Key Formulas
X% of Y = (X/100) × Y
Percent Change = [(New − Old) / Old] × 100
Percent Change = [(New − Old) / Old] × 100
Common Mistakes
- Using the wrong base value when calculating percent change — always divide by the ORIGINAL value, not the new one.
- Adding percentages directly across different bases, like averaging a 10% raise and a 10% cut as "0% overall" — they don't cancel because of differing base amounts.
Frequently Asked Questions
Is there a fast mental shortcut for percentages?
Yes — 10% of any number is found by moving the decimal point one place left; you can build most other percentages (5%, 15%, 20%) from that single reference point.
How do I reverse-calculate the original price after a discount?
Divide the discounted price by (1 − discount rate) — for a 20%-off price of $80, the original price was 80 / 0.80 = $100.
