GCSE · Fractions & decimals

The four operations with fractionsExam-style questions

Why adding fractions needs a common denominator but multiplying doesn't, why dividing flips the second fraction, and why mixed numbers must become improper before multiplying or dividing.

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

DifficultyAllLevel 1Level 2Level 3Level 4Level 5
  1. 1
    (a) Work out 416−1344\frac{1}{6} - 1\frac{3}{4}

    Give your answer as a mixed number.

    (2 marks)

    Omar was asked to work out 423×564\frac{2}{3} \times \frac{5}{6}

    Here is his working and his answer.

    423×56=143×564\frac{2}{3} \times \frac{5}{6} = \frac{14}{3} \times \frac{5}{6}

    =7018= \frac{70}{18}

    =4218= 4\frac{2}{18}

    Omar's answer is wrong.
    (b) What mistake has Omar made?

    (1 mark)
    Level 3 · 3 marksTry it
  2. 2
    Work out

    (a) 38+56\dfrac{3}{8} + \dfrac{5}{6} — give your answer as a mixed number in its simplest form.

    (b) 710−215\dfrac{7}{10} - \dfrac{2}{15} — give your answer in its simplest form.
    Level 3 · 4 marksTry it
  3. 3
    Work out

    (a) 49×310\dfrac{4}{9} \times \dfrac{3}{10} — give your answer in its simplest form.

    (b) 58÷1516\dfrac{5}{8} \div \dfrac{15}{16} — give your answer in its simplest form.
    Level 3 · 4 marksTry it
  4. 4
    Work out 315−1343\tfrac{1}{5} - 1\tfrac{3}{4}

    Give your answer as a mixed number in its simplest form.
    Level 3 · 3 marksTry it