AQA GCSE Mathematics Paper 3 (Higher), June 2025: Question 7

4 marks · Medium difficulty · Short Answer

Convert units to write one quantity as a fraction of another, express a ratio with mixed units in the form 1 : n, and express a ratio of fractions as a single fraction.

Practise this question

Question

Question 7 has three parts. Part (a) asks to write 2 weeks as a fraction of 8 days in its simplest form, worth 1 mark. Part (b) asks to write 56 centimetres to 2.73 metres as a ratio in the form 1 to n, worth 1 mark. Part (c) states that A to B equals 1/5 to 7/10 and asks to write A as a fraction of B, worth 2 marks.

Mark scheme

Show the mark scheme Mark scheme for Question 7: For (a), gives 7/4 with mark B1, noting not to accept 1 3/4 or 1.75. For (b), gives 4.875 or 39/8 or 4 7/8 with mark B1, accepting equivalent decimal, fraction, or mixed number. For (c), M1 is awarded for finding common denominators, writing (1/5)/(7/10), 1/5 times 10/7, 0.2/0.7, or ratio 2 : 7; A1 is awarded for 2/7.

How to answer it

Fractions, Unit Conversions, and Ratios

📌 What this question tests

This question assesses your ability to convert between units of time and length, simplify improper fractions, express quantities as unit ratios in the form 1 : n , and divide fractional ratio components to express one quantity as a fraction of another.

Part (a)

Writing One Quantity as a Fraction of Another

1 Mark

📐 Step-by-Step Solution

Step 1: Convert both quantities to the same unit (days).
There are 7 days in 1 week, so 2 weeks = 2 × 7 = 14 days .
Step 2: Form the fraction "2 weeks as a fraction of 8 days":
Fraction = 14 / 8
Step 3: Simplify fully by dividing the numerator and denominator by their highest common factor (2):
14 ÷ 2 = 7 and 8 ÷ 2 = 4 ➔ 7/4

✅ Correct Answer

7/4

[B1] for fully simplified improper fraction 7/4 .

❌ Common Errors & Traps

  • Changing to a mixed number or decimal: Giving 1 ¾ or 1.75 is explicitly awarded 0 marks (B0). The question asked for a fraction in simplest form.
  • Ignoring units: Writing 2/8 = 1/4 without converting weeks to days first.

🧠 Exam Technique

In GCSE mark schemes, "fraction in its simplest form" for values greater than 1 strictly prefers an improper fraction ( 7/4 ) unless stated otherwise. Do not convert to mixed numbers unless asked!

Part (b)

Writing a Ratio in the Form 1 : n

1 Mark

📐 Step-by-Step Solution

Step 1: Convert both parts of the ratio to the same unit (centimetres).
There are 100 cm in 1 metre, so 2.73 m = 2.73 × 100 = 273 cm .
The ratio is now 56 : 273 .
Step 2: Divide both sides by the first number (56) to get 1 on the left:
1 : (273 ÷ 56)
Step 3: Calculate the value of n:
273 ÷ 56 = 4.875 (or as a fraction: 39/8 or 4 ⅞ or 273/56 ).

✅ Correct Answer

Answer line gives: 1 : _____

Fill in: 4.875 (or 39/8, 4 ⅞, 273/56)

[B1] for 4.875 or equivalent fraction/mixed number. Rounded values 4.88 or 4.9 accepted only if 4.875 is seen in working.

❌ Common Errors & Traps

  • Including units in the ratio: Ratios compare quantities of the same unit and must be unitless. Writing 1 : 4.875 m or 1 : 4.875 cm scores 0 marks (B0).
  • Leaving as an unsimplified fraction: Leaving the answer line as 2.73 / 0.56 scores B0.
  • Premature rounding: Writing 4.9 without showing 4.875 in the working space loses the mark.

Part (c)

Writing One Part as a Fraction of Another

2 Marks

📐 Step-by-Step Solution

Method 1 (Common Denominator):
Convert both fractions to tenths:
A = 1/5 = 2/10
B = 7/10
Since the denominators are equal, A : B = 2 : 7 .
Therefore, A as a fraction of B is simply 2/7.
Method 2 (Direct Division):
"A as a fraction of B" means calculating A ÷ B :
1/5 ÷ 7/10 = 1/5 × 10/7 = 10/35 = 2/7 .

✅ Correct Answer & Marks

2/7

[M1] for finding a common denominator (e.g. 2/10 and 7/10 ), setting up 1/5 × 10/7 , or writing the ratio as whole numbers 2 : 7 .
[A1] for the final answer 2/7 (or equivalent fraction).

❌ Common Errors & Traps

  • Inverting the relationship: Calculating B as a fraction of A ( 7/2 or 3.5 ). This scores a special case [SC1] if no other marks are earned.
  • Stopping at the ratio: Writing 2 : 7 or 0.2 : 0.7 and stopping scores M0 unless the final fraction 2/7 is written.
  • Leaving decimals within fractions: Writing 1 / 3.5 only scores the method mark [M1]; it must be written using whole numbers for full marks.

💡 Key Knowledge: "X as a fraction of Y"

Whenever an exam asks for "X as a fraction of Y", the mathematical operation is always:
Fraction = X / Y
The term that follows the word "of" always goes in the denominator (bottom).

Topics

Number · Ratio, proportion and rates of change · 3.1.2 Fractions, decimals and percentages · 3.3 Ratio, proportion and rates of change

Question and mark scheme from the AQA GCSE Mathematics examination, Paper 3 (Higher), June 2025. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.