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Unit 1 · NumberPearson Edexcel IGCSE · 4MA1 Higher

Fractions & Recurring Decimals

Fraction operations, recurring decimals to fractions. Non-calculator Paper 1 staples.

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Key facts & methods

Fraction operations

  • Add/subtract: find common denominator. 2/3 + 3/4 = 8/12 + 9/12 = 17/12 = 1 5/12.
  • Multiply: multiply numerators × numerators, denominators × denominators. Cancel before multiplying if possible.
  • Divide: keep the first fraction, change ÷ to ×, flip the second. KCF. E.g. 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8.
  • Mixed numbers: convert to improper fractions first for multiply/divide.
  • Always simplify final answers.

Recurring decimals to fractions

  • Let x = the recurring decimal.
  • 1-digit recurrence: multiply by 10. E.g. x = 0.777... → 10x = 7.777... → 9x = 7 → x = 7/9.
  • 2-digit recurrence: multiply by 100. E.g. x = 0.363636... → 100x = 36.3636... → 99x = 36 → x = 36/99 = 4/11.
  • Mixed: e.g. x = 0.1333... → 10x = 1.333... → 100x = 13.333... → 90x = 12 → x = 12/90 = 2/15.
  • Terminating decimals: finite number of decimal places → always a fraction with denominator 2ⁿ × 5ᵐ.
Exam questions — 4 questions · 10 marks · Edexcel 4MA1 style
Show ALL working — the AI awards method marks just like a real examiner. Partial credit for correct working even if the final answer is wrong.
3 marksFraction operations4MA1 Paper 1H style ✏️ No calculator

Work out: 2³⁄₄ ÷ 1¹⁄₂ × ²⁄₃. Give your answer as a fraction in its simplest form. (3 marks)

Hint: Convert all mixed numbers to improper fractions first. For ÷: keep, change, flip (KCF). Then multiply. Simplify at the end.
+30 XP
3 marksRecurring decimal to fraction4MA1 Paper 1H style ✏️ No calculator

Show that 0.̄3̄6̄ (0.363636...) = 4/11. (2 marks) Then convert 0.1̄3̄ (0.1333...) to a fraction. (2 marks)

Hint: For 0.363636...: multiply by 100 (2 recurring digits). Subtract x. For 0.1333...: one non-recurring digit, so multiply by 10 and by 100, then subtract.
+30 XP
1 markWhich is rational4MA1 style

Which of the following is a terminating decimal?

A 1/3
B 1/7
C 3/8
D 2/9
2 marksReverse fraction problem4MA1 Set 2 P1H style ✏️ No calculator

In a class, 5/8 of the students are girls. There are 15 girls. How many students are in the class altogether? (2 marks)

Hint: 5/8 of the total = 15. So total = 15 ÷ (5/8). Dividing by a fraction: multiply by its reciprocal.
+20 XP

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