5/19 (3 4/5 * 5 1/3+4 2/3*3,8) / 0,005

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Эхой

Математика

25 ноября, 15:22

5/19 (3 4/5 * 5 1/3+4 2/3*3,8) / 0,005

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Akel · Answer 1

5/19 * (3 4/5 * 5 1/3 + 4 2/3 * 3,8) : 0,005 = 1377 7/9.

1) 3 4/5 * 5 1/3 = (3 * 5 + 4) / 5 * (5 * 3 + 1) / 3 = 19/5 * 16/3 = (19 * 16) / (5 * 3) = 304/15 = 20 4/15;

2) 4 2/3 * 3,8 = (4 * 3 + 2) / 3 * 38/10 = 14/3 * 38/10 = (14 * 2 * 19) / (3 * 2 * 15) = 266/45 = 5 41/45;

3) 20 4/15 + 5 41/45 = 20 + 5 + 12/45 + 41/45 = 25 + 53/45 = 25 + 1 8/45 = 26 8/45;

4) 5/19 * 26 8/45 = 5/19 * (26 * 45 + 8) / 45 = 5/19 * 1778/45 = (5 * 19 * 62) / (19 * 5 * 9) = 62/9 = 6 8/9;

5) 6 8/9 : 0,005 = 62/9 : 5/1000 = 62/9 * 1000/5 = 62000/45 = 12400/9 = 1377 7/9.