Ratio and proportion

OCR

GCSE

Ratio and proportion quantify multiplicative relationships between quantities, serving as a fundamental bridge between arithmetic and algebra. Candidates must distinguish between ratio (part-to-part comparison) and proportion (part-to-whole comparison), applying the unitary method or multipliers to solve problems efficiently. Mastery requires fluency in converting between ratio, fraction, and percentage forms, and extends to modelling direct and inverse variation algebraically ($y=kx$, $y=k/x$). Assessment focuses on applying these concepts to scale factors, compound measures, and complex multi-step contexts.

Objectives

Exam Tips

Pitfalls

Key Terms

Mark Points

What You Need to Demonstrate

Key skills and knowledge for this topic

Award M1 for a correct method to determine the value of one part (unitary method) or a correct scale factor
Award B1 for expressing a ratio in its simplest integer form, ensuring units are consistent before simplifying
Award M1 for setting up a correct equation of proportionality (e.g., k = y/x or k = yx) in direct/inverse proportion questions
Credit responses that correctly interpret 'difference' problems by equating the difference in parts to the numerical difference
Award A1 for final answers that include required units (e.g., currency, kg) where specified in the question line

Marking Points

Key points examiners look for in your answers

Award M1 for a correct method to determine the value of one part (unitary method) or a correct scale factor
Award B1 for expressing a ratio in its simplest integer form, ensuring units are consistent before simplifying
Award M1 for setting up a correct equation of proportionality (e.g., k = y/x or k = yx) in direct/inverse proportion questions
Credit responses that correctly interpret 'difference' problems by equating the difference in parts to the numerical difference
Award A1 for final answers that include required units (e.g., currency, kg) where specified in the question line

Examiner Tips

Expert advice for maximising your marks

💡When solving 'best buy' problems, explicitly calculate the cost per unit (e.g., 100g or 1 litre) for both items; marks are awarded for the comparison method, not just the choice
💡Annotate ratio parts with the specific names (e.g., write 'Red : Blue' above '3 : 4') to avoid reversing the order in the final answer
💡For inverse proportion questions involving squares (y ∝ 1/x²), write the formula y = k/x² immediately to secure the first method mark before substituting values
💡Check if the question asks for a ratio in the form 1:n or n:1; failing to divide by the correct number to get '1' is a frequent cause of lost accuracy marks

Common Mistakes

Pitfalls to avoid in your exam answers

Dividing the total quantity by one of the ratio parts rather than the sum of the parts (e.g., for 2:3, dividing by 2 instead of 5)
Failing to convert units to a common standard before simplifying ratios (e.g., comparing 50cm to 2m as 50:2)
In 'difference' questions, treating the given value as the total amount rather than the value of the difference between shares
Confusing inverse proportion with direct proportion, often multiplying by a scale factor when division is required

Study Guide Available

Comprehensive revision notes & examples

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Key Terminology

Essential terms to know

Simplification and unitary method (1:n)

Sharing quantities in a given ratio

Direct and inverse proportionality

Compound measures (Speed, Density, Pressure)

Algebraic ratio and scale factors

Likely Command Words

How questions on this topic are typically asked

Calculate

Show that

Express

Work out

Solve

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