📊 Percentage Formulas & Applications
Master the mathematics behind percentage calculations with comprehensive formulas, real-world applications, and practical examples for business, finance, and everyday use.
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🔢 Essential Percentage Formulas
Core Formulas
1. Finding X% of Y
Example: What is 25% of 80?
(25 ÷ 100) × 80 = 0.25 × 80 = 20
2. Finding What % X is of Y
Example: 15 is what % of 60?
(15 ÷ 60) × 100 = 0.25 × 100 = 25%
3. Finding the Whole from Part
Example: 20 is 40% of what number?
20 ÷ (40 ÷ 100) = 20 ÷ 0.4 = 50
Change Formulas
Percentage Increase
Example: Price went from $50 to $65
((65 - 50) ÷ 50) × 100 = 30% increase
Percentage Decrease
Example: Price dropped from $80 to $60
((80 - 60) ÷ 80) × 100 = 25% decrease
Percentage Point Difference
Example: Interest rate: 3% to 5%
5% - 3% = 2 percentage points
💼 Business Applications
Sales & Marketing
Discount Calculations
Original Price: $100, 20% off
Sale Price = $100 - ($100 × 0.20) = $80
Markup Calculations
Cost: $50, 40% markup
Selling Price = $50 + ($50 × 0.40) = $70
Commission Calculations
Sales: $10,000, 5% commission
Commission = $10,000 × 0.05 = $500
Financial Metrics
Profit Margin
Revenue: $1000, Cost: $700
Profit Margin = (($1000 - $700) ÷ $1000) × 100 = 30%
Return on Investment (ROI)
Gain: $200, Investment: $1000
ROI = ($200 ÷ $1000) × 100 = 20%
Growth Rate
Revenue: $500K to $650K
Growth = (($650K - $500K) ÷ $500K) × 100 = 30%
💰 Financial Calculations
Interest Calculations
Simple Interest:
I = P × r × t
Compound Interest:
A = P(1 + r)^t
Tax Calculations
Sales Tax:
Tax = Price × Tax Rate
Income Tax:
Tax = Income × Tax Rate
Investment Returns
Annual Return:
Return = (End - Start) ÷ Start × 100
Dividend Yield:
Yield = Annual Dividends ÷ Price × 100
🎓 Academic & Grade Calculations
Grade Percentage Formulas
Test Score Percentage
Example: 85 out of 100 points
(85 ÷ 100) × 100 = 85%
Weighted Grade Calculation
Example: Midterm 80% (30%), Final 90% (70%)
(80 × 0.3) + (90 × 0.7) = 24 + 63 = 87%
Common Grade Scales
🧠 Mental Math Tips & Tricks
Quick Mental Calculations
Common Percentages
- • 10% = Divide by 10 (move decimal left)
- • 25% = Divide by 4
- • 50% = Divide by 2
- • 75% = 3/4 or 50% + 25%
- • 20% = 10% × 2
Quick Tip Calculations
- • 15% tip = 10% + 5% (half of 10%)
- • 20% tip = 10% × 2
- • 18% tip = 20% - 2%
Verification Methods
Check Your Work
- • Work backwards to verify
- • Use estimation for reasonableness
- • Cross-multiply for proportion checks
- • Remember: part + remainder = whole
Common Mistakes
- • Confusing percentage vs. percentage points
- • Using wrong base for calculations
- • Forgetting to multiply by 100 for %
- • Rounding too early in calculations
Ready to Practice?
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