Ratio and Percentage: The Three Slips, and How to Check

10 September 2026 · by Larry

Your child can tell you that 20% of 50 is 10, without hesitating. Then she reads a question about a shirt that costs $40 after a 20% discount, works confidently for two minutes, and writes $48.

Nothing went wrong with the arithmetic. The arithmetic was fine. What went wrong happened in the first five seconds, before any calculating started, and it is the same thing that goes wrong in almost every ratio and percentage question at upper primary.

These two topics arrive together in P5 and stay through P6, and they are the point where a child who has been comfortable in maths can suddenly start losing marks. It is worth knowing that this is normal, and that the fix is not more sums.

Why these two are different from what came before

Up to this point, most numbers in a maths question have been amounts. Six apples. Forty-two dollars. Three hundred and twelve centimetres. The number tells you how much there is.

Ratio and percentage are not amounts. They are relationships. On their own they tell you nothing about how much there is — only how one thing compares with another.

A ratio of 2 : 3 does not mean two of something and three of something. It could be 2 and 3, or 20 and 30, or 200 and 300. Twenty per cent is not a quantity either; it is twenty out of every hundred of something you have not been told yet.

That is the shift. And a child who has spent five years being told that the numbers in a question are the amounts will keep reading them that way for a while, because it worked every single time before.

Slip one: part to part, read as part to whole

This is the most common one, and the easiest to check for.

The ratio of boys to girls in a class is 2 : 3. What fraction of the class are boys?

A great many children write two-thirds. It is not carelessness — it is a reasonable reading of the numbers they were given. But 2 : 3 compares boys with girls, not boys with the class. There are 2 + 3 = 5 units altogether, so boys are two-fifths.

Once you know to look for it, you will see this everywhere. The question gives a part-to-part relationship and asks for something about the whole, and the child answers using only the two numbers on the page.

The check: ask "how many units altogether?" before anything else. If she can say five, she has understood the ratio. If she looks blank, the difficulty is here and no amount of extra practice on calculating will touch it.

Slip two: percentage of what?

A percentage always sits on top of something, and the something changes.

A price rises by 10%, then falls by 10%. Is it back where it started?

Almost every child says yes. The answer is no, because the rise is 10% of the original price and the fall is 10% of the new, higher price. Ten per cent of a bigger number is a bigger number, so you come back down further than you went up.

This is worth doing once at the kitchen table with a real number, because it is genuinely surprising and it makes the idea stick. Start at $100. Up 10% is $110. Down 10% of $110 is $11, so you land on $99, not $100.

The check: whenever a percentage appears, ask "per cent of what?" and make her point at it. Not calculate it — point at it.

Slip three: working backwards

This is the shirt question, and it is the one that costs the most marks in P6 because it looks so much like a question she can already do.

After a 20% discount, a shirt costs $40. What was the original price?

The instinct is to add 20% of $40, giving $48. But the 20% was taken off the original price, which is the number we do not know yet. So $40 is not the whole thing minus a bit — $40 is 80% of the original.

If 80% is $40, then 10% is $5, and 100% is $50. The check is easy and children like it: take 20% off $50 and you get $40. It works.

Notice what made this hard. It was not the arithmetic — dividing 40 by 8 is something she could do in P3. It was knowing which number the percentage belonged to. That is a reading problem wearing a maths costume, which is exactly the pattern behind word problems where the sums are fine but the story is not.

The one habit that fixes all three

Draw the units.

Every one of these three slips disappears when the relationship is on paper instead of in the head. Two boxes for boys, three for girls, and the question "how many boxes is the whole class?" answers itself. Ten boxes for the original price, cross out two for the discount, and the eight that remain are the $40 — so one box is $5, and ten boxes is $50.

This is the same bar model she is being taught in school, used for a purpose she can feel. If it is not yet second nature, bar models, and how to help without confusing her covers how to support it without teaching a different method from her teacher's.

The reason it works is not that drawing is magic. It is that you cannot draw a ratio without first deciding how many units there are — so the drawing forces the step that was being skipped.

What to do tonight, in two minutes

Take one ratio or percentage question she got wrong. Do not solve it with her, and do not explain it. Ask three questions:

• "How many units altogether?" — for a ratio question.
• "Per cent of what? Point at it." — for a percentage question.
• "Is the answer going to be bigger or smaller than that number?" — before any working.

If she answers all three correctly and still got the question wrong, the problem really is the calculating, and practice will help. If she stumbles on one of them, you have found the actual difficulty, and it is a five-minute conversation rather than a term of worksheets.

That distinction is worth more than any amount of extra work, and it is the same one that applies to fractions when they stop making sense and to decimals. In all three, the arithmetic is rarely the thing that broke.

One thing not to say

Try not to say "but you know how to do percentages". She does. That is precisely why the mistake is confusing for her, and being told she already knows how makes a wrong answer feel like a personal failure rather than a misread question.

"Read me the question again, slowly" does the same job and costs her nothing.