Calculating Percentages
Essential percentage calculations without a calculator
What You'll Learn
The Basic Percentage Formula
The fundamental formula for percentage calculations:
Percentage = (Part ÷ Whole) × 100
Part: The portion you're measuring
Whole: The total amount
Result: The percentage (%)
Example 1: Basic Percentage
What percentage is 15 out of 60?
Step 1: Divide part by whole: 15 ÷ 60 = 0.25
Step 2: Multiply by 100: 0.25 × 100 = 25
Answer: 25%
Finding a Percentage OF a Number
To find a certain percentage of a number, convert the percentage to a decimal and multiply:
Amount = Number × (Percentage ÷ 100)
Example 2: Finding 15% of 80
Method A: Convert to decimal
15% = 0.15
80 × 0.15 = 12
Method B: Fraction method
15% = 15/100
80 × 15/100 = 1200/100 = 12
Mental Math Shortcuts
⚡ Easy Percentages
- 50%= ÷ 2 (half)
- 25%= ÷ 4 (quarter)
- 10%= ÷ 10 (move decimal left)
- 1%= ÷ 100
🧱 Building from 10%
- 20%= 10% × 2
- 30%= 10% × 3
- 5%= 10% ÷ 2
- 15%= 10% + 5%
Example 3: Calculate 15% of 60 Mentally
Step 1: Find 10% of 60 = 6 (move decimal left)
Step 2: Find 5% of 60 = 3 (half of 10%)
Step 3: Add them: 6 + 3 = 9
Calculating Percent Change
Percent Change = (Change ÷ Original) × 100
Where: Change = New Value - Original Value
Example 4: Price Increase
A item's price increased from $40 to $50. What's the percent increase?
Change = 50 - 40 = 10
Percent = (10 ÷ 40) × 100
= 0.25 × 100
Answer: 25% increase
Real-World Applications
Calculating Tips
20% tip on a $45 restaurant bill:
Standard Method
45 × 0.20 = $9.00
Mental Math
10% = $4.50
20% = 2 × $4.50 = $9.00
Calculating Discounts
$80 jacket is 30% off:
Discount = 0.30 × 80 = $24
Sale price = $80 - $24 = $56
💡 Quick tip: For 30% off, pay 70% (80 × 0.70 = $56)
Practice Problems
Test your understanding
1. What is 25% of 120? ▼
25% = 1/4
120 ÷ 4 = 30
2. 18 is what percent of 72? ▼
(18 ÷ 72) × 100 = 0.25 × 100 = 25%
3. A test score improved from 60 to 75. What's the percent increase? ▼
Change = 75 - 60 = 15
(15 ÷ 60) × 100 = 25% increase
4. Calculate a 15% tip on a $32 bill (use mental math) ▼
10% of 32 = $3.20
5% of 32 = $1.60
15% = $3.20 + $1.60 = $4.80
Quick Reference: Common Conversions
| Fraction | Decimal | Percent | Of 100 |
|---|---|---|---|
| 1/2 | 0.50 | 50% | 50 |
| 1/4 | 0.25 | 25% | 25 |
| 3/4 | 0.75 | 75% | 75 |
| 1/5 | 0.20 | 20% | 20 |
Key Takeaways
- ✓ To find a percentage: (Part ÷ Whole) × 100
- ✓ To find percentage OF a number: Number × (Percent ÷ 100)
- ✓ Use 10% as a building block for mental math
- ✓ For discounts, calculate what you PAY (100% - discount%)
- ✓ Always identify what is the "part" and what is the "whole"
Related Lessons
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Continue building your math skills with ratios and proportions.
