Ratio, Sharing and Scale
Simplify ratios, divide quantities, use scale factors and connect ratios with fractions.
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 ratios
Exam cue: Make units consistent, find the value of one ratio part, then scale to each requested quantity.
Concept 2
Sharing in a ratio
Exam cue: Add shared parts back to the total and check that the final ratio is equivalent to the original.
Concept 3
Scale drawings and maps
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
Dividing by one side of a ratio rather than by the total number of parts.
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
Value of one ratio part
Total quantity divided by the sum of ratio parts.
Simplify a ratio
Convert units, then divide every part by a common factor.
Scale factor
Image length divided by corresponding original length.
Ratio, Sharing and Scale: method
Make units consistent, find the value of one ratio part, then scale to each requested quantity.
Ratio, Sharing and Scale: check
Add shared parts back to the total and check that the final ratio is equivalent to the original.
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 — Simplify the ratio 42:63.
Foundation · AO3 problem solving · Either paper — Share £360 in the ratio 5:7. Find the larger share.
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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