Master the three most common percentage problems: finding a percentage of a number, calculating percentage change, and working out what percentage one number is of another.
Step-by-Step Guide
Type 1 — Percentage of a Number
Formula: (Percentage ÷ 100) × Whole = Part. Example: What is 15% of 80? → (15 ÷ 100) × 80 = 12. Practical uses: calculating discounts, tax, tips.
Type 2 — Percentage Change
Formula: ((New − Old) ÷ Old) × 100. Example: price rose from $50 to $65 → ((65 − 50) ÷ 50) × 100 = 30% increase. A negative result means a decrease.
Type 3 — What Percentage is X of Y?
Formula: (Part ÷ Whole) × 100. Example: you scored 42 out of 60 on a test → (42 ÷ 60) × 100 = 70%. Use this for grades, survey results, and ratios.
Reverse Percentage — Find the Original
If an item costs $85 after a 15% discount, what was the original price? Original = Final ÷ (1 − discount rate) = $85 ÷ 0.85 = $100.
Quick Mental Maths Tricks
1% of any number = move decimal 2 places left. 10% = move decimal 1 place left. 25% = divide by 4. 50% = divide by 2. Build complex percentages from these building blocks.
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Frequently Asked Questions
Q: How do I add a percentage to a number?
A: Multiply by (1 + percentage/100). To add 20% to $50: $50 × 1.20 = $60. This is faster than calculating 20% and adding separately.
Q: What is the difference between percentage points and percent?
A: If a rate rises from 5% to 8%, it increased by 3 percentage points but by 60 percent (3 ÷ 5 × 100). These are very different — media reports often confuse them.
Q: How do I calculate compound percentage growth?
A: Use: Final = Start × (1 + rate)^n. Example: $1,000 growing at 5% per year for 3 years → $1,000 × 1.05³ = $1,157.63. This is the compound interest principle.