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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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Corbett MathsRecurring decimals to fractions
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Key facts & methods

Fraction operations — fill in the table

OperationMethod
Add / subtract
Multiply
Divide
Mixed numbers
Simplifying

Recurring decimals to fractions — fill in the table

CaseMethod
Setup
1-digit recurrence
2-digit recurrence
Mixed recurrence
Terminating decimals
Exam questions — 4 questions · 10 marks · Edexcel 4MA1 style
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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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