True or false?

If I earn 100% more than you, then you must earn 50% less than me.

The statement is **false**.

Here’s why:

If you earn 100% more than someone, it means your earnings are **double** theirs. However, that doesn’t mean they earn 50% less than you. Let’s break it down:

### Example:
- Let’s say Person A (you) earns $200.
- Person B (me) earns 100% more than Person A, which means Person B earns double that, or $400.

Now, does Person A earn 50% less than Person B?

- If Person A were to earn 50% less than Person B, we would calculate 50% of $400, which is $200. So, Person A would earn $200, which is not 50% less than $400 but **half** of $400.

Thus, earning 100% more does not imply earning 50% less in the reverse direction.

Would you like to go over this example with more details or ask about any part? Here are 5 related questions to think about:

1. What does "earning X% more" or "X% less" really mean mathematically?
2. How do we calculate percentage differences between two quantities?
3. Can the relationship between percentages be symmetric? Why or why not?
4. What happens if the percentage is less than 100%? How does that change the situation?
5. How can we generalize this to any percentage increase or decrease?

**Tip:** Always be cautious when reversing percentage relationships! The math often doesn’t work the same way in reverse.

True or false? If I earn 100% more than you, then you must earn 50% less than me.

Explore the mathematical reasoning behind why earning 100% more than someone doesn't imply they earn 50% less than you. This problem explains key concepts of percentages and their asymmetric relationships, perfect for students in Grades 6-8.

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