Percentages Made Easy
Discounts, tips, taxes, interest rates — percentages rule the financial world. Here's how to master them.
What Does Percent Mean?
Percent literally means "per hundred" (from Latin "per centum"). So 45% means 45 out of every 100, or 45/100, or 0.45.
The Big Three Conversions
Percentage → Decimal
Divide by 100 (move decimal 2 places left):
- 75% = 0.75
- 8% = 0.08
- 125% = 1.25
- 0.5% = 0.005
Decimal → Percentage
Multiply by 100 (move decimal 2 places right):
- 0.35 = 35%
- 1.5 = 150%
- 0.007 = 0.7%
Fraction → Percentage
Divide numerator by denominator, then multiply by 100:
- 3/4 = 0.75 = 75%
- 1/3 = 0.333... = 33.3%
- 5/8 = 0.625 = 62.5%
Three Types of Percentage Problems
Type 1: What is X% of Y?
Formula: Answer = Y × (X/100)
Example 1: What is 15% of 200?
200 × 0.15 = 30
Example 2: What is 8.5% sales tax on $45?
$45 × 0.085 = $3.83
Type 2: X is what percent of Y?
Formula: Percent = (X / Y) × 100
Example 3: 36 is what percent of 150?
(36 / 150) × 100 = 24%
Example 4: You scored 42 out of 50. What percent?
(42 / 50) × 100 = 84%
Type 3: X is Y% of what number?
Formula: Whole = X / (Y/100)
Example 5: 30 is 25% of what number?
30 / 0.25 = 120
Percentage Increase & Decrease
Formula: % Change = ((New - Old) / Old) × 100
Example 6: Percentage Increase
Price went from $80 to $92. What's the increase?
((92 - 80) / 80) × 100 = (12/80) × 100 = 15% increase
Example 7: Percentage Decrease
Weight went from 200 lbs to 170 lbs.
((170 - 200) / 200) × 100 = (-30/200) × 100 = 15% decrease
Quick Mental Percentage Tricks
- 10%: Move decimal one place left. 10% of $85 = $8.50
- 5%: Find 10%, then halve it. 5% of $85 = $4.25
- 15%: 10% + 5%. 15% of $85 = $8.50 + $4.25 = $12.75
- 20%: 10% × 2. 20% of $85 = $17.00
- 25%: Divide by 4. 25% of $85 = $21.25
- 50%: Divide by 2. 50% of $85 = $42.50
- 1%: Move decimal two places left. 1% of $85 = $0.85
Discounts and Sales
A 30% discount means you pay 70% of the original price.
Example: $120 jacket at 30% off → $120 × 0.70 = $84
Or: Discount = $120 × 0.30 = $36. Sale price = $120 - $36 = $84. Same answer!
Successive Percentages (Tricky!)
A 20% increase followed by a 20% decrease does NOT get you back to the original:
$100 + 20% = $120. Then $120 - 20% = $120 × 0.80 = $96 (not $100!)
Why? Because the 20% decrease is applied to the LARGER number.
🎯 Try It Yourself
Test your understanding with these practice problems.
1. What is 25% of 80?
💡 Hint: 25% = 1/4, so divide 80 by 4
2. What percent is 45 out of 200?
💡 Hint: (45 ÷ 200) × 100
3. A $60 shirt is 30% off. What's the sale price?
💡 Hint: Discount = $60 × 0.30 = $18. Sale price = $60 - $18
4. A stock goes from $40 to $52. What's the percent increase?
💡 Hint: ((52-40)/40) × 100
5. Convert 3/8 to a percentage
💡 Hint: (3 ÷ 8) × 100
⚠️ Common Mistakes
- ✗Calculating percentage change using the NEW value instead of the ORIGINAL. Always divide by the starting value.
- ✗Confusing 'percentage of' with 'percentage more than'. 50% of 100 is 50, but 50% MORE than 100 is 150.
- ✗Thinking a 50% increase followed by a 50% decrease gets you back to the start. It doesn't! 100 → 150 → 75.
- ✗Moving the decimal point the wrong direction when converting percentages to decimals (25% = 0.25, not 2.5).
- ✗Forgetting that 'of' means multiply in percentage problems: 20% OF 150 = 0.20 × 150.
🌍 Real Life Example
Restaurant Bill with Tax and Tip
Your dinner bill is $75.00. Sales tax is 8%: $75 × 0.08 = $6.00, subtotal = $81.00. You tip 20% on the pre-tax amount: $75 × 0.20 = $15.00. Total: $81 + $15 = $96.00. Quick check: 20% tip = double the tax (if tax ≈ 10%), so $6 × 2 ≈ $12 — close enough for a mental estimate!
💡 Key Takeaway
Percent means 'per hundred.' To find X% of Y, multiply: Y × (X/100). To find what percent A is of B, divide: (A/B) × 100. Percentages, decimals, and fractions are three faces of the same thing: 25% = 0.25 = 1/4.