6 5/9+3-7/12; 3 5/12-4/5+31/60; 8 7/15-5 3/4+6; Вычислите: 9 11/8-5 3/4-1 15/36+2 7/9

Question

Алина Кузьмина

Математика

16 января, 07:36

6 5/9+3-7/12; 3 5/12-4/5+31/60; 8 7/15-5 3/4+6; Вычислите: 9 11/8-5 3/4-1 15/36+2 7/9

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Егор Романов · Answer 1

1) 6 5/9 + 3 - 7/12 = (6 * 9 + 5) / 9 + 36/12 - 7/12 = (54 + 5) / 9 + 29/12 = 59/9 + 29/12 = 4 * 59/36 + 3 * 29/36 = (236 + 87) / 36 = 323/36;

2) 3 5/12 - 4/5 + 31/60 = (3 * 12 + 5) / 12 - 12 * 4/60 + 31/60 = 41/12 - 48/60 + 31/60 = 205/60 - 17/60 = 188/60 = 47/15;

3) 8 7/15 - 5 3/4 + 6 = (8 * 15 + 7) / 15 - (5 * 4 + 3) / 4 + 6 = (120 + 7) / 15 - (20 + 3) / 4 + 6 = 127/15 - 23/4 + 6 = 508/60 - 345/60 + 360/60 = (508 - 345 + 360) / 60 = 523/60;

4) 9 11/8 - 5 3/4 - 1 15/36 + 2 7/9 = (9 * 8 + 11) / 8 - (5 * 4 + 3) / 4 - (1 * 36 + 15) / 36 + (2 * 9 + 7) / 9 = 83/8 - 23/4 - 51/36 + 25/9 = 83/8 - 46/8 - 51/36 + 100/36 = 333/72 + 98/72 = 431/72.