Most percentage questions are variations of three relationships: finding a part, finding the percentage, or finding the whole. Identifying the unknown first makes the arithmetic much easier.
Find a percentage of an amount
Convert the percentage to a decimal by dividing by 100, then multiply by the whole amount.
15% of 240 = 15 ÷ 100 × 240 = 36Find what percent one number is of another
Divide the part by the whole, then multiply by 100. The whole cannot be zero.
30 is what percent of 200? 30 ÷ 200 × 100 = 15%Find the original whole
When a part and its percentage are known, divide the part by the decimal form of the percentage.
36 is 15% of what number? 36 ÷ 0.15 = 240Discount and markup examples
A 20% discount on $80 is $16, leaving a sale price of $64. A 20% markup on an $80 cost adds $16, producing $96. Markup and margin are not interchangeable because they use different bases.
- Discounted price = original × (1 − discount rate)
- Marked-up price = cost × (1 + markup rate)
Why equal increases and decreases do not cancel
Reducing 100 by 20% gives 80. Increasing 80 by 20% adds only 16, producing 96. The second percentage uses a smaller base.