Working with FDPCambridge IGCSE Maths: Revision notes

Section 1

How do I order quantities using inequality symbols?

Quantities in different forms (fractions, decimals, percentages) must be converted to a common form before comparing.

Symbol	Meaning
$=$	equal to
$\neq$	not equal to
$>$	greater than
$<$	less than
$\geq$	greater than or equal to
$\leq$	less than or equal to

Example: Order $\frac{3}{5}$ , 0.55, 58% by size. Convert all to decimals: 0.6, 0.55, 0.58 → so 0.55 < 0.58 < 0.6, i.e. 0.55 < 58% < $\frac{3}{5}$

Key termsinequality

Section 2

How do I convert fluently between fractions, decimals and percentages?

From	To	Method
Fraction	Decimal	Divide numerator by denominator
Decimal	Fraction	Write over a power of 10 and simplify
Decimal	Percentage	Multiply by 100
Percentage	Decimal	Divide by 100
Fraction	Percentage	Convert to decimal first, then multiply by 100
Percentage	Fraction	Write over 100 and simplify

Example: Convert $\frac{7}{8}$ to a percentage: 7 ÷ 8 = 0.875, so 87.5%

Exam tip

Memorise common equivalences (1/2 = 0.5 = 50%, 1/4 = 0.25 = 25%, 1/3 = 0.333... = 33.3%) to save time in the exam.

Section 3

Why do different representations of the same value look different?

A fraction, decimal, and percentage can all describe the exact same proportion of a whole — they are simply different notations for the same underlying value.

Example: $\frac{1}{4}$ , 0.25 and 25% all represent exactly one quarter of a whole. Recognising this equivalence is essential for comparing and combining quantities given in mixed forms.

Key termsequivalence

Section 4

How do I use FDP to solve problems in context?

Real exam problems often mix fractions, decimals and percentages within the same question — always convert to a single common form before comparing or combining values.

Example: A shop reduces a $60 item by$ \frac{1}{5} $, then a second shop reduces the same item by 20%. Are the discounts the same?$ \frac{1}{5} $= 0.2 = 20%, so yes — both discounts are identical, giving a saving of$ 12 either way.

Example

Compare 3/8 and 40%: 3/8 = 0.375 = 37.5%, which is less than 40%.

Must Know

Convert all values to the same form (usually decimal) before comparing with =, ≠, >, <, ≥, ≤
Fraction to decimal: divide numerator by denominator
Decimal to percentage: multiply by 100; percentage to decimal: divide by 100
Fractions, decimals and percentages can represent exactly the same value in different notations
Memorise key equivalences: 1/2 = 50%, 1/4 = 25%, 1/3 ≈ 33.3%, 3/4 = 75%
Always convert to a common form before solving mixed FDP problems in context

That's the notes covered.

Carry on to the next subtopic.