This topic summary covers Knowledge Organiser: Fractions — Basics within Fractions Basics for GCSE Mathematics. Revise Fractions Basics in Number for GCSE Mathematics with 12 exam-style questions and 22 flashcards. This topic appears less often, but it can still be a useful differentiator on mixed-topic papers. It is section 14 of 14 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Knowledge Organiser: Fractions — Basics
Key Terms
- Numerator: Top number — how many parts we have
- Denominator: Bottom number — how many equal parts in total
- Proper fraction: Numerator < denominator (less than 1 whole)
- Improper fraction: Numerator ≥ denominator (1 or more wholes)
- Mixed number: Whole number + fraction (e.g. 2¾)
- Equivalent fractions: Different fractions with the same value
Must-Know Facts
- To simplify: divide numerator and denominator by their HCF
- To find fraction of an amount: divide by denominator, multiply by numerator
- ¾ of 80 = 80 ÷ 4 × 3 = 60
- Mixed → improper: (whole × denominator + numerator) / denominator
- Improper → mixed: divide numerator by denominator, remainder is new numerator
- Always simplify your final answer
Key Methods
- Equivalent fractions: multiply or divide both top and bottom by the same number
- Comparing fractions: convert to same denominator (use LCM), then compare numerators
- Simplifying: divide both by HCF
- Fraction of amount: ÷ denominator first, × numerator second
Common Mistakes
- Adding fractions without common denominator: Never add numerators over different denominators — find the LCM first, convert both fractions, then add
- Simplifying incompletely: Divide both numerator and denominator by their HCF, not just any common factor — 12/18 ÷ 2 gives 6/9 which still needs simplifying to 2/3
- Fraction of an amount: Always divide by the denominator first, then multiply by the numerator — reversing the order gives the wrong answer
- Equivalent fractions: Multiply or divide both top and bottom by the same number — changing only one part breaks the equivalence
Practice questions for Fractions Basics
In the fraction 5/8, which number is the denominator?
Explain the difference between a proper fraction, an improper fraction and a mixed number. Give one example of each.
Quick recall flashcards
Visualizing fractions
Pizza model: Whole divided into equal slices
Bar model: Rectangle split into equal parts
Number line: Fractions between 0 and 1
Always think: Parts out of a whole
Parts of a fraction
Numerator = top number (how many parts)
Denominator = bottom number (total parts)
Fraction bar = division line
3/4 means '3 out of 4 equal parts'