Negative Numbers
Negative numbers lie left of zero and represent debts, drops and depth.
About this topic
Negative numbers extend the number line to the left of zero and describe debts, temperatures below freezing, depths below sea level and losses. Two numbers that are the same distance from zero on opposite sides are opposites, such as 5 and −5.
Bigger negatives are smaller values, so −9 is less than −2. Subtracting a negative is the same as adding a positive, which is why 5 − (−3) = 8. Multiplying two negatives gives a positive, a pattern worth understanding rather than just memorising. The rule of signs says that same signs give a positive product and different signs give a negative one.
Think of money. Owing 5 dollars is −5. If someone removes a 3 dollar debt, which is subtracting −3, you are 3 dollars better off. On a thermometer, going from −4 degrees up by 10 degrees gives 6 degrees. Number-line arrows help: adding moves right, subtracting moves left, and a negative sign flips the direction.
Negative numbers are used in accounting, physics for direction and velocity, elevation maps and electric charge. The most common mistake is thinking −8 is greater than −3 because 8 is greater than 3. On the number line −3 is farther right, so it is bigger. Another is confusing the minus sign meaning subtract with the sign meaning negative, so writing brackets, as in 4 + (−6), helps you see what is happening.
Key ideas
- Opposites sit the same distance from zero
- Subtracting a negative adds
- Bigger negatives are smaller values
Quick check
Use cases: where Negative Numbers helps
- Homework: review the key idea behind Negative Numbers before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Negative Numbers without notes.
- Visual learning: play with the interactive lab to see how Negative Numbers changes when you adjust its inputs.
- Teaching a friend: explain Negative Numbers in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Negative Numbers?
Negative numbers lie left of zero and represent debts, drops and depth.
What will I learn in Negative Numbers?
Opposites sit the same distance from zero. Subtracting a negative adds. Bigger negatives are smaller values.
Is Negative Numbers part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Negative Numbers lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Negative Numbers?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.