Решение:
- \( 5 \cdot 84 = 12 \cdot 35 \) \( \Rightarrow 420 = 420 \).
- \( 4 \cdot 27 = 3 \cdot 36 \) \( \Rightarrow 108 = 108 \).
- \( 7 \cdot 60 = 15 \cdot 28 \) \( \Rightarrow 420 = 420 \).
- \( 9 \cdot 55 = 45 \cdot 11 \) \( \Rightarrow 495 = 495 \).
- \( 6 \cdot 65 = 13 \cdot 30 \) \( \Rightarrow 390 = 390 \).
- \( 4 \cdot 114 = 19 \cdot 24 \) \( \Rightarrow 456 = 456 \).
Ответ: 1) 5:12 = 35:84; 2) 4:3 = 36:27; 3) 7:15 = 28:60; 4) 9:45 = 11:55; 5) 6:13 = 30:65; 6) 4:19 = 24:114.