A fraction names equal parts of a whole. The denominator tells you the size of each part and the numerator tells you how many parts you have. Before adding or subtracting fractions, rewrite them using parts of the same size. Multiplication combines proportions, so multiply numerators and denominators. Dividing by a fraction asks how many of that fraction fit; multiplying by its reciprocal gives the same result. A decimal is another way to write a fraction with a denominator such as 10, 100 or 1000. Simplifying does not change the value.
Learning objectives
- Add, multiply and divide fractions.
- Convert between fractions and decimals.
Key ideas
Use equal denominators before adding or subtracting fractions.
Multiply numerators and multiply denominators.
To divide by a non-zero fraction, multiply by its reciprocal.
Convert to a decimal by dividing the numerator by the denominator.
Find a fraction of an amount: divide by the denominator, then multiply by the numerator.
Worked examples
Example 1
Add the fractions and simplify.
Use twelfths.
Answer
Example 2
Write the decimal as a fraction in its simplest form.
Answer
Question styles to prepare for
Original practice guidance aligned to the specification, not a count of past-paper appearances or a prediction. The AO labels below describe the intended practice focus, not official AQA mark allocations.
AO1 · Methods
Calculate with fractions and convert between fractions and decimals.
AO2 · Reasoning
Compare two methods or explain why equal denominators are needed when adding.
AO3 · Problem solving
Find a fraction of an amount and use the remainder in a second step.
When a task asks you to explain, include a mathematical reason. When solving a problem, show how the information becomes a calculation, equation or diagram, then interpret your result.
Avoid this mistake
Adding denominators changes the size of the parts. Keep the common denominator and add only the numerators.
Try it yourself
Attempt each question before opening its answer.
Check 1: Write 0.35 as a fraction in its simplest form.
Answer: 7/20
0.35 = 35/100. Divide the numerator and denominator by 5.
Check 2: Calculate 2/5 ÷ 3/4.
Answer: 8/15
Multiply 2/5 by 4/3: (2 × 4)/(5 × 3) = 8/15.
Explain it in your own words
- Explain why 1/2 + 1/3 is not 2/5.
- Write the decimal and percentage forms of 3/4.
- Invent an amount where finding 2/3 gives a whole-number answer.
Keep practising
Download the compact topic guide (PDF) · Practise this topic in Blitz · All foundation notes
Specification source
AQA Number specification · Assessment objectives. Checked 16 October 2026. Topic references identify related content; these notes do not cover every specification statement.