Fractions, Decimal And Percentages Explained: OxfordAQA IGCSE Mathematics Complete Breakdown

Definition: what Fractions, Decimal and Percentages covers

Fractions, Decimal and Percentages is the topic within the Number strand of the OxfordAQA IGCSE Mathematics specification that asks students to move fluently between three different ways of writing the same value, and to use each form appropriately depending on the context of a question. oxfordaqa igcse fractions, decimal and percentages covers equivalent fractions, conversion between fractions, terminating decimals and percentages, treating each as an operator, and solving percentage change problems including simple and compound interest. It is among the most heavily examined areas of the subject, since these three representations appear constantly across finance, measurement and probability questions throughout both papers.

Across different European school systems, students arrive at IGCSE with slightly different habits around percentages and decimals, particularly around notation for recurring decimals and the way compound interest is taught. This deep dive works from OxfordAQA's own conventions and mark scheme expectations, so the notation used here is exactly what will be rewarded in the exam room.

So what is fractions, decimal and percentages IGCSE study actually testing? These oxfordaqa igcse mathematics notes treat the topic as one connected skill, moving confidently between three representations of the same proportion, rather than three separate skills to be revised in isolation. This fractions, decimal and percentages explained guide opens with a working oxfordaqa igcse mathematics definition of each idea and then works through the exact question styles OxfordAQA sets, so every concept is explained the way it will actually appear on the paper.

Key facts

Converting between fractions, decimals and percentages

Every fraction, decimal and percentage represents a proportion of a whole, and the specification requires fluent, immediate conversion between all three forms.

Worked example 1: converting a fraction to a decimal and a percentage

Write 7/20 as a decimal and as a percentage.

Solution: divide the numerator by the denominator: 7 ÷ 20 = 0.35. To convert a decimal to a percentage, multiply by 100: 0.35 × 100 = 35%.

Worked example: ordering fractions, decimals and percentages together

Arrange the following in ascending order: 3/5, 58%, 0.62, 11/20

Solution: convert every value to a decimal so they can be compared directly. 3/5 = 0.6. 58% = 0.58. 0.62 stays as it is. 11/20 = 0.55. Ordering the decimals: 0.55, 0.58, 0.6, 0.62. Translating back to the original forms: 11/20, 58%, 3/5, 0.62. Converting mixed representations to a single common form, almost always decimals, before comparing or ordering them removes any risk of comparing unlike quantities directly.

Worked example 2: converting a recurring decimal to a fraction

Write 0.4̇ (0.4444...) as a fraction in its simplest form.

Solution: let x = 0.4444... Multiply both sides by 10: 10x = 4.4444... Subtract the original equation: 10x - x = 4.4444... - 0.4444..., giving 9x = 4, so x = 4/9. This algebraic technique, multiplying to shift the recurring block and then subtracting to eliminate it, works for any recurring decimal.

Fractions and percentages as operators

Interpreting a fraction or a percentage as an operator means applying it directly to a given quantity, rather than treating it as an abstract value on its own.

Worked example 3: applying a fraction as an operator

Find 5/8 of 96.

Solution: divide 96 by the denominator, then multiply by the numerator: 96 ÷ 8 = 12, then 12 × 5 = 60.

Expressing one quantity as a fraction or percentage of another

The specification specifically requires expressing one quantity as a fraction or percentage of another, including cases where the fraction is greater than 1 or the percentage exceeds 100%.

Worked example 4: a percentage greater than 100%

A shop's sales were 45,000 last year and 63,000 this year. Express this year's sales as a percentage of last year's sales.

Solution: divide this year's figure by last year's figure: 63,000 ÷ 45,000 = 1.4. Multiply by 100: 140%. This year's sales are 140% of last year's, correctly reflecting growth rather than a fraction less than one.

Percentage change, simple interest and compound interest

Percentage change problems, including increases, decreases, simple interest and compound interest, form a substantial part of this topic, with reverse percentage problems and the compound interest formula added at Extension level.

Worked example 5: percentage increase and decrease

A jacket originally costs 80. Its price increases by 15%, and then the new price is reduced by 20% in a sale. Find the final price.

Solution: apply each percentage as a multiplier to the current value. After the increase: 80 × 1.15 = 92. After the sale reduction: 92 × 0.80 = 73.60. The final price is 73.60.

Worked example 6: compound interest using the formula

1,200 is invested at a compound interest rate of 4% per year. Find the value of the investment after 3 years.

Solution: use value of investment = P(1 + r/100)ⁿ, with P = 1200, r = 4, n = 3. Value = 1200 × (1.04)³ = 1200 × 1.124864 = 1349.84 (to 2 decimal places).

This differs from simple interest, where the interest is calculated on the original principal every year rather than compounding on the growing balance. Confusing the two is one of the most common errors on this part of the specification, since simple interest grows by a fixed amount each year while compound interest grows by an increasing amount.

Worked example 7: a reverse percentage problem

After a 12% increase, the price of a bicycle is 336. Find the original price.

Solution: the final price represents 112% of the original price, since 100% + 12% = 112%. So 336 = original × 1.12. Original = 336 ÷ 1.12 = 300. A common error here is subtracting 12% from 336 directly rather than dividing by 1.12; that approach ignores that the 12% increase was calculated on the original, smaller value, not on 336.

Exam question patterns to recognise

Questions on this topic tend to fall into a handful of recognisable types. A calculation question might ask directly for a specified fraction or percentage of a quantity. A context question, often set in a shop, bank, or population scenario, asks for a percentage increase, decrease, or reverse percentage. A comparison question asks you to express one quantity as a fraction or percentage of another, sometimes deliberately using numbers where the result exceeds 100%, to check whether you apply the definition mechanically or trust your instinct about what a "sensible" answer should be. Finance-flavoured questions at Extension level specifically test the compound interest formula, sometimes across a non-whole number of years or requiring you to compare simple interest against compound interest over the same period.

Across every pattern, the safest general approach is to convert everything to decimal multipliers before combining any percentages, since combining raw percentages by addition or subtraction, rather than as sequential multipliers, is the single most common source of error in this part of the syllabus.

Another pattern worth naming directly is a multi-stage context question that blends a percentage change with a fraction operator in the same problem, for instance finding a discounted price and then finding what fraction of a monthly budget that discounted price represents. These blended questions reward students who treat each stage as its own small calculation, writing down the result of each stage clearly, rather than attempting to combine several operations mentally in one line.

Self-check questions

1. Write 9/16 as a decimal and as a percentage.
2. Find 3/7 of 84.
3. A café's weekly takings rise from 2,400 to 3,000. Express the new takings as a percentage of the original takings.
4. A laptop priced at 650 is reduced by 18% in a sale, then a further 10% is taken off the sale price. Find the final price.
5. 2,000 is invested at 3.5% compound interest per year. Find its value after 4 years, using the compound interest formula.
6. After a 25% reduction, a jacket costs 45. Find its original price.

Attempting these six questions from scratch, without looking back at the worked examples, is the clearest way to confirm the underlying method, and not just the specific numbers used above, has genuinely been understood.

Why this topic threads through the rest of the paper

Once fractions, decimal and percentages is properly oxfordaqa igcse mathematics explained, its reach becomes obvious well beyond the Number section: probability questions expect fraction and percentage answers interchangeably, statistics questions ask for percentage comparisons between data sets, and geometry questions involving scale factors rely on the same operator thinking used for percentage-of-a-quantity problems here. Revisit these oxfordaqa igcse mathematics notes whenever a later topic assumes fluent conversion between the three forms that has not yet become automatic.