AQA GCSE Mathematics Paper 1 (Foundation), June 2025: Question 23

3 marks · Medium difficulty · Multi-step Problem

Calculate the value of 4/15 + 1/5 ÷ 1/2, giving the final answer as a fraction.

Practise this question

Question

Question 23 asks to work out the expression 4 over 15 plus 1 over 5 divided by 1 over 2, giving the answer as a fraction. The question is worth 3 marks and provides working lines followed by an answer line.

Mark scheme

Show the mark scheme Mark scheme for question 23: M1 for correct method to divide by 1/2, implied by 0.4, 2/5, or 1/2.5; M1 for correct method to add two fractions with different denominators, implied by 7/15; A1 for 2/3 or an equivalent fraction like 10/15. Special case SC2 gives 14/15 for calculating (4/15 + 1/5) ÷ 1/2.

How to answer it

Order of Operations with Fractions

📌 What this question tests

This question tests your ability to apply the correct order of operations (BIDMAS/BODMAS) to mixed fraction calculations. Specifically, you need to execute fraction division before fraction addition, find a common denominator, and present your final answer as a fraction.

Question 23 (3 Marks)

Work out 4/15 + 1/5 ÷ 1/2

Give your answer as a fraction.

📐 Step-by-Step Calculation

1 Apply BIDMAS / Priority of Operations:

Division must be carried out before addition. The calculation splits into:

4/15 + (1/5 ÷ 1/2)

2 Carry out the division (Keep, Change, Flip):

1/5 ÷ 1/2 = 1/5 × 2/1 = 2/5

Awarded [M1] for correctly dividing by 1/2 (can also be implied by finding 2/5 or 0.4).

3 Add the fractions using a common denominator:

The expression is now 4/15 + 2/5 . The lowest common multiple of 15 and 5 is 15.

Convert 2/5: multiply numerator and denominator by 3: 2/5 = 6/15

Now add numerators: 4/15 + 6/15 = 10/15

Awarded [M1] for a correct method to add fractions with different denominators.

4 Simplify to simplest form (recommended):

10/15 = (10 ÷ 5) / (15 ÷ 5) = 2/3

Awarded [A1] for 2/3 (or any equivalent fraction like 10/15).

✅ Correct Answer

2/3

Also accepted: any equivalent fraction, e.g., 10/15 , 20/30 .

Mark Breakdown:
• M1: Correct division by 1/2 (gives 2/5)
• M1: Correct addition method with common denominator
• A1: Final fraction answer of 2/3 (or equivalent)

💡 Key Knowledge

  • BIDMAS: Brackets, Indices, Division & Multiplication, Addition & Subtraction.
  • Fraction Division: Multiply by the reciprocal ("Keep, Change, Flip"): a/b ÷ c/d = a/b × d/c .
  • Fraction Addition: Denominators must be identical before adding numerators. Never add denominators together!

❌ Common Errors & Examiner Traps

  • Ignoring BIDMAS (The Left-to-Right Trap):
    Adding first: 4/15 + 1/5 = 7/15 , then dividing by 1/2 to get 14/15 .
    Examiner note: This was very common! The mark scheme awards a special case SC2 for 14/15, costing 1 mark.
  • Converting to Decimal:
    Writing 0.66... or 0.67 as the final answer loses the final accuracy mark because the question strictly specified: "Give your answer as a fraction."
  • Flipping the wrong fraction:
    Turning 1/5 ÷ 1/2 into 5/1 × 1/2 = 5/2 . Only invert the second fraction!

🧠 Exam Technique & Mark Protection

  • Put brackets around operations: When you see mixed symbols (+ and ÷), immediately draw brackets around the division: 4/15 + (1/5 ÷ 1/2) .
  • Read simplifying rules: The question did not say "in its simplest form". Leaving your answer as 10/15 earns full marks!
  • Examiner bonus rule: The mark scheme states: "Ignore incorrect simplification of a correct fraction". For example, writing 10/15 = 4/5 still scored 3/3 marks because 10/15 was already achieved!

Topics

Number · 3.1.1 Structure and calculation · 3.1.2 Fractions, decimals and percentages

Question and mark scheme from the AQA GCSE Mathematics examination, Paper 1 (Foundation), June 2025. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.