GCSE · Fractions & decimals

Converting fractions, decimals and percentagesExam-style questions

One amount can be written as a fraction, a decimal or a percentage. Why per cent means "out of 100", how to move between the three forms in every direction, how to put a mixed list in order, and how to write one quantity as a fraction or a percentage of another, including answers bigger than 100%.

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11 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAllLevel 3Level 4
  1. 1
    On the front wall of a house
    • the area of the window is 4.84.8 m²
    • the area of the whole wall is 3030 m²
    Express the area of the window as a fraction of the area of the wall.

    Give your answer in its simplest form.

    (3 marks)
    Level 4 · 3 marksTry it
  2. 2
    A school library lent 10801080 books last year.

    This year the library lent 13501350 books.
    (a) Write the number of books lent this year as a percentage of the number lent last year.

    (2 marks)

    Mo says,

    "So last year the library lent 25%25\% fewer books than this year."
    (b) Is Mo correct?

    Tick a box.

    Yes ☐ \qquad\qquad No ☐

    Give a reason for your answer.

    (1 mark)
    Level 4 · 3 marksTry it
  3. 3
    There are 240240 students in Year 9.

    Each student chooses one option: art, drama or music.

    38\dfrac{3}{8} of the students choose art.

    35%35\% of the students choose drama.

    The rest of the students choose music.

    What fraction of the students choose music?

    Give your answer in its simplest form.

    (4 marks)
    Level 4 · 4 marksTry it
  4. 4
    Write the following in order of size, smallest first.

    5−10.21331419%5^{-1} \qquad 0.213 \qquad \frac{3}{14} \qquad 19\%

    Show how you decide.

    (3 marks)
    Level 4 · 3 marksTry it
  5. 5
    On Saturday, a bakery made 360360 bread rolls.

    512\dfrac{5}{12} of these rolls were white.

    45%45\% of these rolls were brown.

    The rest of these rolls were seeded.

    On Sunday, the bakery made 280280 bread rolls.

    15%15\% of the rolls made on Sunday were seeded.

    Jia says,

    "A greater proportion of the rolls were seeded on Saturday than on Sunday."

    Is Jia correct?

    You must show how you get your answer.

    (5 marks)
    Level 4 · 5 marksTry it