VA ClassesFinding a Percentage of a Number
Ten percent is the number divided by ten. Almost every percentage question a child will meet can be assembled out of that one fact, without a calculator and without a rule to forget.
Start with 10%
10% of a number is that number divided by 10.
10% is one tenth, and finding a tenth means dividing by ten, which on paper is nothing more than sliding every digit one column to the right.
- 10% of 250 is 25
- 10% of 80 is 8
- 10% of 45 is 4.5
Get that one move solid and everything else on this page is addition.
Building the rest
Three building blocks
10% is the number divided by 10.
5% is half of 10%.
1% is the number divided by 100, or 10% divided by 10.
Any percentage can be assembled from these three, with no calculator.
To find 35% of 200:
- 10% is 20, so 30% is 20 × 3 = 60
- 5% is half of 20, which is 10
- Add them: 60 + 10 = 70
The restaurant tip trick
To leave a 15% tip, find 10%, halve that for 5%, and add the two together. On a 60 dollar bill: 6, then 3, then 9 dollars. Adults do this at restaurant tables every week without ever calling it maths, and pointing out to your child that it is precisely the method on this page does more for their confidence than a page of practice questions.
Sale prices
Shop questions carry a trap, and it has nothing to do with the arithmetic.
"20% off 45 dollars" has two perfectly good answers depending on what was asked. The discount is 9 dollars and the price you actually pay is 36, and a child who works out the first one flawlessly still scores nothing if the question wanted the second.
The faster route to the sale price
Taking 20% off leaves 80% behind, so go straight for 80% rather than finding the discount and then subtracting it. 10% of 45 is 4.5, so 80% is 4.5 × 8 = 36. One calculation instead of two, and one fewer opportunity to answer the wrong question.
Worked examples
A straightforward percentage
- Start with 10%. Divide 250 by 10 to get 25.
- 30% is three lots of 10%.
- 25 × 3 = 75.
- Sense check: 30% is under a third, and 75 is under a third of 250. Good.
Building an awkward one
- 10% of 60 is 6.
- 5% is half of that, so 3.
- 15% is 10% plus 5%, so 6 + 3 = 9.
- No calculator needed at any point, which is the whole reason to learn it this way.
A sale price
- The question asks for the price paid, not the discount. Note that before starting.
- Taking 25% off leaves 75%, so find 75% of 80.
- 10% of 80 is 8, so 70% is 56. 5% is 4. Together that is 60.
- Check the other way: 25% of 80 is 20, and 80 − 20 = 60. Same answer.
Common mistakes
1. Giving the discount when the question wanted the price
20% of 45 gets worked out correctly, 9 goes on the answer line, and the mark is lost because the question asked what you pay. Across a paper this costs more marks than every arithmetic slip put together, and the only reliable cure is to read the last line of the question again immediately before writing anything down.
2. Dividing by the percentage
20% of 45 becomes 45 ÷ 20, because there are two numbers and division seems like the thing to do with them. The 10% method sidesteps this entirely, since it never asks you to divide by anything except ten. A child dividing by the percentage itself is guessing at a rule rather than following one, which is worth noticing, because guessing will keep producing new and different wrong answers.
3. Stacking two discounts by adding them
20% off followed by another 10% off gets added up to 30% off. The second discount is taken from the already reduced price, not the original, so the total always comes out a little under 30%. Shops know this perfectly well, which is a reason to teach it before your child is old enough to be caught by it.
Practice questions
Seven questions. One attempt each, and the explanation appears once the answer is in.
Check yourself
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For parents
Practise this at the till rather than at the kitchen table. Point at a sale sign on the way in and ask what the new price will be, then let the receipt settle it. Real money, an answer that arrives within minutes, and no way to fudge it. Ten of those conversations will teach more than any worksheet, and your child will remember which ones they got right.
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