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 same before-and-after thinking carries over to average questions, where the total changes each time someone joins or leaves a group.
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.
Bar models for ratio
Easy: sharing and simplifying warm-ups
Easy: sharing in a given ratio
Ann and Ben share some money in the ratio 2 : 5. Ann receives $18. How much does Ben receive?
Show the worked solution
2 units = $18, so 1 unit = $9.
Ben = 5 units = 5 × $9 = $45.
Easy: simplifying a ratio
Express 24 : 36 in its simplest form.
Show the worked solution
Divide both parts by their common factor, 12: 24 ÷ 12 = 2, 36 ÷ 12 = 3.
2 : 3.
Easy: three-way sharing
$120 is shared among X, Y and Z in the ratio 1 : 2 : 3. How much does Y receive?
Show the worked solution
Total units: 1 + 2 + 3 = 6 units = $120, so 1 unit = $20.
Y = 2 units = $40.
Easy: ratio as a fraction of the whole
In a class, the ratio of boys to girls is 3 : 4. What fraction of the class are boys?
Show the worked solution
Total units = 3 + 4 = 7. Boys = 3 units.
Boys as a fraction of the class = 3/7.
Exam: changing ratios and comparisons
Exam: 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. ✓
Exam: 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. ✓
Exam: ratio and a given difference in a collection
The ratio of Pei Ling's stamps to Farhan's stamps is 4 : 7. Farhan has 36 more stamps than Pei Ling. How many stamps do they have altogether?
Show the worked solution
Difference: 7 − 4 = 3 units = 36 stamps, so 1 unit = 12.
Total = 4 + 7 = 11 units = 11 × 12 = 132 stamps.
Exam: a quantity added changes the ratio
A box has red and green marbles in the ratio 3 : 2. After 10 more green marbles are added, the ratio becomes 3 : 4. How many red marbles are in the box?
Show the worked solution
Red never changes, so scale both ratios to the same number of red units: 3 : 2 and 3 : 4 already share "3" for red — good, no scaling needed.
Green goes from 2 units to 4 units, a rise of 2 units, which equals the 10 marbles added: 2 units = 10, so 1 unit = 5.
Red = 3 units = 15 marbles.
Check: red 15, green 10 (ratio 3:2); +10 green → green 20, ratio 15:20 = 3:4. ✓
Exam: ratio and perimeter
A rectangle has length to breadth in the ratio 5 : 3. Its perimeter is 96 cm. Find its length.
Show the worked solution
Perimeter = 2 × (length + breadth), so length + breadth = 48 cm = 5 units + 3 units = 8 units.
1 unit = 6 cm. Length = 5 units = 30 cm.
PSLE challenge: ratio with fractions and combined groups
PSLE challenge: ratio equalised after two changes
Kai and Lina have money in the ratio 5 : 3. After Kai spends $40 and Lina receives $20 more, they have the same amount of money. How much money did Kai have at first?
Show the worked solution
Let 1 unit = u, so Kai = 5u, Lina = 3u at first.
After the changes: Kai has 5u − 40; Lina has 3u + 20. These are equal.
5u − 40 = 3u + 20, so 2u = 60, and u = 30.
Kai at first = 5 × 30 = $150.
Check: Kai $150 − $40 = $110; Lina $90 + $20 = $110 — equal. ✓
PSLE challenge: combining two ratios
The ratio of cats to dogs in a shelter is 2 : 3, and the ratio of dogs to rabbits is 4 : 5. Find the ratio of cats to dogs to rabbits.
Show the worked solution
Make the "dogs" term match in both ratios. Cats : dogs = 2 : 3 = 8 : 12 (×4). Dogs : rabbits = 4 : 5 = 12 : 15 (×3).
Now dogs = 12 in both: cats : dogs : rabbits = 8 : 12 : 15.
PSLE challenge: ratio, a fraction donated, and a remainder
Farah and Gopal share a sum of money in the ratio 3 : 5. Farah donates 1/4 of her share to charity, leaving her with $54. How much money did Farah and Gopal share altogether?
Show the worked solution
Farah kept 3/4 of her share, so 3/4 of her share = $54, meaning her full share = $72.
Her share is 3 units, so 1 unit = $24. Total = 3 + 5 = 8 units = 8 × $24 = $192.
Check: Farah $72 → donates $18 → left $54. ✓
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 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 Primary Mathematics syllabus, Primary 6 Ratio includes the concepts below. (P6-M-05 is Test Paper's own topic code, not an MOE reference.)
- 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.
Where to go next
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