Primary 6 Maths: Ratio
Ratio connects fractions, percentage and algebra, and anchors many PSLE Paper 2 questions. The changing-ratio structure, common mistakes, and worked examples.
Most schools typically cover this topic in Term 1, around weeks 7–8 — though every school sets its own sequence.
Under the 2021 MOE syllabus, ratio is taught at Primary 6 — and it arrives with PSLE weight attached. Ratio questions are rarely hard because of the arithmetic; they're hard because the relationship changes mid-problem. Beads are removed, money is spent, people join a group — and the ratio your child wrote down in line one no longer holds in line three.
Ratio is also the great connector: a ratio of 3 : 5 is the fraction 3/8 of the whole, is 37.5%, is "0.6 times as many". Children who see those as one idea move through PSLE Paper 2 noticeably faster than children who treat them as three topics.
The mistakes to watch for
- Units treated as amounts. Writing "red = 5" instead of "red = 5 units". The habit seems harmless until a changing-ratio question punishes it.
- Ratios not simplified — or simplified at the wrong time. Simplifying 12 : 18 to 2 : 3 is right at the end, but simplifying before applying a change ("then 6 more red beads are added") destroys the information.
- The unchanged quantity going unnoticed. In many problems one quantity stays constant (often the total, often one person's share). Spotting what didn't change is usually the entire solution.
- Answering in units. Finishing with "4 units" instead of converting back to beads, dollars or people.
Example question — changing ratio
Try it: the ratio changes
The ratio of the number of red beads to blue beads in a box is 5 : 3. After 12 red beads are removed, there are equal numbers of red and blue beads. How many blue beads are in the box?
Show the worked solution
Blue beads never change. Start: red = 5 units, blue = 3 units.
After removing 12 red beads, red equals blue: 5 units − 12 = 3 units.
So 2 units = 12, and 1 unit = 6.
Blue beads = 3 units = 18 beads.
Check: red starts at 30; remove 12 → 18 red, 18 blue. Equal. ✓
Try it: sharing with a difference
A sum of money is shared between Wei Ming and Jun Hao in the ratio 7 : 5. Wei Ming receives $24 more than Jun Hao. How much money is shared altogether?
Show the worked solution
The difference is 7 − 5 = 2 units, and that difference is $24.
So 1 unit = $12.
Total = 7 + 5 = 12 units = 12 × $12 = $144.
Check: Wei Ming $84, Jun Hao $60 — difference $24, ratio 84 : 60 = 7 : 5. ✓
How to practise this topic
The changing-ratio structure deserves deliberate, repeated practice — it is the single most common shape of a P6 ratio exam question. Practise identifying the unchanged quantity before computing anything. And because ratio leans on P5 fraction skills, a child struggling here often needs a short detour back to P6 Fractions rather than more ratio drills.
What this topic covers
In the MOE syllabus, Primary 6 Ratio (P6-M-05) includes:
- Ratio and its relationship to fractions
- Equivalent ratios
- Ratio involving two quantities
- Ratio involving three quantities
- Changing ratios (before and after)
- Ratio word problems
Before this topic
These topics feed into Ratio — if this one wobbles, check them first: Primary 6 Fractions.
Is Ratio actually solid?
A 15-minute check-up maps exactly which concepts your child has mastered — and re-tests them days later to prove the fixes stuck. Free.
Start the free check-up