Fractions: Equivalence and Operations
Simplify, compare and calculate with fractions, mixed numbers and fractions of quantities.
How to study for GCSE Mathematics
Use 601 original multiple-choice questions to learn connected methods, explain why they work, practise exact non-calculator execution and use a calculator strategically on designated papers.
Core concepts
Concept 1
Equivalent and simplified fractions
Exam cue: Use a common denominator for addition or subtraction; multiply numerators and denominators; invert the divisor for division.
Concept 2
Four operations with fractions
Exam cue: Simplify fully and compare the answer with the sizes and signs of the original fractions.
Concept 3
Fractions of quantities
Exam cue: Represent the information clearly, choose a justified method and communicate each step with correct notation and units.
Targeted study blocks
Tier coverage
Foundation and Higher
The core techniques are assessed at both tiers. Higher questions can combine them with less scaffolding, algebraic generalisation and unfamiliar multi-step contexts.
Calculator structure
Prepare for calculator and non-calculator papers
Any part of a board's specification may be assessed on any paper. Non-calculator does not define a smaller syllabus; questions are designed so exact arithmetic and reasoning are feasible without a calculator.
Risk pitfalls and guardrails
Adding denominators or inverting the wrong fraction in division.
Guardrail: Do not hide an invalid model behind arithmetic: check assumptions, signs, bounds, units, scale, required accuracy and the original question.
Giving an unsupported answer when the command requires working, proof, reasoning or interpretation.
Guardrail: Do not hide an invalid model behind arithmetic: check assumptions, signs, bounds, units, scale, required accuracy and the original question.
Assuming a topic belongs only to calculator or non-calculator papers; any specification content can be assessed on any paper.
Guardrail: Any part of a board's specification may be assessed on any paper. Non-calculator does not define a smaller syllabus; questions are designed so exact arithmetic and reasoning are feasible without a calculator.
Memory anchors
Add fractions
Use a common denominator, then add or subtract the numerators.
Divide by a fraction
Multiply by its reciprocal.
Fraction of an amount
Divide by the denominator and multiply by the numerator.
Fractions: Equivalence and Operations: method
Use a common denominator for addition or subtraction; multiply numerators and denominators; invert the divisor for division.
Fractions: Equivalence and Operations: check
Simplify fully and compare the answer with the sizes and signs of the original fractions.
Checkpoint rule
Do the check-up only after you can summarize each concept in one sentence and identify one dangerous pitfall from memory.
Knowledge Check (after reading)
Short check-up to confirm understanding of this module.
Check-up Questions
Foundation · AO1 technique · Non-calculator — Calculate 3/4 + 5/6. Give the answer as an improper fraction.
Shared F/H · AO1 technique · Non-calculator — Calculate 2 1/3 × 1 1/2.
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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