Ratio and Rate: Every Exam Question Type

All the ratio and rate skills a Grade 8–9 exam tests — simplifying, sharing in a ratio, finding a missing part, equivalent ratios, increasing/decreasing in a ratio, and unit rates — each worked in full, with a worksheet.

A ratio compares two quantities of the same kind (blue paint to red paint), while a rate compares quantities of different kinds (kilometres to hours). This guide covers every ratio and rate question an exam sets.

1Type 1: Simplifying a ratio

Simplify like a fraction: divide both parts by their highest common factor. Units must be the same first.

Sharing in the ratio 3 : 5 splits the whole into 8 equal parts — 3 in one share, 5 in the other.

Worked ExampleExample 1: simplify 12 : 18

1
HCF of 12 and 18 is 6.
The largest number dividing both.
2
12 ÷ 6 = 2 and 18 ÷ 6 = 3.
Divide both parts equally.
3
Answer: 2 : 3.

2Type 2: Sharing an amount in a ratio

Worked ExampleExample 2: share R400 in the ratio 3 : 5

1
Add the parts: 3 + 5 = 8.
The total number of equal shares.
2
One share: R400 ÷ 8 = R50.
Divide the total by the SUM of the parts.
3
Multiply out: 3 × R50 = R150 and 5 × R50 = R250.
Check: R150 + R250 = R400 ✓

3Type 3: Finding a missing part (equivalent ratios)

If two ratios are equal, find the multiplier from the known pair and apply it.

Worked ExampleExample 3: 2 : 3 = 8 : ?

1
How do you get from 2 to 8? Multiply by 4.
8 ÷ 2 = 4 is the scale factor.
2
Apply the same to the other part: 3 × 4 = 12.
Both parts scale by the same factor.
3
Answer: 2 : 3 = 8 : 12.

4Type 4: Increasing or decreasing in a ratio

Worked ExampleExample 4: increase 60 in the ratio 5 : 3

1
The new amount compares to the old as 5 : 3, so multiply by 5⁄3.
The first number is the 'new', the second the 'old'.
2
60 × 5⁄3 = 60 ÷ 3 × 5 = 100.
5 : 3 is bigger than 1, so it increases.
3
Answer: 100.

5Type 5: Rates and unit rates

Worked ExampleExample 5: a car travels 240 km in 3 hours

1
Rate = distance ÷ time = 240 ÷ 3.
A rate compares two different units.
2
= 80 km/h.
This is the unit rate ('per 1 hour').

Worked ExampleExample 6: best buy: 500 g for R30 vs 800 g for R44

1
Price per gram: R30 ÷ 500 = R0,06 vs R44 ÷ 800 = R0,055.
Compare using the same unit (per gram).
2
The 800 g pack is cheaper per gram, so it's the better buy.
Lower unit rate = better value.

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Keep the order. A ratio of 3 : 5 is not the same as 5 : 3 — the order must match the order named in the question.

⚠️

Divide by the SUM of the parts, not one part. Splitting R400 in ratio 3 : 5 uses 8 shares — a very common exam slip is dividing by 3 or 5.

Ratio and rate come up in financial maths, measurement and Maths Literacy too, so the practice below pays off well beyond Grade 8. Work through every type.

Practice exercises

Work each one out, then click to reveal the answer.

📄 Worksheet ✅ Memo 📝 Exam paper 🗝️ Marking guide

1
Simplify 15 : 25 (simplify)
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÷5 → 3 : 5
2
Simplify 24 : 36 (simplify)
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÷12 → 2 : 3
3
Share 56 sweets in the ratio 3 : 4 (share)
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7 parts → 8 each; 24 and 32
4
Share R720 in the ratio 2 : 3 : 4 (share)
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9 parts → R80 each; R160, R240, R320
5
Complete: 3 : 4 = 15 : ? (equivalent)
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×5 → 20
6
Complete: 5 : 2 = ? : 8 (equivalent)
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×4 → 20
7
Increase 40 in the ratio 7 : 5 (increase)
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40 × 7⁄5 = 56
8
Decrease 90 in the ratio 2 : 3 (decrease)
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90 × 2⁄3 = 60
9
A worker earns R900 in 6 hours. Rate per hour? (rate)
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900 ÷ 6 = R150/h
10
Which is cheaper: 2 kg for R50 or 3 kg for R72? (best buy)
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R25/kg vs R24/kg → 3 kg pack