Negative numbers describe positions below zero, such as temperatures and debts. Adding moves you along the number line; subtracting a negative reverses that direction. Multiplication and division follow a separate sign rule: matching signs give a positive result and different signs give a negative result. When a calculation contains several operations, brackets show what belongs together. Powers come next, then multiplication and division from left to right, then addition and subtraction from left to right. This agreed order lets everyone read the same expression in the same way.
Learning objectives
- Calculate with positive and negative numbers.
- Apply the agreed order of operations.
Key ideas
Numbers further right on a number line are greater.
Subtracting a negative means adding its positive opposite.
For multiplication and division: matching signs give positive; different signs give negative.
Calculate brackets, then powers, then multiplication and division, then addition and subtraction.
At the same priority, work from left to right.
Worked examples
Example 1
Calculate the expression in the correct order.
Calculate the bracket first.
Multiply before adding.
Answer
Example 2
Subtract a negative number.
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 a signed-number expression, with brackets or powers.
AO2 · Reasoning
Explain an incorrect sign or order-of-operations step.
AO3 · Problem solving
Model a temperature change or an account balance with signed numbers.
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
Do not calculate every expression from left to right. Operation priority comes first.
Try it yourself
Attempt each question before opening its answer.
Check 1: Calculate -7 - (-4).
Answer: -3
Subtracting -4 means adding 4, so -7 + 4 = -3.
Check 2: Calculate 24 ÷ 6 × 2.
Answer: 8
Division and multiplication have the same priority. Work left to right: 24 ÷ 6 = 4, then 4 × 2 = 8.
Explain it in your own words
- Draw a number line to explain -3 + 5.
- Write one example with a positive product and one with a negative product.
- Explain why 24 ÷ 6 × 2 is not 24 ÷ 12.
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.