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Calculate X% of Y% for compound and chained percentage calculations. Find percentages of percentages with detailed solutions.
Formula: (P1/100) × (P2/100) × 100
Example: 50% of 80% = (0.50 × 0.80) × 100 = 40%
Enter percentages to calculate
Convert both percentages to decimals, multiply them, and convert back to percentage:
Result = (P1 × P2) / 100
Example: 25% of 60% = (25 × 60) / 100 = 1500 / 100 = 15%
Double Discounts: A store offers 20% off, then an additional 10% off the sale price. The total discount is NOT 30%. It's 20% + (10% of 80%) = 20% + 8% = 28%. You pay 72% of the original price.
50% of 80% = (0.50 × 0.80) × 100 = 0.40 × 100 = 40%. This means half of 80% equals 40%.
For successive discounts, multiply the remaining percentages. For 20% off then 10% off: you pay 80% then 90% of that = 0.80 × 0.90 = 0.72 = 72% of original (28% total discount).
Yes! Percentage multiplication is commutative. Both equal 5%: (0.10 × 0.50) = (0.50 × 0.10) = 0.05 = 5%.
The second discount applies to the already-reduced price, not the original. After 20% off, you pay 80%. Then 10% off that 80% = 8% more off, totaling 28% off, not 30%.
100% of any percentage equals that same percentage. 100% of 75% = 75%. This is because 1.00 × 0.75 = 0.75.
Chain them: (P1/100) × (P2/100) × (P3/100) × 100. For example, 50% of 80% of 60% = 0.50 × 0.80 × 0.60 × 100 = 24%.
Only if one percentage is greater than 100%. For normal percentages (≤100%), the result is always less than or equal to the smaller percentage.
25% of 40% = (0.25 × 0.40) × 100 = 0.10 × 100 = 10%. One quarter of 40% is 10%.
Calculating a percentage of a percentage involves multiplying two fractional values. This concept is crucial for understanding compound calculations, successive discounts, and chained percentage changes. The key is converting percentages to decimals, multiplying, and converting back.