OCR GCSE Mathematics: Fractions, Decimals and Percentages — Revision Notes

Condensed for the final weeks. For the full explanation, use the Fractions, Decimals and Percentages study guide.

The multiplier method

Increase by x%:  multiplier = 1 + (x / 100)
Decrease by x%:  multiplier = 1 - (x / 100)

Using a single multiplier, rather than calculating the percentage and adding/subtracting separately, is faster, less error-prone, and the only practical method for compound growth/decay.

Worked example: reverse percentage

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

£68 = (100% - 15%) = 85% of the original price
Original price = £68 / 0.85 = £80

Calculating 15% of £68 and adding it back (£78.20) is wrong — £68 is 85% of the original, not 100% minus something.

Worked example: compound growth

£1,800 grows by 5% per year, compounded annually, for 2 years.

multiplier = 1.05
value after 2 years = £1,800 x 1.05^2 = £1,984.50

Fraction skills — two distinct types

Fraction of an amount (division then multiplication): 3/5 of £45 → £45 ÷ 5 × 3 = £27. Adding/subtracting fractions (common denominator first): 2/3 + 1/4 → 8/12 + 3/12 = 11/12. Confident students sometimes default to one method for both — practise recognising which skill a question actually needs.

Converting between fractions, decimals and percentages

Fraction -> decimal:   divide numerator by denominator
                        e.g. 3/8 = 3 (divided by) 8 = 0.375
Decimal -> percentage: multiply by 100
                        e.g. 0.375 x 100 = 37.5%
Percentage -> fraction: write over 100, then simplify
                        e.g. 40% = 40/100 = 2/5

Practise moving between all three forms fluently in both directions, not just fraction-to-decimal-to-percentage in one direction, since ordering questions (2.4) require converting a mixed set to a common form before comparison, and the common form needed depends on what is easiest to compare in the specific question.

Worked example: expressing one quantity as a percentage of another

A student scores 42 out of 56 on a test. Express this as a percentage.

Step 1: write as a fraction -- 42/56
Step 2: convert to a decimal -- 42 (divided by) 56 = 0.75
Step 3: convert to a percentage -- 0.75 x 100 = 75%

This three-step method (fraction, then decimal, then percentage) is more reliable under exam conditions than attempting to estimate a percentage directly, particularly on the non-calculator paper where the division needs to be done by hand.

Recurring decimals to fractions (Higher tier)

A recurring decimal such as 0.333… converts to a fraction using algebra: let x = 0.333…, then 10x = 3.333…, so 10x − x = 3, giving 9x = 3 and x = 3/9 = 1/3. This Higher-tier skill is often under-revised because it feels like Number-topic content, even though it is examined here as part of fluency with the fraction-decimal relationship – worth including explicitly in a revision plan rather than treating as a separate, optional extra.

Key terms

Multiplier — a single number (e.g. 1.05, 0.85) applied to represent a percentage increase or decrease in one step. Reverse percentage — finding an original value from a value after a known percentage change, by dividing by the resulting percentage as a decimal. Compound change — a percentage change applied repeatedly to a growing/shrinking amount, calculated using a multiplier raised to a power.

Direction of a percentage change

Before any percentage calculation, decide whether the question gives you the original value (calculate a percentage of it directly) or the final value after a change (use a reverse-percentage approach instead). This is the single most examined distinction in this topic – more marks are lost from misreading which value a question has given than from an incorrect calculation method once the right approach is chosen.

Common mistakes

• Reverse percentage errors — calculating a percentage of the final value instead of treating the final value as a percentage of the original.
• Confusing simple and compound percentage change.
• Getting the multiplier direction wrong (e.g. using 0.85 for an increase).
• Ordering fractions, decimals and percentages “by eye” instead of converting to a common form first.
• Defaulting to a common-denominator method when a question asks for a fraction of an amount.

Quick self-test

1. A shirt costs £34 after a 20% discount. Find the original price.
2. £2,000 grows by 3% per year for 3 years, compounded annually. Find the value.
3. Find 2/5 of £60.
4. Calculate 3/4 − 1/6.
5. Order 0.6, 3/5, 58% from smallest to largest.
6. Convert the recurring decimal 0.777… to a fraction.

Answers: 1. £34 ÷ 0.80 = £42.50. 2. £2,000 × 1.03³ = £2,185.45 (2 d.p.). 3. £60 ÷ 5 × 2 = £24. 4. 9/12 − 2/12 = 7/12. 5. 58% = 0.58, 3/5 = 0.6, 0.6 = 0.6 → order: 58%, then 3/5 and 0.6 (equal). 6. Let x = 0.777…; 10x = 7.777…; 10x − x = 7; 9x = 7; x = 7/9.

How this connects forward

Topic 1 (Number operations and integers) established calculation with whole numbers; this topic extends the same four operations to non-integer values – a student shaky on long division will also struggle converting a fraction to a decimal by division. Topics 1 and 2 together form the foundation 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. Since any topic can appear on any paper, practise both calculator and non-calculator percentage methods rather than assuming one paper will avoid them.

Related resources

• Fractions, Decimals and Percentages study guide
• Fractions, Decimals and Percentages practice questions

Official syllabus

OCR, GCSE (9-1) Mathematics (J560) Specification at a Glance, Topic 2 — ocr.org.uk.