Fractions, Decimals and Percentages

OCR

GCSE

Fractions, decimals, and percentages constitute the fundamental representations of rational numbers, requiring candidates to switch fluently between forms to solve problems efficiently. Assessment focuses on the four operations with fractions and decimals, ordering values by magnitude, and applying percentage multipliers for growth, decay, and reverse calculations. Mastery of this topic is critical for interpreting data in probability and statistics, as well as solving financial problems involving interest and depreciation.

Objectives

Exam Tips

Pitfalls

Key Terms

Mark Points

Subtopics in this area

Fractions, Decimals and Percentages

Learning Objectives

What you need to know and understand

Add, subtract, multiply and divide simple fractions.
Calculate a fraction of a quantity.
Calculate a percentage of a quantity.
Increase or decrease a quantity by a simple percentage.

Example Examiner Feedback

Real feedback patterns examiners use when marking

"You have correctly identified the percentage change, but check your method for finding the original amount — remember to divide by the multiplier."
"Good use of a common denominator. Ensure you simplify your final fraction to its lowest terms to secure the final accuracy mark."
"For this 'Show that' question, you skipped the subtraction step. Write out '100x - 10x' explicitly to demonstrate the proof."
"Excellent use of the multiplier method. To access the top band, ensure you apply this efficiently in multi-step compound interest problems."

Marking Points

Key points examiners look for in your answers

Award M1 for a complete method to establish a common denominator when adding or subtracting fractions (e.g., showing /12 for 1/3 + 1/4)
Award B1 for correctly converting a recurring decimal to a fraction using an algebraic method, showing the subtraction of equations
Award M1 for identifying the correct decimal multiplier for a percentage increase or decrease (e.g., 1.05 or 0.88)
Award A1 for the correct final answer, rounded to the specified degree of accuracy (e.g., 2 decimal places for currency)
Method marks (M1) are awarded for establishing a correct multiplier (e.g., × 1.20 for a 20% increase) even if the final calculation is incorrect.
In fraction arithmetic, conversion of mixed numbers to improper fractions is often the first required step to access method marks.
For ordering tasks, credit is given for converting all values to a common format (all decimals or common denominator) before ranking.
In 'Show that' questions involving fractions, every step of the calculation, including the common denominator and intermediate additions, must be clearly written to gain full credit.

Examiner Tips

Expert advice for maximising your marks

💡For percentage change questions, always use the multiplier method (e.g., x 0.85 for a 15% decrease); this is faster and reduces arithmetic errors compared to finding the amount and subtracting.
💡When asked to 'Show that' a recurring decimal equals a specific fraction, you must define x, multiply by a power of 10, and show the subtraction explicitly to gain full credit.
💡In compound interest problems, do not round intermediate values; keep the full calculator display value until the final step to avoid accuracy penalties.
💡On calculator papers, always use the multiplier method for percentage changes (e.g., × 0.85 for a 15% decrease) as it is faster and less prone to arithmetic errors than finding 15% and subtracting.
💡Memorize common FDP equivalences (e.g., 1/8 = 0.125 = 12.5%) to save significant time on non-calculator papers.
💡When solving reverse percentage problems, write an algebraic statement first (e.g., 1.1x = 550) to ensure you divide rather than multiply.

Common Mistakes

Pitfalls to avoid in your exam answers

Incorrectly adding fractions by summing numerators and denominators separately (e.g., 1/2 + 1/3 = 2/5) rather than finding a common denominator
Calculating reverse percentages by subtracting a percentage of the final amount instead of dividing by the multiplier (e.g., calculating 10% of 110 and subtracting it, rather than dividing 110 by 1.1)
Failing to show full working in 'Show that' questions; examiners require every step of the calculation, including unsimplified fractions, to be visible
Incorrectly calculating reverse percentages by subtracting a percentage of the final amount (e.g., subtracting 20% of the final price instead of dividing by 1.2).
Adding denominators together when adding fractions (e.g., 1/3 + 1/4 = 2/7) rather than finding a common denominator.
Failing to simplify the final fraction answer when the question explicitly asks for the 'simplest form'.
Confusing simple interest with compound interest; applying the interest rate to the original principal every year instead of the accumulated total.

Key Terminology

Essential terms to know

Equivalence and conversion between forms

Arithmetic operations with fractions and mixed numbers

Percentage change, compound interest, and reverse percentages

Recurring decimals and exact fractional forms

Equivalence and Conversion

Ordering and Comparing Rational Numbers

Arithmetic Operations with Fractions

Terminating and Recurring Decimals

Percentage of Amounts and Multipliers

Percentage Increase and Decrease

Reverse Percentages

Compound Interest and Growth/Decay

Likely Command Words

How questions on this topic are typically asked

Calculate

Show that

Work out

Estimate

Order

Write

Practical Links

Related required practicals

•{"code":"Financial Maths","title":"Interest and Depreciation","relevance":"Application of percentage multipliers to compound interest and depreciation scenarios"}
•{"code": "Financial Maths", "title": "Personal Finance Applications", "relevance": "Application of percentage multipliers to calculate VAT, income tax, and compound interest on savings accounts."}

Ready to test yourself?

Practice questions tailored to this topic