Ratio and Proportion in P6: The Step-by-Step Guide That Actually Makes Sense

In my years of teaching, I could predict with some confidence which topics would appear in every parent-teacher meeting after a P6 term test. Ratio was always on the list.

The reason isn't that ratio is conceptually complex — the underlying idea is simple. The problem is that ratio questions in HK primary exams come in many formats, and students who haven't seen all the formats confidently misapply the approach from one type to another.

This guide covers every major P6 ratio question type. Work through it with your child and you'll have closed most of the mark-loss risk before the next exam.

The Core Concept

A ratio expresses a relationship between quantities. The ratio 3:2 means "for every 3 of this, there are 2 of that."

This relationship is multiplicative, not additive. If the ratio of boys to girls is 3:2 and you have 15 boys, you have 10 girls — not 14 (which would be the additive error: 15 − 1).

The fundamental operation: find the value of one "part."

If boys:girls = 3:2 and total = 25 students:

• Total parts = 3 + 2 = 5
• Each part = 25 ÷ 5 = 5 students
• Boys = 3 × 5 = 15
• Girls = 2 × 5 = 10

Master this one calculation and 60% of ratio questions become straightforward.

Question Type 1: Find One Quantity Given the Total

"A bag of 36 sweets contains strawberry and mango flavours in the ratio 5:4. How many strawberry sweets are there?"

1. Total parts = 5 + 4 = 9
2. Each part = 36 ÷ 9 = 4 sweets
3. Strawberry = 5 × 4 = 20 sweets
4. Mango = 4 × 4 = 16 sweets (check: 20 + 16 = 36 ✓)

Always check that your parts sum to the total. This catch prevents errors from propagating.

Question Type 2: Find the Ratio from Given Quantities

"A recipe uses 250g of flour and 150g of sugar. Write the ratio of flour to sugar in its simplest form."

1. Write as a ratio: 250:150
2. Find the HCF of 250 and 150. HCF = 50
3. Divide both by 50: 5:3

Common error: dividing by a common factor that isn't the highest common factor, leaving a ratio that isn't fully simplified (e.g., 25:15 instead of 5:3).

Fix: After simplifying, ask "Can I divide both numbers by anything else?" If yes, keep simplifying.

Question Type 3: Three-Quantity Ratios

"A:B:C = 2:3:5. If A = 12, find C."

Method 1 (via one unit): A = 2 parts. 2 parts = 12, so 1 part = 6. C = 5 parts = 5 × 6 = 30

Method 2 (via ratio): A:C = 2:5. If A = 12, then C = 12 × (5/2) = 30

Both methods work. The first (find one unit) is more reliable for beginners because it generalises to any three-quantity problem.

Common exam variation: "A:B = 2:3 and B:C = 3:5. What is A:B:C?" Since B appears in both ratios with the same value (3), just read across: A:B:C = 2:3:5

But if the B values don't match — "A:B = 2:3 and B:C = 4:5" — you need to find the LCM: Scale A:B so B = 12: A:B = 8:12 Scale B:C so B = 12: B:C = 12:15 Now A:B:C = 8:12:15

This is the hardest version of the three-quantity ratio question. Expect it in P6 exams.

Question Type 4: Ratio Change Problems

"The ratio of Peter's savings to John's savings is 3:5. After Peter saves $40 more, the ratio becomes 1:1. How much did Peter originally save?"

These are the most challenging P6 ratio questions. Use a before-and-after table:

	Peter	John
Before	3 parts	5 parts
After	3 parts + 40	5 parts
After ratio	1	1

Since the after ratio is 1:1, the after amounts are equal: 3 parts + 40 = 5 parts 40 = 2 parts 1 part = 20

Peter originally = 3 × 20 = $60 John = 5 × 20 = $100 Check: 60 + 40 = 100 ✓ (equal ratio after change)

Question Type 5: Ratio and Fractions Combined

"⅔ of the students in a class are girls. The ratio of girls to boys is ___."

Girls = ⅔ of total → boys = ⅓ of total Girls:Boys = ⅔ : ⅓ = 2:1

Multiply both by 3 to remove fractions: 2:1

This question type confuses students who treat fractions and ratios as completely separate topics. Connecting them — a fraction of a total is equivalent to a ratio of parts — is an important P6 understanding.

Common Ratio Errors Summarised

Error	Example	Fix
Additive ratio thinking	Ratio 3:2, total 15; thinks one part = 15-1=14	Always find "one part" by dividing total by sum of ratio
Not simplifying fully	10:15 simplified to 5:7.5	Find HCF, check no further simplification possible
Wrong total in three-quantity	A:B:C = 2:3:5, finds each from 2+3 not 2+3+5	Always sum ALL ratio parts for the total
Forgetting to check	Answer: Peter $60, John $100, no verification	Always substitute answer back into original conditions

Ratio is learnable. The question types are finite. Work through each type with two or three examples and the marks will come.