When changing between percentages and ratios, it’s easy to make mistakes that can cause confusion. Here are some common problems to watch out for:

1. Misunderstanding Percentages:

   • Percentages show parts out of 100. For example, 25% means 25 out of 100.
   • To change a percentage to a ratio, the percentage number goes on top (the numerator) and 100 goes on the bottom (the denominator). So, 25% becomes the ratio 25:100.

2. Incorrectly Simplifying Ratios:

   • After you make a ratio from a percentage, it needs to be simplified. Using 25:100 again, it can be simplified to 1:4.
   • A common mistake is saying it’s 5:20 without realizing it can be simplified even more.

3. Mixing Up Ratios and Fractions:

   • Ratios and fractions are not the same, but people often confuse them. A ratio compares two amounts, while a fraction shows part of a whole. Make sure you understand the difference, especially when dealing with percentages.

4. Not Converting First:

   • If you need to turn a percentage into a ratio, do the conversion before you simplify. For example, 60% converts to 60:100, which simplifies to 3:5. If you skip this step, you might get the wrong answer.

5. Missing Percentage Relationships:

   • When you have a ratio and need to find its percentage, you must know the total first. For example, if the ratio is 2:3, add 2 and 3 together to get 5. Then, you can find what percentage 2 is of 5 by doing (2/5) x 100 = 40%.

6. Ignoring What It Means:

   • It's very important to understand what the ratio or percentage is about in a real-life situation. Always think back to the problem to avoid mistakes in understanding.

By remembering these common mistakes, students can get better at changing between percentages and ratios. This will help them improve their math skills!