Fractions (Edexcel IGCSE Maths): Revision notes

Section 1

What is an equivalent fraction, and how do I find one?

Equivalent fractions represent the same value written with different numbers.

To find an equivalent fraction, multiply (or divide) the numerator and denominator by the same non-zero number:

$\dfrac{2}{3} = \dfrac{2 \times 4}{3 \times 4} = \dfrac{8}{12}$

This works because you are really multiplying by $\dfrac{4}{4} = 1$ , so the value never changes — only the way it looks.

Fraction	\times 2	\times 3	\times 5
$\dfrac{1}{4}$	$\dfrac{2}{8}$	$\dfrac{3}{12}$	$\dfrac{5}{20}$

Key termsEquivalent fractionsNumeratorDenominator

Exam tip

Whatever you do to the numerator, you must do the exact same thing to the denominator.

Section 2

How do I simplify a fraction to its lowest terms?

To simplify (or cancel down) a fraction, divide the numerator and denominator by their highest common factor (HCF).

Method:

Find the HCF of the numerator and denominator.
Divide both by the HCF.
Repeat until no common factor remains other than 1.

Example: Simplify $\dfrac{18}{24}$ .

HCF of 18 and 24 is 6, so: $\dfrac{18 \div 6}{24 \div 6} = \dfrac{3}{4}$

A fraction is fully simplified (in its lowest terms) when the numerator and denominator share no common factor other than 1.

Key termsSimplifyHighest common factor (HCF)Lowest terms

Common mistake

Dividing only the numerator or only the denominator changes the value of the fraction — always divide both by the same number.

Example

Simplify $\dfrac{45}{60}$ : HCF is 15, so $\dfrac{45 \div 15}{60 \div 15} = \dfrac{3}{4}$ .

Section 3

How do mixed numbers and improper fractions relate?

A mixed number has a whole number part and a fraction part, e.g. $2\dfrac{3}{4}$ .

An improper fraction has a numerator larger than (or equal to) its denominator, e.g. $\dfrac{11}{4}$ .

Mixed number to improper fraction: $2\dfrac{3}{4} = \dfrac{(2 \times 4) + 3}{4} = \dfrac{11}{4}$

Improper fraction to mixed number: Divide the numerator by the denominator; the remainder becomes the new numerator. $\dfrac{11}{4} = 11 \div 4 = 2 \text{ remainder } 3 = 2\dfrac{3}{4}$

Key termsMixed numberImproper fractionProper fraction

Think of it like this

Think of $2\dfrac{3}{4}$ pizzas as 2 whole pizzas plus 3 out of 4 slices of a third pizza — converting to $\dfrac{11}{4}$ just counts every quarter-slice across all the pizzas.

Section 4

How do I add or subtract fractions?

Fractions can only be added or subtracted once they share a common denominator.

Method:

Find the lowest common multiple (LCM) of the denominators — this is the common denominator.
Convert each fraction to an equivalent fraction with that denominator.
Add or subtract the numerators, keeping the denominator the same.
Simplify the answer, converting to a mixed number if needed.

Example: $\dfrac{1}{3} + \dfrac{1}{4} = \dfrac{4}{12} + \dfrac{3}{12} = \dfrac{7}{12}$

For mixed numbers, either convert both to improper fractions first, or add the whole numbers and fraction parts separately (carrying over if the fraction part becomes improper).

Key termsCommon denominatorLowest common multiple (LCM)

Common mistake

Never add or subtract numerators and denominators straight across — $\dfrac{1}{3} + \dfrac{1}{4} \ne \dfrac{2}{7}$ .

Exam tip

With mixed numbers, converting to improper fractions first avoids errors when subtraction requires 'borrowing' from the whole number.

Section 5

How do I multiply or divide fractions?

Multiplying fractions: multiply the numerators together and the denominators together, then simplify. $\dfrac{2}{3} \times \dfrac{4}{5} = \dfrac{2 \times 4}{3 \times 5} = \dfrac{8}{15}$

Dividing fractions: flip (find the reciprocal of) the second fraction, then multiply. $\dfrac{2}{3} \div \dfrac{4}{5} = \dfrac{2}{3} \times \dfrac{5}{4} = \dfrac{10}{12} = \dfrac{5}{6}$

For mixed numbers, always convert to improper fractions before multiplying or dividing.

Key termsReciprocal

Exam tip

Remembered as 'Keep, Change, Flip': keep the first fraction, change $\div$ to $\times$ , flip the second fraction.

Example

$1\dfrac{1}{2} \div \dfrac{3}{4} = \dfrac{3}{2} \times \dfrac{4}{3} = \dfrac{12}{6} = 2$

Must Know

Equivalent fractions: multiply or divide numerator and denominator by the same number.
To simplify, divide by the HCF until no common factor remains.
Mixed number $\to$ improper fraction: $\dfrac{(\text{whole} \times \text{denominator}) + \text{numerator}}{\text{denominator}}$ .
To add/subtract, first find a common denominator (LCM) — never add across.
To multiply, multiply straight across; to divide, keep-change-flip (multiply by the reciprocal).
Always convert mixed numbers to improper fractions before multiplying or dividing, and always give your final answer in its simplest form.

That's the notes covered.

Carry on to the next subtopic.