Who this is for: Cambridge IGCSE Mathematics (0580/0607) students who want Fractions, Decimals and Percentages — converting between forms, calculating percentages and finding reverse percentages — to become a reliable source of marks instead of a topic they only half-remember.
What query it owns: how to understand and revise Fractions, Decimals and Percentages in Cambridge IGCSE Mathematics.
Why this is safe: this page owns the Fractions, Decimals and Percentages revision-guide angle, while Tutopiya’s Fractions, Decimals and Percentages subtopic page owns the learning resource and the free Fractions, Decimals and Percentages quiz owns the practice.

Fractions, Decimals and Percentages are tested throughout Cambridge IGCSE Mathematics (0580/0607) — in Number, Algebra and even Statistics. If you can convert fluently, calculate a percentage of an amount, and work backwards from a percentage change, you pick up marks that many students lose on basic arithmetic. This guide explains exactly what the subtopic covers, how to handle the question types that actually appear, and where to practise each skill.

Key takeaways

• Percent means “out of 100” — 35% = 35/100 = 0.35.
• To find x% of an amount, multiply by x/100 (or × 0.01x).
• Percentage increase/decrease = (change ÷ original) × 100.
• Reverse percentage: treat the new amount as (100 ± x)% of the original.

What are Fractions, Decimals and Percentages in Cambridge IGCSE Maths?

Fractions, Decimals and Percentages is the study of three equivalent ways to express parts of a whole. In Cambridge IGCSE Mathematics it covers converting between the three forms, ordering and comparing values, calculating percentages of quantities, percentage increase and decrease, and reverse percentages. Examiners test it in both pure calculation and applied contexts.

You can read the full explanation, worked examples and notes on Tutopiya’s Fractions, Decimals and Percentages subtopic page before you attempt questions.

The core ideas you must master

These five ideas appear again and again. Learn what each one means and the exam phrasing that signals it.

Idea	What it means	How the exam uses it
Convert fraction → decimal	Divide numerator by denominator	”Write 3/8 as a decimal”
Convert decimal → %	× 100	”Write 0.45 as a percentage”
% of an amount	Multiply by the percentage	”Find 15% of $240”
% increase/decrease	(change ÷ original) × 100	”Calculate the percentage decrease”
Reverse %	New value = (100 ± x)% of original	”After a 20% discount, the price is $64…”

How to work out a reverse percentage — step by step

Reverse percentage questions ask for the original amount before a change. The key is to treat the given value as a percentage of the original.

1. Identify the percentage the new amount represents. After a 20% increase, the new amount = 120% of the original.
2. Set up an equation. 120% of original = new amount → original = new ÷ 1.20.
3. Calculate. If the price after 20% increase is $96: original = 96 ÷ 1.20 = $80.
4. For a decrease, use (100 − x)%. A 15% discount means the sale price = 85% of original.

Once you have worked through a few, test yourself with the free Fractions, Decimals and Percentages quiz — it tells you fast whether the method has actually stuck.

Percentage of vs percentage change: which method applies?

Students lose marks by using the wrong percentage formula. Match the question type to the method.

Question type	Method	Example
Find x% of an amount	Multiply by x/100	20% of 150 = 30
Percentage change	(change ÷ original) × 100	Price rises 12→15: (3÷12)×100 = 25%
Reverse after increase	Divide by (1 + x/100)	New = $120 after 20% rise → 120÷1.2
Reverse after decrease	Divide by (1 − x/100)	Sale price $68 after 15% off → 68÷0.85

Fractions, Decimals and Percentages in past-paper wording: command words that matter

Most lost marks come from misreading the command word or using the wrong base for a percentage.

Command word / phrase	What the question wants	Typical stem
Write … as a decimal / percentage	Convert between forms	”Write 7/20 as a percentage.”
Find …% of	Multiply by the percentage	”Find 12% of 350.”
Calculate the percentage increase/decrease	(change ÷ original) × 100	”Calculate the percentage decrease from 80 to 68.”
Work out the original price	Reverse percentage	”After a 25% discount, the price is $45. Work out the original price.”
Express … as a fraction in its simplest form	Cancel to lowest terms	”Express 0.375 as a fraction in its simplest form.”
Show that	Prove a stated equivalence	”Show that 3/4 = 75%.”

Worked exam-style stems (how to answer the wording)

Practising the wording — not just the maths — is what full marks reward.

1. “Find 18% of $450.” 0.18 × 450 = $81. Reward: correct multiplier, correct answer.
2. “A shirt costs $40. In a sale it is reduced to $34. Calculate the percentage decrease.” Change = 6. (6 ÷ 40) × 100 = 15%. Reward: change found, divided by original (not new price).
3. “After an increase of 15%, a laptop costs $575. Work out the original price.” 575 = 115% of original → original = 575 ÷ 1.15 = $500. Reward: correct percentage identified, division shown.

When you can recognise the wording instantly, work the full set on the Number topical past-paper questions and the Fractions, Decimals and Percentages quiz to lock the method in.

How Fractions, Decimals and Percentages connects to the rest of Number

Percentage skills underpin Earnings, Simple and Compound Interest and Ratios and Proportions. Simplifying fractions uses HCF from Factors and Multiples. When you are ready to mix topics, the Cambridge IGCSE Maths resource hub lets you move straight from a weak subtopic into the next.

Common mistakes students make

• Dividing by the new price instead of the original when finding percentage change.
• Forgetting that increase means multiply by more than 1, decrease means less than 1.
• Converting 3/8 to a decimal by writing 0.38 instead of dividing (0.375).
• Adding percentages directly: 10% + 15% ≠ 25% of the same base unless stated.

When you need more support

If reverse-percentage or conversion questions keep tripping you up, work through the Ratios and Proportions quiz and the Number topical past-paper questions to pinpoint the exact gap, then get focused help from a Cambridge IGCSE Maths tutor to fix it quickly.

Frequently asked questions

Are Fractions, Decimals and Percentages hard in Cambridge IGCSE Maths? No — the methods are standard. The challenge is choosing the right conversion or percentage formula and using the original amount as the base.

How do I convert a fraction to a percentage? Divide to get a decimal, then multiply by 100. Or multiply the fraction by 100 directly: 3/5 = 60%.

What is a reverse percentage? Finding the original amount before a percentage change. If a price is $85 after a 15% discount, the sale price is 85% of the original, so original = 85 ÷ 0.85.

How do I revise Fractions, Decimals and Percentages effectively? Read the subtopic notes, practise conversions and reverse-percentage questions by hand, then take the Fractions, Decimals and Percentages quiz to check your method.

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