What Are Percentages and Why They Matter
The word "percent" literally means "per hundred." When you see 25%, you're seeing 25 per 100, or 25/100, or 0.25. That's it. Every percentage is just a way of expressing a portion of a whole.
Percentages are everywhere in daily life because they make comparisons easy. It's simpler to say "20% off" than "£4 off a £20 item." Percentages give context regardless of the original number—everyone immediately understands what 50% means, whether you're talking about £10 or £1000.
Why Percentages Are Powerful:
- • Universal comparison: Compare things of different sizes easily
- • Quick mental math: 10% is always one-tenth, 50% is always half
- • Financial literacy: Interest rates, returns, discounts all use percentages
- • Clear communication: "75% complete" is clearer than "3 out of 4 tasks"
The 6 Essential Percentage Calculations
1. What is X% of Y?
The most common percentage calculation. Used for discounts, taxes, tips, and more.
Example: What is 20% of 150?
- Step 1: 20 ÷ 100 = 0.20
- Step 2: 0.20 × 150 = 30
- Answer: 30
2. X is what % of Y?
Find what percentage one number represents of another. Perfect for test scores and completion rates.
Example: 45 is what % of 60?
- Step 1: 45 ÷ 60 = 0.75
- Step 2: 0.75 × 100 = 75
- Answer: 75%
3. Increase X by Y%
Add a percentage to a number. Used for price increases, salary raises, and inflation calculations.
Example: Increase 200 by 15%
- Step 1: 200 × 0.15 = 30
- Step 2: 200 + 30 = 230
- Answer: 230
4. Decrease X by Y%
Subtract a percentage from a number. Essential for calculating sale prices and discounts.
Example: Decrease 80 by 25%
- Step 1: 80 × 0.25 = 20
- Step 2: 80 - 20 = 60
- Answer: 60
5. % Change from X to Y
Calculate the percentage increase or decrease between two values. Used for growth rates, stock changes, and performance metrics.
Example: % change from 50 to 75
- Step 1: 75 - 50 = 25
- Step 2: 25 ÷ 50 = 0.5
- Step 3: 0.5 × 100 = 50
- Answer: +50% (increase)
6. % Difference between X and Y
Find the percentage difference between two numbers (order doesn't matter). Used for comparing alternatives and statistical variance.
Example: % difference between 80 and 120
- Step 1: |120 - 80| = 40
- Step 2: (80 + 120) ÷ 2 = 100
- Step 3: 40 ÷ 100 = 0.4
- Step 4: 0.4 × 100 = 40
- Answer: 40%
Real-World Percentage Examples
Shopping Discounts
You find a jacket originally priced at £120 with a 30% off tag. How much do you pay?
Method 1 (Calculate discount):
- Discount: 30% of £120 = 0.30 × 120 = £36
- Final price: £120 - £36 = £84
Method 2 (Quick way):
- 30% off means you pay 70%
- Final price: 70% of £120 = 0.70 × 120 = £84
Restaurant Tips
Your dinner bill is £85 and you want to leave an 18% tip. What's the total?
- Tip amount: 18% of £85 = 0.18 × 85 = £15.30
- Total bill: £85 + £15.30 = £100.30
- Quick trick: 10% = £8.50, so 20% ≈ £17. 18% is slightly less.
Sales Tax
In a region with 8% sales tax, you're buying items totaling $200. What's the final price?
- Tax amount: 8% of $200 = 0.08 × 200 = $16
- Final price: $200 + $16 = $216
- Or use the multiplier: $200 × 1.08 = $216
Test Scores and Grades
You answered 42 out of 50 questions correctly on an exam. What's your percentage score?
- Formula: (42 ÷ 50) × 100
- 42 ÷ 50 = 0.84
- 0.84 × 100 = 84%
Investment Returns
You invested £5,000 in stocks and now it's worth £6,250. What's your percentage return?
- Gain: £6,250 - £5,000 = £1,250
- % Return: (£1,250 ÷ £5,000) × 100
- 1,250 ÷ 5,000 = 0.25
- 0.25 × 100 = 25% return
Quick Reference: Common Percentage Formulas
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