Pearson Edexcel International GCSE in Mathematics (Specification A) · 4MA1 · Free · no account needed

Fractions & Mixed Numbers

In one sentence. Adding, multiplying and dividing fractions with certainty — and the bar-model picture that makes worded fraction problems fall open.

Number — one of 8 modules in this strand, and one of 53 in Pearson Edexcel International GCSE Mathematics. Both tiers.

This module ends with Leonardo Fibonacci. Learn Fractions & Mixed Numbers, teach it, then defend it against Leonardo Fibonacci.

Where this sits in the specification

Specification 4MA1, 1.2 Fractions. Incandio is aligned to this specification; it is not published by, endorsed by or affiliated with Pearson, and the sub-topic numbers are given so you can check every module against your own copy.

  • 1.2 — Fractions

1 · Understand it

What it is

A fraction is a division waiting to happen: 3/8 is 3 ÷ 8, and also '3 parts of a whole cut into 8'. The four operations each have one reliable method: common denominators to add or subtract; multiply straight across; and dividing by a fraction is multiplying by its reciprocal.

Why it works

You can only add things that are the same size — 2 fifths + 1 third is like adding 2 apples and 1 orange until you rename both in a common unit (fifteenths). Dividing by a half doubles a number because '÷ 1/2' asks HOW MANY halves fit — which is why the reciprocal rule works: it is not a trick, it is the meaning of division.

When a question is asking for it

Any exact-answer arithmetic (fractions never round), any 'what fraction of…' or 'a tank is 5/8 full' problem, and inside almost every other topic: probability, ratio, algebraic fractions and gradients all lean on this module.

How to hold it in your head

Picture a bar. 5/8 full means 5 of 8 equal slices are shaded. Every worded fraction problem becomes: how many slices changed, and what is one slice worth? Once one slice has a value, the whole bar follows.

2 · The mistakes that cost marks

  • Adding tops and bottoms: 1/2 + 1/3 is NOT 2/5. (2/5 is smaller than 1/2 — the answer got smaller by adding, which should ring an alarm.)
  • Finding a common denominator to multiply. Multiplication needs no common denominator — that effort belongs to + and −.
  • Dividing by flipping the FIRST fraction. Only the divisor (the second fraction) is flipped.
  • Multiplying mixed numbers without converting: 2¾ × 1⅓ is not 2×1 and ¾×⅓ glued together. Convert to improper fractions first.

3 · Worked examples

Laid out the way an examiner wants working shown — every step is a mark.

Work out 2¾ × 1⅓.

  1. Convert to improper fractions: 2¾ = 11/4 and 1⅓ = 4/3.
  2. Multiply straight across: (11 × 4)/(4 × 3) = 44/12.
  3. Simplify (or cancel the 4s before multiplying): 11/3.

Answer: 11/3 (= 3⅔)

A tank is 5/8 full. After 42 litres are drained it is 1/4 full. How much does a full tank hold?

  1. The drained amount as a fraction of the tank: 5/8 − 1/4 = 5/8 − 2/8 = 3/8.
  2. So 3/8 of the tank = 42 litres, meaning 1/8 = 14 litres.
  3. The full tank is 8 eighths: 8 × 14.

Answer: 112 litres

4 · Prove it — the five questions

The five questions climb Grade 6 → 9+ and are marked inside Incandio on your own device, against authored accepted forms, with a diagnosis of the wrong answer you actually gave. The answers stay in the app so that the practice is worth doing; the questions themselves are here.

  1. Grade 6 — Work out 2/5 + 1/3, giving your answer as a fraction in its simplest form.
  2. Grade 7 — Work out 2¾ × 1⅓, giving your answer as an improper fraction in its simplest form.
  3. Grade 8 — Work out 3⅕ ÷ 2⅔, giving your answer as a fraction in its simplest form.
  4. Grade 9 — A water tank is 7/10 full. After 39 litres are drained, it is exactly 2/5 full. How many MORE litres must now be added to fill the tank completely? (answer in litres)
  5. 9+ — Work out (1/2 + 1/3) ÷ (1/2 − 1/3).

Think you understand it?

Reading is the start. On Incandio a topic counts as mastered only once you have taught it and defended it — the two things a revision guide cannot ask of you.

Incandio this topic → Prove it. Teach it. Defend it. What does “Incandio it” mean?

  1. Prove it — five questions on Fractions & Mixed Numbers, marked on the spot, that tell you what was missing rather than just what was wrong.
  2. Teach it — Explain how Fractions & Mixed Numbers works — and why — to Ember, an AI pupil who does not have it yet. The method matters more than the vocabulary.
  3. Defend it — Argue Fractions & Mixed Numbers against Leonardo Fibonacci — three rounds, marked against descriptors you can read before you begin.
  4. Then the exam — read all 11 authored exam-style questions on this unit, each with its command word and its tariff, then have them marked on Incandio with the mistake you actually made named.

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Carry on through the course