Найдите значение выражения: 1) 15 4/9 - 4 4/9 * 3 3/8; 2) 81/88 * (6 - 1 13/15 * 1 19/21); 3) (5 1/16 - 1 1/8) (5/6 3/14); 4) 5 1/16 - 1 1/8 * (5/6 3/14).

Question

Татьяна Семенова

Математика

4 мая, 13:01

Найдите значение выражения: 1) 15 4/9 - 4 4/9 * 3 3/8; 2) 81/88 * (6 - 1 13/15 * 1 19/21); 3) (5 1/16 - 1 1/8) (5/6 3/14); 4) 5 1/16 - 1 1/8 * (5/6 3/14).

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Даниил Савин · Answer 1

1. 15 4/9 - 4 4/9 * 3 3/8 = 4/9;

1) 4 4/9 * 3 3/8 = 40/9 * 27/8 = 5/1 * 3/1 = 15;

2) 15 4/9 - 15 = 4/9.

Ответ: 4/9.

2. 81/88 * (6 - 1 13/15 * 1 19/21) = 2 1/4;

1) 1 13/15 * 1 19/21 = 28/15 * 40/21 = 4/3 * 8/3 = 32/9 = 3 5/9;

2) 6 - 3 5/9 = 54/9 - 32/9 = 22/9 = 2 4/9;

3) 81/88 * 2 4/9 = 81/88 * 22/9 = 9/4 * 1/1 = 9/4 = 2 1/4.

Ответ: 2 1/4.

3. (5 1/16 - 1 1/8) (5/6 + 3/14) = 4 1/8;

1) 5 1/16 - 1 1/8 = 81/16 - 9/8 = (81 * 1 - 9 * 2) / 16 = 63/16;

2) 5/6 + 3/14 = (5 * 7 + 3 * 3) / 42 = 44/42 = 22/21 = 1 1/21;

3) 63/16 * 1 1/21 = 63/16 * 22/21 = 3/8 * 11/1 = 33/8 = 4 1/8.

Ответ: 4 1/8.

4. 5 1/16 - 1 1/8 * (5/6 + 3/14) = 4 7/48;

1) 5/6 + 3/14 = (5 * 7 + 3 * 3) / 42 = 44/42 = 22/21 = 1 1/21;

2) 1 1/8 * 1 1/21 = 9/8 * 22/21 = 1/4 * 11/3 = 11/12;

3) 5 1/16 - 11/12 = 81/16 - 11/12 = (81 * 3 - 11 * 4) / 48 = (243 - 44) / 48 = 199/48 = 4 7/48.

Ответ: 4 7/48.