Percent Change Game

Percent Change Quiz/Game
Welcome to Percent Change Game. This game is designed to help you master percent change formula \(\frac{\text{New} - \text{Old}}{\text{Old}} \times 100\%\). There are some shortcut mental strategies that you can use. Scroll down the page for a more detailed explanation.

 

 

How to play the Percent Change Game

1. The Core Formula
   Before you start, memorize the formula shown on the main menu. It is the key to every level:\(\frac{\text{New} - \text{Old}}{\text{Old}} \times 100\%\)

2. How to Play a Round
   Once you click Start, follow these three steps for every challenge:
   Find the Difference: Subtract the Old Value from the New Value.
   Example: If Old is 40 and New is 50, the difference is +10.
   Example: If Old is 80 and New is 60, the difference is -20.
   

Divide by the Start:
Divide that difference by the Old Value.
10 ÷ 40 = 0.25

Convert to Percent:
Multiply the result by 100 (move the decimal two spots to the right).
0.25 = 25%

3. Key Rules
   The Negative Sign: If the value went down, your answer must include a negative sign (e.g., -25).
   The Streak: Every correct answer adds to your 🔥 streak.
   The Reset: An incorrect answer shakes the screen and resets your streak to 0. The game will show you the calculation steps so you can learn from the mistake.
   

Quick Calculation Tips
Use these shortcuts to find the answer faster:

If the Difference is…	And the Old Value is…	Then the Change is…
Half of the Old	20 → 30	+50%
One-Quarter of Old	40 → 50	+25%
One-Tenth of Old	80 → 88	+10%
Double the Old	10 → 20	+100%

1. The “Half” Strategy (+50% or -50%)
   Logic: If the amount added (or subtracted) is exactly half of the starting number, the change is 50%.
   Example A (+50%): Old = 60. New = 90.
   Difference is 30. Since 30 is half of 60, it’s a +50% increase.
   Example B (-50%): Old = 120. New = 60.
   Difference is -60. Since 60 is half of 120, it’s a -50% decrease.
   

2. The “Quarter” Strategy (+25% or -25%)
   Logic: If the difference is a “half of a half” of the starting number, the change is 25%.
   Example A (+25%): Old = 40. New = 50.
   Difference is 10. Since 10 is one-quarter of 40, it’s a +25% increase.
   Example B (-25%): Old 80. New = 60.
   Difference is -20. Since 20 is one-quarter of 80, it’s a -25% decrease.
   

3. The “Tenth” Strategy (+10% or -10%)
   Logic: Move the decimal point of the old value one spot to the left. If that matches your difference, the change is 10%.
   Example A (+10%): Old = 70. New = 77.
   The difference is 7. Since 7 is 10% of 70.
   Example B (-10%):Old = 30,000. New = 27,000.
   Difference is -3,000. Since 3,000 is one-tenth of 30,000, it’s a -10% decrease.
   

4. The “Double” Strategy (+100%)
   Logic: If the New Value is exactly twice the Old Value, the increase is 100%. (Common mistake: people think doubling is a 200% increase, but the change is only equal to the original 100%).
   Example: Old = 50. New = 100.Difference is +50. You gained exactly what you started with. That is a +100% increase.
   

Finding Percent Change (Formula)

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