OCR GCSE Mathematics: Fractions, Decimals and Percentages (J560)

This guide covers Topic 2: Fractions, decimals and percentages, the second of twelve topic areas in OCR GCSE (9-1) Mathematics (J560), for first assessment 2017. As with every OCR maths topic, content is arranged by topic area and applies to both Foundation and Higher tier – any topic may be assessed on any of the three papers a candidate sits, so this content reappears throughout the paper rather than being confined to a single question.

Syllabus coverage

OCR GCSE (9-1) MATHEMATICS J560 – TOPIC 2 FRACTIONS, DECIMALS AND PERCENTAGES

• 2.1 Fractions – simplifying fractions, converting between mixed numbers and improper fractions, comparing the size of fractions, and carrying out the four operations (addition, subtraction, multiplication and division) with fractions, including mixed numbers.
• 2.2 Decimal fractions – converting between fractions and decimals, ordering decimals, and using place value to multiply and divide by powers of ten.
• 2.3 Percentages – understanding that a percentage is “number of parts per hundred”; converting between fractions, decimals and percentages; calculating a percentage of a given quantity, and expressing one quantity as a percentage of another, with and without a calculator; increasing or decreasing a quantity by a percentage, including using decimal or fractional multipliers; and applying this to original-value problems and simple interest.
• 2.4 Ordering fractions, decimals and percentages – converting between the three forms as needed to compare and order a mixed set of values.

Why this topic follows Number directly

Topic 1 (Number operations and integers) established calculation with whole numbers; Topic 2 extends the same four operations to non-integer values, which is why fluent recall of the Topic 1 methods matters here – a student who is shaky on long division, for instance, will also struggle converting a fraction to a decimal by dividing numerator by denominator. Topics 1 and 2 together form the foundation that Topic 5 (Ratio, proportion and rates of change) builds on directly, since ratio and proportion problems are, structurally, fraction and percentage problems in a different context.

Worked example: reverse percentage (original value)

A jacket costs £68 after a 15% discount. Find the original price.

£68 represents (100% − 15%) = 85% of the original price.

original price = £68 ÷ 0.85 = £80

This “reverse percentage” or “original value” calculation is one of the most commonly misapplied percentage skills on this specification – students often calculate 15% of £68 and add it back on, which gives the wrong answer (£78.20) because £68 is 85% of the original, not 100% of it minus something.

Worked example: percentage multiplier

A quantity of £1,800 grows by 5% per year, compounded annually, for two years. Find its value after two years.

multiplier = 1 + (5 ÷ 100) = 1.05

value after two years = £1,800 × 1.05² = £1,800 × 1.1025 = £1,984.50

Using a single multiplier (1.05) rather than calculating 5% and adding it on each year is faster and less error-prone, and generalises directly to compound growth and decay problems that reappear in Topic 5.

Common mistakes

• Reverse percentage errors, as above – calculating a percentage of the final value instead of recognising the final value as a percentage of the original.
• Confusing simple and compound percentage change – using repeated addition of the same percentage of the original amount (simple interest logic) when a question specifies compounding, or vice versa.
• Losing accuracy converting recurring decimals to fractions, a Higher-tier skill that is often skipped in revision because it feels like a Number-topic task, even though it is examined as part of fluency with the fraction-decimal relationship.
• Getting the direction of a percentage multiplier wrong – writing 0.85 for a 15% increase instead of a 15% decrease, or forgetting that a multiplier above 1 always represents growth.
• Ordering a mixed set of fractions, decimals and percentages by eye rather than converting them all to a common form first, which is unreliable once denominators or decimal places differ.

Worked example: fraction of an amount versus fraction arithmetic

It is worth distinguishing two skills that both fall under 2.1 but are tested differently. Finding a fraction of a quantity – for example, three-fifths of £45 – is a division-then-multiplication calculation: £45 divided by 5, then multiplied by 3, gives £27. Adding or subtracting two fractions, by contrast, requires a common denominator first: 2/3 + 1/4 requires converting to twelfths (8/12 + 3/12 = 11/12) before the numerators can be combined. Students who are confident with one skill sometimes default to it for both – for example, trying to find a common denominator when the question actually asks for a fraction of an amount – which wastes time without being wrong in principle, just inefficient under exam conditions. The specification treats both as part of the same 2.1 Fractions sub-topic, so a revision plan that only drills one of the two skills leaves a genuine gap.

How to approach it

Because this topic is tested through calculation fluency rather than recall of facts, the most effective revision is doing calculations under timed conditions rather than re-reading notes – fraction arithmetic, percentage-of-a-quantity, percentage change and reverse percentage problems, in that order, since each builds on the last. Build the multiplier method (1 ± percentage/100) into every percentage calculation from the start, since it removes an entire category of errors around adding or subtracting the wrong amount, and it is the only practical method for compound growth and decay questions. Practise identifying, from the wording of a question alone, whether you are given the original value (calculate a percentage of it directly) or the final value after a change (use a reverse-percentage approach) – this is the single most examined distinction in this topic. Finally, since any topic can appear on any paper, do not assume percentage questions will be confined to a “non-calculator” or “calculator” paper specifically – practise both mental-method and calculator-method percentage calculations.

Related resources

• Fractions, Decimals and Percentages revision notes
• Fractions, Decimals and Percentages practice questions

Official syllabus

OCR, GCSE (9-1) Mathematics (J560) Specification at a Glance, Content overview, Topic 2 Fractions, decimals and percentages, https://www.ocr.org.uk/qualifications/gcse/mathematics-j560-from-2015/specification-at-a-glance/, fetched and verified in full 2026-09-02. Full specification PDF: https://www.ocr.org.uk/Images/168982-specification-gcse-mathematics.pdf.