1.2

Fractions, decimals and percentages

Cambridge IGCSE Mathematics (0580)  · Unit 1: Number  · 10 flashcards

Fractions, decimals and percentages is topic 1.2 in the Cambridge IGCSE Mathematics (0580) syllabus , positioned in Unit 1 — Number , alongside Types of number, Operations and order of operations and Powers and roots.  In one line: An improper fraction is a fraction where the numerator is greater than or equal to the denominator.

This topic is examined across Paper 1 (Core) or Paper 2 (Extended) — non-calculator — and Paper 3 (Core) or Paper 4 (Extended) — calculator.

The deck below contains 10 flashcards — 3 definitions — covering the precise wording mark schemes reward.  Use the 3 definition cards to lock down command-word answers (define, state), then move on to the concept and application cards to handle explain, describe and compare questions.

Key definition

An improper fraction? Give an example

An improper fraction is a fraction where the numerator is greater than or equal to the denominator.

Example: 7/3 is an improper fraction, as 7 > 3.
Key Concept Flip

Convert 0.375 into a fraction in its simplest form.

Answer Flip

0.375 is equivalent to 375/1000. Both numerator and denominator can be divided by 125, resulting in the simplified fraction 3/8. Therefore, 0.375 = 3/8.

Key Concept Flip

Express 5/8 as a decimal.

Answer Flip

To convert a fraction to a decimal, divide the numerator by the denominator. 5 ÷ 8 = 0.625. Therefore, 5/8 is equivalent to the decimal 0.625.

Key Concept Flip

Convert 45% to a fraction in its simplest form.

Answer Flip

Percent means 'out of 100', so 45% is equal to 45/100. Simplify this fraction by dividing both numerator and denominator by their greatest common factor, which is 5. This gives 9/20.

Definition Flip

What is an improper fraction? Give an example.

Answer Flip

An improper fraction is a fraction where the numerator is greater than or equal to the denominator.

Example: 7/3 is an improper fraction, as 7 > 3.
Key Concept Flip

Convert the improper fraction 11/4 into a mixed number.

Answer Flip

Divide 11 by 4, which gives 2 with a remainder of 3. The whole number part is 2, and the remainder becomes the numerator of the fraction part, with the original denominator of 4. Thus, 11/4 = 2 3/4.

Definition Flip

What is a recurring decimal? Give an example.

Answer Flip

A recurring decimal is a decimal in which one or more digits repeat indefinitely.

Example: 1/3 = 0.3333... , which can be written as 0.3.
Key Concept Flip

A price increases from $20 to $24. Calculate the percentage increase.

Answer Flip

Percentage increase = [(New Value - Original Value) / Original Value] x 100. In this case, [($24 - $20) / $20] x 100 = (4/20) x 100 = 20%.

Key Concept Flip

A shop sells a shirt for $30 after a 25% discount. What was the original price?

Answer Flip

If the price is $30 after a 25% discount, then $30 represents 75% of the original price. To find the original price, divide $30 by 0.75: $30 / 0.75 = $40.

Definition Flip

What is the difference between a terminating and recurring decimal?

Answer Flip

A terminating decimal has a finite number of digits after the decimal point (

Example: 0.25), whereas a recurring decimal has a digit or group of digits that repeats indefinitely (. 0.333...).
Key Concept Flip

Express 0.15 as a percentage.

Answer Flip

To convert a decimal to a percentage, multiply by 100. So, 0.15 x 100 = 15%. Therefore, 0.15 is equal to 15%.

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1.1 Types of number 1.3 Operations and order of operations

Key Questions: Fractions, decimals and percentages

What is an improper fraction? Give an example.

An improper fraction is a fraction where the numerator is greater than or equal to the denominator.

Example: 7/3 is an improper fraction, as 7 > 3.
What is a recurring decimal? Give an example.

A recurring decimal is a decimal in which one or more digits repeat indefinitely.

Example: 1/3 = 0.3333... , which can be written as 0.3.
What is the difference between a terminating and recurring decimal?

A terminating decimal has a finite number of digits after the decimal point (

Example: 0.25), whereas a recurring decimal has a digit or group of digits that repeats indefinitely (. 0.333...).

Tips to avoid common mistakes in Fractions, decimals and percentages

More topics in Unit 1 — Number

Fractions, decimals and percentages sits alongside these Mathematics decks in the same syllabus unit. Each uses the same spaced-repetition system, so progress in one informs the next.

Cambridge syllabus keywords to use in your answers

These are the official Cambridge 0580 terms tagged to this section. Mark schemes credit responses that use the exact term — weave them into your answers verbatim rather than paraphrasing.

fraction decimal percentage convert equivalent simplify improper fraction mixed number recurring decimal terminating decimal percentage increase percentage decrease reverse percentage original value

Key terms covered in this Fractions, decimals and percentages deck

Every term below is defined in the flashcards above. Use the list as a quick recall test before your exam — if you can't define one of these in your own words, flip back to that card.

Improper fraction? Give an example
Recurring decimal? Give an example
The difference between a terminating and recurring decimal

Related Mathematics guides

Long-read articles that go beyond the deck — cover the whole subject's common mistakes, high-yield content and revision pacing.

How to study this Fractions, decimals and percentages deck

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