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AQASpec N2-N12Foundation & Higher~30 min

Fractions, Decimals & Percentages

Mathematics · Topic revision workspace

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Topic overview

What you need to know

Fractions, Decimals & Percentages is a key part of GCSE Mathematics. Build fluency with the method, then apply it to unfamiliar and multi-step problems. Fractions that represent the same value, e.g. 1/2 = 2/4 = 3/6. A fraction where the numerator is greater than or equal to the denominator, e.g. 7/4. A number consisting of a whole number and a proper fraction, e.g. 1¾.

Exam tip

Write every stage of your method. Method marks can still be earned when the final answer is wrong.

Revision notes

Core ideas

Secure these ideas first. Say each definition in your own words, then connect it to the topic overview.

  • Equivalent Fractions: Fractions that represent the same value, e.g. 1/2 = 2/4 = 3/6.
  • Improper Fraction: A fraction where the numerator is greater than or equal to the denominator, e.g. 7/4.
  • Mixed Number: A number consisting of a whole number and a proper fraction, e.g. 1¾.
  • Recurring Decimal: A decimal number that has a digit or group of digits that repeat infinitely, e.g. 0.333… = 1/3.

Revision notes

Apply it in the exam

The exam will rarely ask for an isolated definition. Practise selecting the right idea and using it as part of a complete explanation or method.

  • Percentage Increase: New value = original × (1 + percentage/100). To increase by 15%, multiply by 1.15.
  • Percentage Decrease: New value = original × (1 − percentage/100). To decrease by 20%, multiply by 0.80.
  • Percentage Change Formula: (Change ÷ Original) × 100. Used to find the percentage increase or decrease.
  • Compound Interest: Interest calculated on the original amount and on accumulated interest. Formula: amount = P × (1 + r/100)ⁿ.

Core knowledge

Key facts for Fractions, Decimals & Percentages

1

Equivalent Fractions

Fractions that represent the same value, e.g. 1/2 = 2/4 = 3/6.

2

Improper Fraction

A fraction where the numerator is greater than or equal to the denominator, e.g. 7/4.

3

Mixed Number

A number consisting of a whole number and a proper fraction, e.g. 1¾.

4

Recurring Decimal

A decimal number that has a digit or group of digits that repeat infinitely, e.g. 0.333… = 1/3.

5

Percentage Increase

New value = original × (1 + percentage/100). To increase by 15%, multiply by 1.15.

6

Percentage Decrease

New value = original × (1 − percentage/100). To decrease by 20%, multiply by 0.80.

7

Percentage Change Formula

(Change ÷ Original) × 100. Used to find the percentage increase or decrease.

8

Compound Interest

Interest calculated on the original amount and on accumulated interest. Formula: amount = P × (1 + r/100)ⁿ.

Active recall

Close the notes and answer these

  1. 1.Without looking, explain equivalent fractions and give one example or consequence.
  2. 2.Without looking, explain improper fraction and give one example or consequence.
  3. 3.Without looking, explain mixed number and give one example or consequence.
  4. 4.Without looking, explain recurring decimal and give one example or consequence.

Content reviewed 23 July 2026 against the current linked specification.

Finished learning?

Mark the notes complete, then test what you can recall.

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