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)

Решение:

1. \( \frac{4 \cdot 5}{25 \cdot 6} = \frac{4 \cdot 5}{(5 \cdot 5) \cdot (2 \cdot 3)} = \frac{2 \cdot 2 \cdot 5}{5 \cdot 5 \cdot 2 \cdot 3} = \frac{2}{5 \cdot 3} = \frac{2}{15} \)
2. \( \frac{8 \cdot 13}{39 \cdot 2} = \frac{(4 \cdot 2) \cdot 13}{(3 \cdot 13) \cdot 2} = \frac{4 \cdot 2 \cdot 13}{3 \cdot 13 \cdot 2} = \frac{4}{3} \)
3. \( \frac{3 \cdot 38}{19 \cdot 27} = \frac{3 \cdot (2 \cdot 19)}{19 \cdot (3 \cdot 9)} = \frac{3 \cdot 2 \cdot 19}{19 \cdot 3 \cdot 9} = \frac{2}{9} \)
4. \( \frac{2 \cdot 3 \cdot 4 \cdot 5}{4 \cdot 5 \cdot 6 \cdot 7} = \frac{2 \cdot 3 \cdot 4 5}{4 5 (2 3) 7} = \frac{1}{7} \)
5. \( \frac{6 \cdot 7 \cdot 8 \cdot 9 \cdot 10}{7 \cdot 9 \cdot 11 \cdot 12} = \frac{(2 3) 7 8 9 10}{7 9 11 (3 4)} = \frac{2 3 7 8 9 10}{7 9 11 3 4} = \frac{2 8 10}{11 4} = \frac{2 2 4 10}{11 4} = \frac{40}{11} \)
6. \( \frac{3 16 - 8 3}{27} = \frac{3 (2 8) - 8 3}{27} = \frac{(3 8 2) - (8 3)}{27} = \frac{48 - 24}{27} = \frac{24}{27} = \frac{8}{9} \)
7. \( \frac{9 13 + 9 2}{54 13} = \frac{9(13+2)}{54 13} = \frac{9 15}{(6 9) 13} = \frac{15}{6 13} = \frac{3 5}{(2 3) 13} = \frac{5}{2 13} = \frac{5}{26} \)
8. \( \frac{27 15 - 7 27}{9 15 - 9 11} = \frac{27(15-7)}{9(15-11)} = \frac{(3 9) 8}{9 4} = \frac{3 9 8}{9 4} = \frac{3 8}{4} = 3 2 = 6 \)
9. \( \frac{24 2 + 6 24}{60 7 - 5 60} = \frac{24(2+6)}{60(7-5)} = \frac{24 8}{60 2} = \frac{24 8}{120} = \frac{192}{120} = \frac{192 \div 24}{120 \div 24} = \frac{8}{5} \)

Ответ: 1) \( \frac{2}{15} \); 2) \( \frac{4}{3} \); 3) \( \frac{2}{9} \); 4) \( \frac{1}{7} \); 5) \( \frac{40}{11} \); 6) \( \frac{8}{9} \); 7) \( \frac{5}{26} \); 8) 6; 9) \( \frac{8}{5} \).