225. Сократите: 1) 4.5/25.6; 2) 8.13/39.2; 3) 3.38/19.27; 4) 2·3·4·5/4·5·6·7; 5) 6·7·8·9·10/7·9·11·12; 6) 3·16·8·3/27; 7) 9·13+9·2/54·13; 8) 27·15-7·27/9·15-9·11; 9) 24·2+6·24/60·7-5·60

Для сокращения дробей необходимо разложить числитель и знаменатель на простые множители и сократить одинаковые множители.

1. 4.5/25.6 = (4 × 5)/(25 × 6) = (2 × 2 × 5)/(5 × 5 × 2 × 3) = (2 × 2 × 5)/(5 × 5 × 2 × 3) = 2/(5 × 3) = 2/15

   Ответ: 2/15

2. 8.13/39.2 = (8 × 13)/(39 × 2) = (2 × 2 × 2 × 13)/(3 × 13 × 2) = (2 × 2 × 2 × 13)/(3 × 13 × 2) = (2 × 2)/3 = 4/3

   Ответ: 4/3

3. 3.38/19.27 = (3 × 38)/(19 × 27) = (3 × 2 × 19)/(19 × 3 × 3 × 3) = (3 × 2 × 19)/(19 × 3 × 3 × 3) = 2/(3 × 3 × 3) = 2/27

   Ответ: 2/27

4. (2 × 3 × 4 × 5)/(4 × 5 × 6 × 7) = (2 × 3 × 4 × 5)/(4 × 5 × 2 × 3 × 7) = (2 × 3 × 4 × 5)/(4 × 5 × 2 × 3 × 7) = 1/7

   Ответ: 1/7

5. (6 × 7 × 8 × 9 × 10)/(7 × 9 × 11 × 12) = (6 × 7 × 8 × 9 × 10)/(7 × 9 × 11 × 6 × 2) = (6 × 7 × 8 × 9 × 10)/(7 × 9 × 11 × 6 × 2) = (8 × 10)/(11 × 2) = (4 × 2 × 10)/(11 × 2) = (4 × 2 × 10)/(11 × 2) = (4 × 10)/11 = 40/11

   Ответ: 40/11

6. (3 × 16 × 8 × 3)/27 = (3 × 16 × 8 × 3)/(3 × 3 × 3) = (3 × 16 × 8 × 3)/(3 × 3 × 3) = (16 × 8)/3 = (2 × 2 × 2 × 2 × 2 × 2)/(3) = 128/3

   Ответ: 128/3

7. (9 × 13 + 9 × 2)/(54 × 13) = (9 × (13 + 2))/(54 × 13) = (9 × 15)/(6 × 9 × 13) = (9 × 3 × 5)/(6 × 9 × 13) = (3 × 5)/(6 × 13) = (3 × 5)/(2 × 3 × 13) = 5/(2 × 13) = 5/26

   Ответ: 5/26

8. (27 × 15 - 7 × 27)/(9 × 15 - 9 × 11) = (27 × (15 - 7))/(9 × (15 - 11)) = (27 × 8)/(9 × 4) = (3 × 9 × 2 × 4)/(9 × 4) = (3 × 9 × 2 × 4)/(9 × 4) = (3 × 2) = 6

   Ответ: 6

9. (24 × 2 + 6 × 24)/(60 × 7 - 5 × 60) = (24 × (2 + 6))/(60 × (7 - 5)) = (24 × 8)/(60 × 2) = (2 × 12 × 8)/(2 × 30) = (2 × 12 × 8)/(2 × 30) = (12 × 8)/30 = (4 × 3 × 8)/(10 × 3) = (4 × 3 × 8)/(10 × 3) = (4 × 8)/10 = 32/10 = 16/5

   Ответ: 16/5