Understanding the Concepts
* Increase: A value gets bigger.
* Decrease: A value gets smaller.
Calculating Increases
1. Find the amount of increase: Subtract the original value from the new value.
* Example: Original price: $100, New price: $120. Increase = $120 - $100 = $20
2. Calculate the percentage increase: Divide the amount of increase by the original value, then multiply by 100%.
* Example: Increase = $20, Original price = $100. Percentage increase = ($20 / $100) * 100% = 20%
Calculating Decreases
1. Find the amount of decrease: Subtract the new value from the original value.
* Example: Original price: $100, New price: $80. Decrease = $100 - $80 = $20
2. Calculate the percentage decrease: Divide the amount of decrease by the original value, then multiply by 100%.
* Example: Decrease = $20, Original price = $100. Percentage decrease = ($20 / $100) * 100% = 20%
Key Formulas
* Percentage Increase: (New Value - Original Value) / Original Value * 100%
* Percentage Decrease: (Original Value - New Value) / Original Value * 100%
Examples
* Increase: A shirt originally priced at $25 is now $30. What is the percentage increase?
* Increase = $30 - $25 = $5
* Percentage increase = ($5 / $25) * 100% = 20%
* Decrease: A phone that cost $500 is now on sale for $400. What is the percentage decrease?
* Decrease = $500 - $400 = $100
* Percentage decrease = ($100 / $500) * 100% = 20%
Important Notes
* Original Value: Always use the original value as the denominator in your percentage calculations.
* Context: Pay attention to the context of the problem. Are you dealing with a price, a quantity, or something else?
* Word Problems: Carefully read the problem to determine whether it's asking for the amount of change or the percentage change.
Let me know if you have specific problems you'd like help solving!
