1.4 Fractions, decimals, percentages and ratio
Move fluently among numerical forms and use proportional reasoning for comparison, sharing and change.
How to study WJEC GCSE Mathematics and Numeracy
Move from concept and notation to a justified method, show a complete mathematical chain, check scale and units, and interpret the answer in context.
Core concepts
Concept 1
Find equivalent forms, order values and convert among fractions, decimals, percentages and ratios.
Exam cue: Confirm the unit, entered tier, calculator condition and available formula list before choosing a method.
Concept 2
Calculate fractions or percentages of quantities, percentage change and reverse percentage where specified.
Exam cue: Identify the whole, part and multiplier before choosing a fraction, percentage or ratio method.
Concept 3
Simplify, divide and apply ratios and proportional relationships in mathematical and real-world contexts.
Exam cue: Show a complete mathematical chain, use correct notation and units, and interpret or check the result in its original context.
Concept 4
Current matrix coverage: Unit 1, Unit 2, Unit 3. Read the exact subpoint scope in each applicable unit column.
Concept 5
Foundation content is shown in standard type in the specification; bold additions apply only to Higher Tier.
Risk pitfalls and guardrails
Using the final value as the denominator for a percentage change when the original value is required.
Guardrail: Do not import the outgoing separate qualifications, assume a universal tier across units or ignore calculator, formula-list, context and accuracy conditions.
Assuming that every subpoint in a cross-unit strand appears in all three papers, rather than reading the correct matrix column.
Guardrail: Read the precise subpoint in the applicable unit column; a cross-unit strand does not mean every subpoint appears in every paper.
Using a Higher-only method or expectation for a Foundation entry, or importing the outgoing Mathematics/Mathematics-Numeracy structure.
Guardrail: Standard type applies to Foundation and Higher; bold specification additions are Higher-only. There is no Intermediate Tier.
Memory anchors
Equivalent forms
Equivalent fractions, decimals and percentages represent the same proportion.
Percentage multiplier
A multiplier combines the original whole with the required percentage change.
Reverse percentage
Divide by the known multiplier to recover the original whole.
Simplest ratio
Divide every part by their highest common factor.
Proportion
Proportion expresses how quantities vary relative to one another.
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
Express 35 as a fraction of 84 in its lowest terms.
Adding 24 litres changes a tank from 3/5 full to 9/10 full. What is its capacity?
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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