Ratio & ProportionStudy Notes

Common Mistakes

Part of Ratio Problems · GCSE GCSE Mathematics revision

This study notes covers Common Mistakes within Ratio Problems for GCSE Mathematics. Revise Ratio Problems in Ratio & Proportion for GCSE Mathematics with 14 exam-style questions and 3 flashcards. This topic shows up very often in GCSE exams, so students should be able to explain it clearly, not just recognise the term. It is section 7 of 8 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 7 of 8

Practice

14 questions

Recall

3 flashcards

Common Mistakes

✗ £2 : 50p = 2:50 ✓ Convert first: 200p : 50p = 4:1

✗ 12:18 = 6:9 (stopped too early) ✓ 12:18 = 6:9 = 2:3 (keep simplifying!)

✗ 8:12:16 = 4:6:16 (only divided some parts) ✓ Divide ALL parts: 8:12:16 = 2:3:4

Practice Questions

Q1 Simplify: 15:20 [1 mark]

[1] HCF = 5, so 15:20 = 3:4

Q2 Simplify: £1 : 40p [2 marks]

[1] £1 = 100p, so 100:40

[1] HCF = 20, so 100:40 = 5:2

Q3 Simplify: 16:24:40 [2 marks]

[1] HCF = 8

[1] 16:24:40 = 2:3:5

Q4 Simplify: 1 hour : 36 minutes [2 marks]

[1] 1 hour = 60 mins, so 60:36

[1] HCF = 12, so 60:36 = 5:3

Q5 Simplify: 6:9 [1 mark]

[1] HCF = 3, so 6:9 = 2:3

Q6 Simplify: 10:25 [1 mark]

[1] HCF = 5, so 10:25 = 2:5

Q7 Simplify: 24:36 [2 marks]

[1] HCF = 12

[1] 24:36 = 2:3

Q8 Simplify: £3 : 60p [2 marks]

[1] £3 = 300p, so 300:60

[1] HCF = 60, so 300:60 = 5:1

Q9 Simplify: 2 hours : 30 minutes [2 marks]

[1] 2 hours = 120 mins, so 120:30

[1] HCF = 30, so 120:30 = 4:1

Q10 Simplify: 6:9:12 [2 marks]

[1] HCF = 3

[1] 6:9:12 = 2:3:4

Q11 Simplify: 18:27 [2 marks]

[1] HCF = 9

[1] 18:27 = 2:3

Q12 Write 0.5 : 1.5 as a ratio in simplest form [3 marks]

[1] Multiply by 10 to remove decimals: 5:15

[1] HCF = 5

[1] 5:15 = 1:3

Q13 Simplify: 2 km : 500 m [3 marks]

[1] 2 km = 2000 m, so 2000:500

[1] HCF = 500

[1] 2000:500 = 4:1

Q14 Simplify: 12:18:24:30 [3 marks]

[1] HCF of all four = 6

[1] Divide all by 6: 2:3:4:5

[1] 2:3:4:5

Q15 Simplify: 1.5 kg : 250 g [3 marks]

[1] 1.5 kg = 1500 g, so 1500:250

[1] HCF = 250

[1] 1500:250 = 6:1

Q16 Simplify: 144:108 [2 marks]

[1] HCF = 36

[1] 144:108 = 4:3

Q17 Write 1/2 : 1/3 as a ratio in simplest form [3 marks] Challenge

[1] Multiply both by 6 (LCM of 2 and 3): 3:2

[1] Already simplified

[1] 3:2

Q18 A recipe uses 300g flour and 200g butter. Write this as a ratio in simplest form. [3 marks]

[1] Ratio: 300:200

[1] HCF = 100

[1] 3:2

Q19 Car A travels at 60 mph, Car B at 45 mph. Write their speeds as a ratio in simplest form. [4 marks] Challenge

[1] Ratio: 60:45

[1] HCF = 15

[1] 60:45 = 4:3

[1] 4:3

Q20 Simplify: £2.50 : £1.25 [3 marks]

[1] Convert to pence: 250:125

[1] HCF = 125

[1] 250:125 = 2:1

Q21 Simplify: 40:100 [2 marks]

[1] HCF = 20

[1] 40:100 = 2:5

Q22 A paint mixture uses 20 ml red, 30 ml blue, and 50 ml white. Write as a ratio in simplest form. [3 marks]

[1] Ratio: 20:30:50

[1] HCF = 10

[1] 2:3:5

Q23 Tom works 8 hours per day, Sarah works 300 minutes per day. Write their working times as a ratio in simplest form. [4 marks] Challenge

[1] 8 hours = 480 minutes

[1] Ratio: 480:300

[1] HCF = 60

[1] 8:5

Q24 Rectangle A has dimensions 6cm × 8cm. Rectangle B has dimensions 9cm × 12cm. Write the ratio of their areas in simplest form. [4 marks] Challenge

[1] Area A = 6 × 8 = 48 cm²

[1] Area B = 9 × 12 = 108 cm²

[1] Ratio: 48:108, HCF = 12

[1] 4:9

Q25 Simplify: 35:42 [2 marks]

[1] HCF = 7

[1] 35:42 = 5:6

Q26 Town A has 15,000 people, Town B has 25,000 people. Write as a ratio in simplest form. [4 marks]

[1] Ratio: 15000:25000

[1] HCF = 5000

[1] 15000:25000 = 3:5

[1] 3:5

Q27 40% of students walk to school, 60% travel by bus. Write this as a ratio in simplest form. [4 marks] Challenge

[1] Ratio: 40:60

[1] HCF = 20

[1] 40:60 = 2:3

[1] 2:3

Q28 Simplify: 2.5 kg : 750 g : 0.5 kg [5 marks] Challenge

[1] Convert to grams: 2500:750:500

[1] HCF = 250

[1] Divide all by 250: 10:3:2

[2] 10:3:2

Q29 The ratio of boys to girls in a school is 7:8. There are 450 students. Write the ratio in a different form showing boys:girls:total. [4 marks] Challenge

[1] Total parts = 7 + 8 = 15

[1] Boys:Girls:Total = 7:8:15

[2] 7:8:15

Q30 A garden is 15 m long and 900 cm wide. Write the ratio length:width in simplest form. [5 marks] Challenge

[1] Convert 15 m to cm: 1500 cm

[1] Ratio: 1500:900

[1] HCF = 300

[1] 1500:900 = 5:3

[1] 5:3

Examiner says: Always convert to the same units FIRST - this is the most common mistake in ratio questions. Choose the smaller unit to avoid decimals (cm not m, pence not pounds, minutes not hours).

Keep building this topic

Read this section alongside the surrounding pages in Ratio Problems. That gives you the full topic sequence instead of a single isolated revision point.

Worked Example 3: Three-Part Ratio Knowledge Organiser: Simplifying Ratios What Is a Ratio?Key Rules for Simplifying

Practice Questions for Ratio Problems

A recipe uses flour and sugar in the ratio 5:2. What fraction of the mixture is flour?

A. 5/2
B. 5/7
C. 2/5
D. 2/7

1 markfoundation

The ratio of apples to oranges in a basket is 2:3. Sarah says "2/3 of the fruits are apples." Explain why Sarah is wrong.

2 marksstandard

Quick Recall Flashcards

Unit Rule

ALWAYS convert to the SAME units before simplifying (e.g., all in pence, all in minutes)

Simplifying Ratios

Divide ALL parts by their Highest Common Factor (HCF). Keep going until you can't simplify further.

14 questions on Ratio Problems — practise free

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Worked Example 3: Three-Part Ratio

Knowledge Organiser: Simplifying Ratios