Finding a Percentage of a Number
Ten percent is just the number divided by ten. Almost every percentage question you will ever meet can be built out of that one fact.
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. On paper that just moves every digit one column to the right.
- 10% of 250 is 25
- 10% of 80 is 8
- 10% of 45 is 4.5
Learn that one move properly and the rest of this topic 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 it to get 5%, and add the two. On a 60 dollar bill: 6, then 3, then 9 dollars. Adults use this every week without calling it maths, and showing your child that it is the same method is worth more than a page of practice.
Sale prices
Shop questions have a trap in them, and it is not the arithmetic.
"20% off 45 dollars" has two possible answers. The discount is 9 dollars. The price you pay is 36 dollars. Read the question and decide which one it wants.
The faster route to the sale price
Taking 20% off leaves 80%, so find 80% directly instead of finding the discount and subtracting. 10% of 45 is 4.5, so 80% is 4.5 × 8 = 36. One step instead of two, and one fewer place to slip.
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
Working out 20% of 45 correctly, writing 9, and losing the mark because the question asked what you pay. This costs more marks than any arithmetic error on this topic. Read the last line of the question again before writing.
2. Dividing by the percentage
Working out 20% of 45 as 45 ÷ 20. The 10% method avoids this completely, because it never asks you to divide by anything except 10. If a child is dividing by the percentage, they are guessing at a rule rather than using one.
3. Stacking two discounts by adding them
Thinking 20% off and then another 10% off is 30% off. The second discount comes off the already reduced price, so the total is a little less than 30%. Worth knowing before anyone shops a sale.
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, not at the table. Point at a sale sign and ask for the new price before you reach the counter, then check it on the receipt. The stakes are real, the feedback is instant, and ten of those beat a worksheet.
What to learn next
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