Adding and Subtracting Negative Numbers
Adding and subtracting negative numbers follows two sign rules: same signs become a plus and different signs become a minus. On a number line, adding moves right and subtracting moves left.
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What Are Negative Numbers?
- Negative numbers are to the left of zero on a number line.
- Zero is neither positive nor negative.
How to Add and Subtract Using a Number Line?
- Adding a positive number means move right on the number line.
- Subtracting a positive number means move left on the number line.
How Are Negative Numbers Used in Real Life?
- A drop in temperature means you subtract.
- You may end with a negative answer if you go below zero.
How to Remove Brackets?
- Same signs next to brackets become a plus.
- Different signs next to brackets become a minus.
How to Remove Brackets with Several Numbers?
- If there is a minus before brackets, change all signs inside.
- You can also work out what is inside the brackets first.
Practice Questions
Test your understanding
If the temperature is −F and increases by F, what is the new temperature?
Correct! 🎉 +10 pointsNot quite right
Starting at −F, adding F gives .
Simplify −7 − (−4) + (−2).
Correct! 🎉 +10 pointsNot quite right
First, simplify −7 − (−4). Subtracting −4 is the same as adding 4, so . Then, .
Simplify −12 + (−8) − (−15).
Correct! 🎉 +20 pointsNot quite right
First, simplify −12 + (−8), which gives −20. Then, subtracting −15 is the same as adding 15, so .
If you owe £20 and pay back £8, how much do you still owe?
Correct! 🎉 +20 pointsNot quite right
Owing £20 means starting at −20. Paying back £8 is adding 8: , so you still owe £12.
Simplify (−14 + 5) − (−10 − 7).
Correct! 🎉 +20 pointsNot quite right
First, simplify −14 + 5, which gives −9. Next, simplify −10 − 7, which gives −17. Subtracting −17 is the same as adding 17, so .
A submarine is at −120 metres below sea level. It ascends 50 metres and then descends 30 metres. What is its final depth?
Correct! 🎉 +30 pointsNot quite right
Starting at −120, ascending 50 metres gives . Descending 30 metres is subtracting 30, so .
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Interactive Activity
Add or subtract values to reach the target on the number line
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Students Also Ask
The questions students bump into most on this topic
When you subtract a negative number, you reverse the subtraction. This works the same as adding. For example, 5 − (−3) removes a negative value, leaving you with more. The two minus signs cancel each other, giving 5 + 3 = 8. The sign rules confirm this: same signs give a plus.
Zero is neither negative nor positive. It sits at the boundary between negative and positive numbers on the number line. In maths, zero is described as neutral. Every negative number sits to the left of zero, and every positive number sits to the right.
When you subtract a negative number, the two minus signs become a plus. For example, 5 − (−3) becomes 5 + 3, which equals 8. On a number line, you move to the right instead of the left. The sign rules explain this: same signs always give a plus.
Flip the sign of every term inside the brackets. A positive term becomes negative, and a negative term becomes positive. Then remove the brackets and simplify. For example, −(−12 + 5) becomes +12 − 5, which equals 7. You can check your answer by working out the brackets first.
Yes. Start at the first number on the number line. When you subtract a positive number, move to the left. When you subtract a negative number, the two minus signs become a plus, so you move to the right instead. The number line helps you see the direction and size of each move.