Выполнить действие: 1). (1/3-5/16) : (1/6-1/8) = ? 2). (5/7-2/3) : (4/9-5/12) = ? 3) (5/12+5/8) : (1/4+3/8) = ?

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Гоша

Математика

25 августа, 15:14

Выполнить действие: 1). (1/3-5/16) : (1/6-1/8) = ? 2). (5/7-2/3) : (4/9-5/12) = ? 3) (5/12+5/8) : (1/4+3/8) = ?

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Masik · Answer 1

1.

(1/3 - 5/16) : (1/6 - 1/8) = 1/2.

1). 1/3 - 5/16 = (1 * 16) / (3 * 16) - (5 * 3) / (16 * 3) = 16/48 - 15/48 = 1/48;

2). 1/6 - 1/8 = (1 * 8) / (6 * 8) - (1 * 6) / (8 * 6) = 8/48 - 6/48 = 2/48 = 1/24;

3) 1/48 : 1/24 = 1/48 * 24/1 = 24/48 = 1/2.

2.

(5/7 - 2/3) : (4/9 - 5/12) = 1 5/7.

1). 5/7 - 2/3 = (5 * 3) / (7 * 3) - (2 * 7) / (3 * 7) = 15/21 - 14/21 = 1/21;

2). 4/9 - 5/12 = (4 * 12) / (9 * 12) - (5 * 9) / (12 * 9) = 48/108 - 45/108 = 3/108 = 1/36;

3). 1/21 : 1/36 = 1/21 * 36/1 = 36/21 = 12/7 = 1 5/7.

3.

(5/12 + 5/8) : (1/4 + 3/8) = 1 2/3.

1). 5/12 + 5/8 = (5 * 2) / (12 * 2) + (5 * 3) / (8 * 3) = 10/24 + 15/24 = 25/24 = 1 1/24;

2). 1/4 + 3/8 = 2/8 + 3/8 = 5/8;

3). 25/24 : 5/8 = 25/24 * 8/5 = 5/3 * 1 = 5/3 = 1 2/3.