2/6 - 1/4 = 1/6 - 1/4 = 2/12 - 3/12 = - 1/12.

1) 1/2 - 1/3 = (1 * 3) / (2 * 3) - (1 * 2) / (3 * 2) = 3/6 - 2/6 = 1/6;

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

Ответ: 1/2 - 1/3 - 1/4 = - 1/12.

№2.

2/3 - 1/4 - 1/6 = 8/12 - 3/12 - 1/6 = 5/12 - 1/6 = 5/12 - 2/12 = 3/12 = 1/4.

1) 2/3 - 1/4 = (2 * 4) / (3 * 4) - (1 * 3) / (4 * 3) = 8/12 - 3/12 = 5/12;

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

Ответ: 2/3 - 1/4 - 1/6 = 1/4.

№3

1/8 - 1/4 - 1/2 = 1/8 - 2/8 - 1/2 = - 1/8 - 1/2 = - 1/8 - 4/8 = - 5/8.

1) 1/8 - 1/4 = 1/8 - (1 * 2) / (4 * 2) = 1/8 - 2/8 = - 1/8;

2) - 1/8 - 1/2 = - 1/8 - (1 * 4) / (2 * 4) = - 1/8 - 4/8 = - 5/8.

Ответ: 1/8 - 1/4 - 1/2 = - 5/8.