Percentages appear everywhere — sale prices, tax rates, interest, test scores, tips, and poll results. Mastering a handful of formulas means you'll never be confused by a "25% off" tag or a "3.5% APR" loan again.
The Three Core Percentage Calculations
1. What Is X% of Y?
The most common use: finding a discount, tax amount, or tip.
Result = (X ÷ 100) × Y
Example: What is 20% of $85?
(20 ÷ 100) × 85 = $17
A 20% tip on an $85 restaurant bill is $17, making the total $102.
2. X Is What Percent of Y?
Use this for test scores, progress tracking, and comparisons.
Percent = (X ÷ Y) × 100
Example: You scored 42 out of 50 on a test. What's your percentage?
(42 ÷ 50) × 100 = 84%
3. Percentage Increase or Decrease
Used for price changes, salary increases, population growth, etc.
% Change = ((New Value − Old Value) ÷ Old Value) × 100
Example: A product went from $40 to $52. What's the increase?
((52 − 40) ÷ 40) × 100 = 30% increase
Real-World Examples
Shopping Discounts
A jacket costs $120 and is 35% off. What's the sale price?
- Discount amount: (35 ÷ 100) × 120 = $42
- Sale price: $120 − $42 = $78
Sales Tax
A $329 item with 8.5% sales tax:
- Tax: (8.5 ÷ 100) × 329 = $27.97
- Total: $329 + $27.97 = $356.97
Investment Return
You invested $5,000 and now have $6,750. What's your return?
- ((6,750 − 5,000) ÷ 5,000) × 100 = 35% return
Salary Increase
Your salary goes from $52,000 to $56,500. What's the raise?
- ((56,500 − 52,000) ÷ 52,000) × 100 = 8.65% raise
Reverse Percentage (Finding the Original)
If you know the final price after a discount and want to find the original:
Original = Final Price ÷ (1 − Discount%/100)
Example: You paid $85 after a 15% discount. What was the original price?
85 ÷ (1 − 0.15) = 85 ÷ 0.85 = $100
Quick Mental Math Tricks
- 10% = move the decimal one place left ($73 → $7.30)
- 5% = half of 10%
- 15% = 10% + 5%
- 20% = double the 10% amount
- 25% = divide by 4
- 1% = move the decimal two places left
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