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Maths · KS3 and GCSE · Interactive lesson

Adding and subtracting negative numbers

Use a number line to explore negative numbers. See which way to move, then practise addition and subtraction with step-by-step hints.

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Explore an interactive example, then try the questions at your own pace.

Lesson options

Start with the idea, then use the method when you are ready. Changing these settings changes the example. Your current practice question is kept.

Start with the idea explains the basics. Use the method builds on them with more detail.

KS3 / GCSE foundations. Begin with a number line and the idea of numbers below zero.

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KS3 / GCSE · start with the idea

By the end of this lesson: Use a number line to explain adding or subtracting a negative number.

The interactive diagram and controls are in Stage 2, “Explore one example”. Read the idea here, then try it next.

The idea in small steps
  • On a number line, smaller numbers are to the left and larger numbers are to the right.
  • Adding a positive number moves right. Adding a negative number moves left.
  • Subtracting a number means adding its opposite.
What do the words mean?
Negative
A number below zero.
Opposite
The same distance from zero on the other side: the opposite of −5 is 5.

Change the example

Something to try

Keep the two numbers the same. Switch between Add and Subtract. Which way does the arrow point?

Notice what changes

−14−12−10−8−6−4−202468101214Start −3Move 5 units right
−3 − (−5) = 2
About this model

Each tick is one unit. Selected values are labelled. Orange marks the start; purple marks the answer. Numbers increase to the right.

The example you chose
−14−12−10−8−6−4−202468101214Start −3Move 5 units right

−3 − (−5) = 2

Still picture of the example from Stage 2. Use the back arrow to change it.

Work through it

Starting example: read the steps below

  1. Start at −3.
  2. Subtracting −5 means adding its opposite: 5.
  3. Move 5 units right (increase).
  4. You land on 2.

Try on your own

Your turn. No rush.

Question 1

Calculate −4 − (−7).

Enter a number or fraction, such as −3, 0.75 or 3/4. You can include the matching unit shown above. If rounding is needed, the question tells you how many decimal places to use.

About these questions

Questions appear in a mixed order. Work at your own pace and stop whenever you like.

These questions use their own numbers, separate from the lesson example. You can stop whenever you like. Answers last for this visit to the page.

A good place to pause

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Can you explain which way adding or subtracting moves you on a number line?

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Next topic: Fractions, decimals and percentages →Back to topics

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Notes for parents and tutors

These lessons cover selected KS3 and GCSE ideas for England; they are not a complete course. The level notes explain where GCSE methods or optional extensions begin. Maurice can help you choose material for your course and exam board.

The content draws on the DfE Maths curriculum, DfE Science curriculum and AQA GCSE Physics specification. Level labels are guidance, not exam-board endorsements. For AQA Radioactivity, calculating net decline as a ratio is Higher-tier work. Net means the overall change; ask Maurice whether this extension is relevant to your course. Explanations and practice were reviewed during development on 21 October 2026; Maurice should check their fit before assigning work.

Topic labels and your lesson-view preference are saved in this browser. This tab also remembers the last lesson stage, so you can choose to continue there. If you choose revision, selected activities and suggested revisit dates are saved here too. Recent question codes are also kept to reduce repeats. Reflection notes are saved automatically per topic when you type them; you can delete a note in the recap. They stay in this browser and are visible to other people using it. Practice answers and enquiry details are not saved. Clearing browser data removes the labels.