Find 15% of 80
10%: 80 ÷ 10 = 85%: 8 ÷ 2 = 415%: 8 + 4 = 12Check: 15% lies between 10% and 20%, so the answer must lie between 8 and 16. Twelve fits.
Method 01 • percentages
Percentages in plain steps
Before calculating a percentage, ask one small question: a percentage of what? Once the whole is clear, the arithmetic usually becomes much calmer.
Start with ten per cent
Build an answer from familiar pieces
“Per cent” means “per hundred”. A percentage describes a share of a particular whole: 15% means 15 parts out of every 100 equal parts. That whole might be a bill, a recipe quantity or the number of items in a group. Identify it before you start. If a charge applies only to part of a bill, using the entire bill will give the wrong answer even if your arithmetic is perfect.
For many everyday questions, 10% is a useful first step. Divide the starting amount by 10. To find 5%, halve that result. To find 1%, divide the starting amount by 100. You can combine these pieces: 15% is 10% plus 5%, while 12% is 10% plus two lots of 1%. These are exact methods when you keep the intermediate values exact.
Find 12% of 250
10% = 25; 1% = 2.512% = 25 + 2.5 + 2.5 = 30Check: 30 ÷ 250 = 0.12, which is 12%. A calculator can confirm the reverse step.
You do not have to choose the same route every time. For 25%, a quarter is often simpler: divide by four. For 50%, halve the amount. For an awkward percentage such as 17.3%, multiplying by 0.173 with a calculator may be clearer than assembling many small pieces. A shortcut should reduce the work, not create more of it.
Separate the saving from the final amount
A percentage reduction produces two different answers: the amount removed and the amount remaining. If an illustrative item starts at 80 and is reduced by 15%, the reduction is 12. The final amount is 80 − 12 = 68. Write a label beside each answer so that a correct saving does not accidentally become an incorrect final price.
A second route is to work with what remains. After a 15% reduction, 85% of the original amount remains. Multiplying 80 by 0.85 also gives 68. This gives you an independent check because it approaches the same question from the other direction.
The same care is needed with consecutive reductions. Two reductions of 10% leave 90% of 90%, or 81% of the original amount. The combined reduction is 19%, not 20%. Keep each stage separate, and use the amount at that stage as the new starting point.
Measure a change using the original amount
To describe how much a quantity has increased, subtract the old amount from the new one, then divide that difference by the old amount. Finally multiply by 100. If a quantity moves from 40 to 50, the increase is 10. Since 10 ÷ 40 = 0.25, the percentage increase is 25%. Dividing by 50 instead would answer a different question.
When the starting amount is zero, this calculation cannot give an ordinary percentage increase because division by zero is undefined. State the actual change instead. With negative starting amounts, percentage descriptions can also be confusing; a clear explanation of the values is often more useful than a single percentage.
Check what the percentage actually describes
Percentage points describe the difference between two percentages. A rate moving from 20% to 25% rises by five percentage points. Relative to 20%, it rises by 25%. Both statements can be true, but they are not interchangeable. Use “percentage points” when you mean simple subtraction between rates.
For money, keep enough decimal places during the calculation and round the final payable amount according to the relevant rules. Actual taxes, service charges and discounts may have conditions that mental arithmetic cannot tell you. Check the written terms and use an exact calculation when the consequence matters.
Further explanations
Khan Academy explains arithmetic foundations. Math is Fun provides another explanation of percentages. BBC Bitesize offers practice material across maths topics.