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.
An improper fraction? Give an example
An improper fraction is a fraction where the numerator is greater than or equal to the denominator.
Convert 0.375 into a fraction in its simplest form.
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.
Express 5/8 as a decimal.
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.
Convert 45% to a fraction in its simplest form.
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.
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.
Convert the improper fraction 11/4 into a mixed number.
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.
What is a recurring decimal? Give an example.
A recurring decimal is a decimal in which one or more digits repeat indefinitely.
A price increases from $20 to $24. Calculate the percentage increase.
Percentage increase = [(New Value - Original Value) / Original Value] x 100. In this case, [($24 - $20) / $20] x 100 = (4/20) x 100 = 20%.
A shop sells a shirt for $30 after a 25% discount. What was the original price?
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.
What is the difference between a terminating and recurring decimal?
A terminating decimal has a finite number of digits after the decimal point (
Express 0.15 as a percentage.
To convert a decimal to a percentage, multiply by 100. So, 0.15 x 100 = 15%. Therefore, 0.15 is equal to 15%.
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.
What is a recurring decimal? Give an example.
A recurring decimal is a decimal in which one or more digits repeat indefinitely.
What is the difference between a terminating and recurring decimal?
A terminating decimal has a finite number of digits after the decimal point (
Tips to avoid common mistakes in Fractions, decimals and percentages
- ● For combined percentage changes, use multipliers: 12% increase means multiply by 1.12. Then find the total percentage change from the combined multiplier.
- ● Divide by (1 + the decimal percentage increase) to unwind a percentage increase back to the original number.
- ● Always double-check if you can simplify your final fraction before writing it on the answer line.
- ● Express the answer exactly, either as a simplified fraction (e.g. 1/4) or a decimal with all digits shown.
- ● Master the correct step-by-step methods for simplifying, dividing, and multiplying fractions.
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.
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.
Related Mathematics guides
Long-read articles that go beyond the deck — cover the whole subject's common mistakes, high-yield content and revision pacing.
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