5/12•2 3/7+5/12•3 4/7

Question

Артём Ильин

Математика

26 июня, 04:48

5/12•2 3/7+5/12•3 4/7

+5

Ответы (1)

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Зека · Answer 1

5/12 * 2 3/7 + 5/12 * 3 4/7 = 5/12 * (2 3/7 + 3 4/7) = 2 1/2.

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

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

Или:

1) 5/12 * 2 3/7 = 5/12 * (2 * 7 + 3) / 7 = 5/12 * (14 + 3) / 7 = 5/12 * 17/7 = (5 * 17) / (12 * 7) = 85/84 = 1 1/84;

2) 5/12 * 3 4/7 = 5/12 * (3 * 7 + 4) / 7 = 5/12 * 25/7 = (5 * 25) / (12 * 7) = 125/84 = 1 41/84;

3) 1 1/84 + 1 41/84 = 1 + 1 + (1 + 41) / 84 = 2 42/84 = 2 42 / (42 * 2) = 2 1/2.