When it comes to simplifying ratios, I’ve found some helpful ways to avoid common mistakes. Here are a few strategies:

1. Factor Method: Break down the numbers in the ratio into their prime factors. This helps you see common factors more easily. For example, with the ratio 12:16, you can factor it into $2^2 \times 3$ and $2^4$.

2. Divide by the GCD: Find the greatest common divisor (GCD) of the two numbers and divide both by it. For 8 and 12, the GCD is 4. So, you would do $8 \div 4$ and $12 \div 4$, which gives you $2:3$.

3. Double-check Your Work: Always go back and check if both parts of the ratio are simplified correctly. Make sure they still have the same relationship.

4. Practice: The more problems you work on, the better you get at spotting mistakes.

Using these techniques can really help!