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 7 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 7
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).