Negative Numbers
Negative numbers are values less than zero, shown to the left of zero on a number line.
▶ Interact
Play with the controls to see the idea in action.
📘 Learn
Negative numbers are values less than zero, shown to the left of zero on a number line.
- Adding a negative moves left
- Subtracting a negative is the same as adding
- Two negatives multiplied give a positive
🧠 Quick quiz
Three questions. Score 2 or more to complete the topic.
What is Negative Numbers?
Within Mathematics, which covers numbers, algebra, geometry, trigonometry and statistics from first principles to exam level, this topic explains Negative Numbers. Maths builds step by step, so each topic here gives you a rule, a picture and a quick check you can use on homework and in exams.
Check that you can explain Negative Numbers in your own words and give one example from everyday life. If you can do that, you have understood the core idea.
Understanding Negative Numbers gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
Negative Numbers in detail
Negative numbers are numbers less than zero, written with a minus sign, and they extend the number line to the left of zero. Adding a negative is the same as subtracting, and subtracting a negative is the same as adding, so 5 − (−3) = 8. Multiplying or dividing two numbers with the same sign gives a positive result, and with different signs gives a negative result.
They describe real situations such as temperatures, debts, depths below sea level and changes that decrease a quantity. Comparing negatives takes care: −8 is smaller than −2 because it lies further left on the number line.
How the interactive helps you understand Negative Numbers
Move the slope and y-intercept sliders. The line and its equation update, so you can see how the slope sets the steepness and the intercept sets where the line crosses the y-axis.
Before you change anything, predict the result. Then change one value at a time and check whether your prediction was right. This is a quick way to build a correct mental model of Negative Numbers.
Real-life uses and examples
- Explain Negative Numbers to a friend with a simple picture, such as a row of tiles or a bag of sweets.
- Spot Negative Numbers in exam questions, where it often sits inside a short word problem.
- Check a homework answer about Negative Numbers by estimating first, then working it out step by step.
Common mistakes to avoid
- Memorising the steps for Negative Numbers without checking why they work.
- Forgetting units, signs or brackets when you apply Negative Numbers.
- Learning the definition without testing it. Use the quiz and the interactive to check that you can apply the idea.
Frequently asked questions about Negative Numbers
What is Negative Numbers?
Negative numbers are values less than zero, shown to the left of zero on a number line.
What are the most important points about Negative Numbers?
The main points are: Adding a negative moves left; Subtracting a negative is the same as adding; Two negatives multiplied give a positive.
Why is Negative Numbers useful?
Understanding Negative Numbers gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
How can I practise Negative Numbers?
Open the interactive at the top of this page and change the controls one at a time. Predict the result before each change, then take the three-question quiz. A score of two or more marks the topic as complete on this device.
Which topics are related to Negative Numbers?
Related topics in Mathematics include Adding and Subtracting Fractions, Decimals, Percentage Change.