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Percentage change formula: % = ((New Value − Old Value) ÷ Old Value) × 100. Positive result = increase. Negative result = decrease. Example: from $80 to $100 → ((100−80)÷80)×100 = +25%.
How to Calculate Percentage Change — 3 Steps
Subtract: New Value − Old Value$120 − $100 = $20 (the change amount).
Divide by the Old Value$20 ÷ $100 = 0.20
Multiply by 100 to get the percentage0.20 × 100 = +20% increase. If the result is negative, it's a decrease.
Percentage Change Formula — Both Directions
| Situation | Formula | Example |
|---|
| Price increase | ((New−Old)÷Old)×100 | $80→$100 = +25% |
| Price decrease | ((New−Old)÷Old)×100 | $100→$80 = −20% |
| Salary raise | ((New−Old)÷Old)×100 | $14k→$16k = +14.3% |
| Discount amount | ((Sale−Original)÷Original)×100 | $60→$45 = −25% |
12 Percentage Change Examples
Percentage Change vs Percentage Difference
These are NOT the same thing. Percentage change measures how much one value changed relative to the starting value — it has a direction (increase or decrease). Percentage difference compares two values without a "start" or "end" — useful when neither value is the reference point. For comparing prices at two different stores, use percentage difference. For tracking how a price evolved over time, use percentage change.
Common Mistakes
- Using the wrong base: always divide by the OLD value, not the new one. From $80 to $100: divide by 80, not 100.
- Confusing percentage points with percent change: if a rate goes from 4% to 6%, it increased by 2 percentage points but by 50% in relative terms.
- Adding percentages: +20% followed by −20% does NOT return to the original. $100 → $120 → $96 (not $100).
Also useful
More Practice Problems
Problem 1 — Identify the formulaBefore calculating, make sure you know which formula to use. Write down what you know and what you need to find.
Problem 2 — Substitute carefullyReplace variables with their values. Double-check every substitution before computing.
Problem 3 — Verify your answerPlug your answer back into the original equation or condition. If it works, you're done!
Problem 4 — Real-world applicationThink about where you'd use this in real life: shopping discounts, cooking measurements, engineering calculations, finance.
Frequently Asked Questions
How many problems should I practice?Aim for 10-20 problems per concept, gradually increasing difficulty. Consistent daily practice (even 15 minutes) beats occasional marathon sessions.
What if I get stuck?1) Re-read the problem. 2) List all given information. 3) Identify what you need to find. 4) Choose the right formula. 5) Calculate step by step.
Why should I show my work?Writing each step helps you spot errors, earns partial credit on tests, and builds the habit of organized mathematical thinking.
Key Tips for Success
- Practice daily: 15 minutes every day beats 2 hours once a week.
- Understand, don't memorize: If you understand why a formula works, you'll never forget it.
- Always verify: Check your answer before moving on.
- Learn from mistakes: Analyze every wrong answer to understand what went wrong.