Up 50%, Down 50% — And Still Lost Money? 🤔
Learn why percentages can be tricky! Discover why going up 50% and then down 50% doesn't bring you back to where you started. This fun lesson will blow your mind! 🤯
The Surprising Truth!
Here's the big surprise: If you start with $100 and it goes UP by 50%, then DOWN by 50%, you don't end up with $100... you only have $75! 😱
Let's See How This Works!
Starting with $100
First, it goes UP 50%
Then, it goes DOWN 50%
Why Does This Happen?
The Secret: Percentages Change Based on the Starting Number!
The Big Lesson
Percentages are always based on the current amount, not the original amount! So a 50% increase followed by a 50% decrease does NOT cancel out. The decrease is bigger because it's calculated on a larger number!
More Examples: Meet Person A and Person B!
Scenario 1: Both Average 20% — But Who Wins?
Return Percentages
| Year | Person A | Person B |
|---|---|---|
| Year 1: | +40% | +10% |
| Year 2: | -20% | +10% |
| Net Avg: | 20% | 20% |
Result: Dollar Amounts
| Year | Person A | Person B |
|---|---|---|
| Year 1 |
$140
(100+40)
|
$110
(100+10)
|
| Year 2 |
$112
(140-28)
|
$121
(110+11)
|
| Total: |
$112
❌ Lost $9
|
$121
✅ Winner!
|
Person A: The Roller Coaster!
Person B: Slow and Steady!
🏆 The Winner Is...
Scenario 2: The Most Extreme Example! 😱
Return Percentages
| Year | Person A | Person B |
|---|---|---|
| Year 1: | +50% | 0% |
| Year 2: | -50% | 0% |
| Net Avg: | 0% | 0% |
Result: Dollar Amounts
| Year | Person A | Person B |
|---|---|---|
| Year 1 |
$150
(100+50)
|
$100
(100+0)
|
| Year 2 |
$75
(150-75)
|
$100
(100+0)
|
| Total: |
$75
❌ Lost $25
|
$100
✅ Safe!
|
Person A: The Wild Ride!
Person B: The Safe Choice!
😱 Shocking Result!
See It in Action!
Watch how the money changes with each step
What You Should Remember!
Percentages Change!
A percentage is always based on the current amount, not the starting amount. That's why up 50% and down 50% don't cancel out!
Losses Hurt More!
When you go up 50% then down 50%, you lose money because the down percentage is calculated on a bigger number!
Steady Wins!
Slow and steady growth often beats wild ups and downs, even when the "average" looks the same!
Don't Trust Averages!
Two people can have the same average return but end up with very different amounts of money!
Try It Yourself!
Practice Problem 1:
If you have $200 and it goes up 25%, then down 25%, how much money do you have?
Click to see the answer!
Practice Problem 2:
Your friend says, "I gained 30% then lost 30%, so I'm back where I started!" Are they correct?
Click to see the answer!
Learn More Cool Math!
Note for Parents & Teachers
This concept introduces the mathematical principle that percentages are multiplicative, not additive. It's a crucial foundation for understanding compound growth, investment returns, and why volatility can erode wealth over time. Encourage kids to practice with real-world examples like sales discounts, sports statistics, or video game bonuses!