Primary 5 · Mathematics

P5 ratio

Ratio is one of the first topics where a fair-looking shortcut gives a wrong answer. Adding the same number to each term feels reasonable, and it quietly breaks the ratio. Here is the sentence where it happens, and how to catch it.

Level
P5
Usually taught
Term 2
Covers
2 concepts

What changes at P5

In Primary 5, ratio arrives as a new way to compare quantities: not how much bigger one is, but how many equal parts each one has. Two to three means two parts of one thing for every three of another, whatever the actual amounts are.

Most of the work is writing equivalent ratios and simplifying them. Both rest on a single rule: whatever you do to one term, you do to every term, by multiplying or dividing. Get that rule right and the rest is arithmetic.

The sentence that costs the mark

Write a ratio equivalent to 2 : 3 that starts with 4.

What the working usually does

+ 2 each2 : 3=4 : 5

Adds 2 to each term. The gap of 1 between them stays the same, so it feels like nothing important has changed.

What the question asked

× 2 each2 : 3=4 : 6

Multiplies each term by 2. The proportion is kept, which is exactly what an equivalent ratio has to do.

Both start with 4 and both look like tidy ratios, so neither stands out as wrong. The difference is that 4 : 6 is really the same split as 2 : 3 and 4 : 5 is not. The setup decides it, and the setup is one operation.

Doubling every term keeps the 2-to-3 split. Four to six is the same ratio as two to three, drawn twice as long.

The same question, worked properly

  1. Find what turns 2 into 4

    2 × 2 = 4

    The first term goes from 2 to 4. Ask what does that: multiply by 2. Adding 2 would land on 4 as well, which is the coincidence that makes the wrong method look right.

  2. Do the same to every term

    3 × 2 = 6

    This is the step that fails. Whatever you did to the first term, you do to all of them, so the 3 is multiplied by 2 as well. Adding 2 here instead gives 5, and 4 : 5 is a different ratio.

  3. Write the equivalent ratio

    2 : 3 = 4 : 6

    Same relationship, larger numbers. That is what equivalent means: the split has not changed, only the size of the units it is counted in.

  4. Check it divides back

    4 : 6 = 2 : 3 (÷ 2)

    Divide every term by 2 and you return to 2 : 3, so 4 : 6 really is equivalent. Try the same on 4 : 5 and it will not divide back, which is the tell that adding broke it.

How can you tell it has clicked?

You do not need to know the answer to check this. Ask your child to turn 2 : 3 into an equivalent ratio, then ask the one question that catches the mistake: does the new ratio divide back down to 2 : 3?

If it divides back, the ratio was kept. If they made 4 : 5 by adding, it will not divide back, and that is the exact moment to point at. The check works even when you cannot remember any of this yourself.

One thing to try tonight

Use a recipe. Two cups of flour to three cups of milk is 2 : 3. To make twice as much, you double both, four cups to six, and it is still 2 : 3.

Then ask what happens if you add one cup to each instead, making it four to five. The mixture comes out wrong. Ratios scale up and down, they do not shift by adding.

What your child will meet in this topic

  • Ratios
  • Equivalent Ratios

Most Singapore schools introduce this in Term 2, though schools do differ by a term either way. If your child’s school runs a different order, you can set it in the schedule on your dashboard.

What it leads to

Equivalent ratios are the engine behind almost all of P6 ratio, where a quantity is shared into parts and the question asks for one of them. The same rule, multiply or divide every term, does the heavy lifting there too.

A child comfortable here also finds fractions and percentage easier, because all three describe a part against a whole. The habit of multiplying rather than adding carries straight across.

The methods your child will use here

Each one is the same method wherever it turns up, so it is worth learning once.

The same topic in other years

It comes back each year and gets harder, so it helps to see what came before and what is coming.

More in Primary 5

Other topics in the same year, so you can see what sits either side of this one.

Struggling with the working rather than the topic itself? How to help your child with problem sums

See how your child is doing on this topic

StudyLah marks each step separately, so you can see whether it was the setup or the arithmetic that cost the mark.

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