Understanding percentages: calculate a share and compare change
Percentages help you understand a share of a whole and compare figures in study, work and shopping. Start with the quantity the percentage applies to, then distinguish the resulting amount from a change in the percentage itself.
Three questions, three kinds of answer
Percent means per hundred. “What is 15% of 280?” asks for an amount: 42. “The price rose from 280 to 322; what was the increase?” asks for a percentage: 15%. The first answer should not be written as 42%.
A rate moving from 20% to 25% rises by 5 percentage points, but by 25% relative to its old level. Name the comparison instead of treating those two statements as interchangeable.
References: Math Is Fun — Introduction to Percents
Why stacked discounts do not add up
The second discount usually applies to the reduced price. Check the offer terms if its base is unclear. Two discount codes do not automatically mean that their percentages can be added.
A quick check before trusting the result
Write down the original and final prices, then subtract to check the saving. For different package sizes, compare the discounted price per kilogram or litre rather than the discount label.
- A 50% fall followed by a 50% rise does not restore the original: 100 becomes 50, then 75.
- Ordinary percentage change is undefined when the original value is zero. Report the absolute change instead.
- Round the final amount for the currency; avoid repeatedly rounding intermediate steps.
Worked comparison: two offers on the same bag
The list price is 360. A 25% discount saves 90 and leaves 270. A 20% discount followed by another 10% gives 360 × 0.8 × 0.9 = 259.2.
The second offer saves an extra 10.8. Its effective discount is 28%, not 30%. This comparison assumes the same product and no differing fees or conditions.