Maths
What are negative numbers?
Quick answer
Negative numbers are numbers less than zero, written with a minus sign, like −3. You meet them in cold temperatures, bank overdrafts and floors below ground.
In one sentence
Negative numbers are the numbers below zero, like −1, −2 and −3.
Explained
On a freezing morning the thermometer might show −5 °C, said "minus five degrees". That means five degrees colder than 0 °C. Numbers like this, with a minus sign in front, are negative numbers. Numbers above zero are positive, and zero itself is neither.
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The best way to understand them is a number line that carries on past zero to the left:
… −5, −4, −3, −2, −1, 0, 1, 2, 3, 4, 5 …
Numbers get smaller as you move left. That means −8 is smaller than −2, even though 8 is bigger than 2. Think of it as colder: −8 °C is colder than −2 °C.
Adding and subtracting. Adding a positive number moves you right; subtracting moves you left. So 2 − 6 starts at 2, moves left 6 and lands on −4. And −5 + 3 starts at −5, moves right 3 and lands on −2.
To find the gap between a negative and a positive number, go via zero. From −3 to 9 is 3 steps up to zero, then 9 more: 12 altogether.
Older students learn two more rules. Subtracting a negative is the same as adding: 5 − (−2) = 5 + 2 = 7. And when multiplying or dividing, two negatives make a positive (−3 × −4 = 12), while one negative makes a negative (−3 × 4 = −12).
Examples
- A lift goes from floor 2 down to floor −1 (the basement). That is 3 floors down.
- 0 − 6 = −6
- −10 + 4 = −6
- −2 − 5 = −7
- 4 − (−3) = 7
- −20 ÷ 5 = −4
Common mistakes
- Thinking −9 is bigger than −3. Fix: picture the number line or a thermometer.
- Forgetting to count through zero when finding a difference, so the gap from −2 to 5 comes out as 3. Fix: split it into −2 to 0 and 0 to 5. The answer is 7.
- Mixing up the minus sign and subtraction. In −4 − 3, the first sign belongs to the number, the second means "take away". Answer: −7.
Quick quiz
Negative numbers
Check what you know with 5 quick questions.
Question 1 of 5
Which number is the smallest?
Practise it
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Browse maths worksheets for number line and negative number practice.
For grown-ups
Related topics
Number line
A number line is a straight line with numbers marked at equal steps, smallest on the left and biggest on the right. It helps you count, compare, add and subtract.
Subtraction
Subtraction is taking one amount away from another, or finding the difference between two numbers. The sign is −, so 9 − 4 = 5.
Addition
Addition is putting amounts together to find a total. The sign is +, and the answer is called the sum or total, so 4 + 3 = 7.
Coordinates
Coordinates are a pair of numbers that give an exact position on a grid, like (3, 5). The first number is how far across (x) and the second is how far up (y).
2D shapes
2D shapes are flat shapes with length and width but no thickness, like circles, triangles, squares and hexagons. You can draw them on paper.
3D shapes
3D shapes are solid shapes with length, width and height, like cubes, spheres, cylinders and pyramids. They have faces, edges and vertices.