Percentages become much easier when you first identify what the whole is, what the part is and which value you are trying to find. These three patterns cover most bills, discounts, grades and business reports.
1. Find a percentage of a number
Convert the percentage to a decimal by dividing it by 100, then multiply by the original number. The formula is: result = number × percentage ÷ 100.
For example, 15% of 80 is 80 × 15 ÷ 100 = 12. This is the pattern to use when you know the full amount and want to find a specific share of it.
2. Find what percentage one number is of another
Divide the part by the whole and multiply by 100. If 18 out of 24 tasks are complete, the calculation is 18 ÷ 24 × 100 = 75%.
The denominator matters: it must represent the relevant whole. Reversing the values is the most common reason a percentage answer looks wrong.
3. Measure percentage change
Subtract the original value from the new value, divide that difference by the original value, then multiply by 100. A price rising from €50 to €60 changes by (60 − 50) ÷ 50 × 100 = 20%.
A negative answer indicates a decrease. When the original value is zero, percentage change is undefined because division by zero is not possible; describe the absolute change instead.
Discounts and mark-ups are not opposites
A 20% reduction followed by a 20% increase does not return to the starting value because the second percentage uses a smaller base. €100 reduced by 20% becomes €80; increasing €80 by 20% produces €96.
- Discount amount = original price × discount rate
- Sale price = original price − discount amount
- Percentage increase = change ÷ original value × 100
A quick accuracy check
Estimate before trusting the exact result. Ten percent of 240 is 24, so 12% should be slightly higher at 28.8. This simple sense check catches misplaced decimal points and reversed values.