AQA GCSE Maths

Algebraic fractions

AQA GCSE Maths revision on Algebraic fractions. Aligned to the AQA GCSE Mathematics 8300 specification. This bank has 16 practice questions on this topic.

Sample questions (3 of 16)

  1. Question 1

    A student attempts to simplify (x + 3) / (x + 5) by crossing out the x in the numerator and denominator to get 3 / 5. Why is this incorrect?

    • A) The x in the numerator is a term, not a factor.
    • B) You can only cancel terms if they are both negative.
    • C) The fraction must be multiplied by x first.
    • D) The x in the denominator should have been squared.
    Show answer

    Answer: The x in the numerator is a term, not a factor.

    In an algebraic fraction, you can only cancel terms that are factors of the entire numerator and denominator. Since x is being added to 3 and 5, it is part of a sum, not a multiplier, meaning it cannot be isolated and cancelled independently.

  2. Question 2

    When adding two algebraic fractions with different denominators, what is the mandatory first step?

    • A) Add the numerators together directly.
    • B) Find a common denominator.
    • C) Cancel any common factors in the first fraction.
    • D) Multiply the two fractions together.
    Show answer

    Answer: Find a common denominator.

    Just like numerical fractions, algebraic fractions represent parts of a whole. To combine them, you must express them in terms of the same unit, which is achieved by finding the lowest common multiple of the denominators.

  3. Question 3

    Which algebraic technique is most useful for simplifying a fraction where the numerator is x^2 - 9 and the denominator is x - 3?

    • A) Completing the square
    • B) Difference of two squares
    • C) Quadratic formula
    • D) Expanding brackets
    Show answer

    Answer: Difference of two squares

    The expression x^2 - 9 fits the pattern a^2 - b^2, which factorises to (x - 3)(x + 3). By identifying this, you can cancel the (x - 3) factor from both the numerator and denominator.

Want to test yourself on the remaining cards for this topic?

13 more questions on Algebraic fractions — plus mistakes tracking and spaced repetition across the whole Maths spec.

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