# What Is a Negative Number?

A negative number is a number less than zero.

#### Dictionary Definition

The Merriam-Webster dictionary defines a negative number as "less than zero and opposite in sign to a positive."

# Examples of Negative Numbers

A negative number is any number less than zero. Negative numbers can be any type of number: whole numbers, fractions, or irrational numbers.

Some of examples of negative numbers are given below:

# How Are Negative Numbers Written?

Negative numbers will have a minus sign ('-') in front of them. For example, the negative number negative two can be written as:

# Negative Numbers on the Number Line

The image below shows the negative numbers on the number line. Negative numbers are to the left of 0:

Note: 0 is not a negative number. Negative numbers can be fractional, so they can be between the numbers labelled.

# Ordering of Negative Numbers

Look at the order of the negative numbers on the number line above.

The order (left to right) goes: -5, -4, -3, -2, -1.

This is the opposite of how we'd write positive numbers: 1, 2, 3, 4, 5.

This tells us about the ordering of negative numbers.
For a negative number, the bigger the number after the - sign, the smaller the number!
• -5 is smaller than -4 (as 5 is bigger than 4).
• -4 is smaller than -3 (as 4 is bigger than 3).
• -3 is smaller than -2 (as 3 is bigger than 2).
• -2 is smaller than -1 (as 2 is bigger than 1).

# Arithmetic With Negative Numbers

Special care needs to be taken when adding, subtracting, multiplying or dividing by negative numbers.

• Adding a negative number is equivalent to subtracting the (positive) number.
2 + (-1) = 2 - (+1) = 2 - 1 = 1
• Subtracting a negative number is equivalent to adding the (positive) number. (Two negatives make a positive!)
2 - (-1) = 2 + (+1) = 2 + 1 = 3
Multiplying and Dividing

Multiplying/dividing a number by a negative number changes the sign of that number:
• Multiplying a positive number with a negative number creates a negative number.
2 × (-2) = -(2 × 2) = -4
• Multiplying a negative number with a negative number creates a positive number. (Two negatives make a positive!)
-2 × (-2) = --(2 × 2) = +(2 × 2) = +4 = 4
• Dividing a positive number with a negative number creates a negative number.
4 ÷ (-2) = -(4 ÷ 2) = -2
• Dividing a negative number with a negative number creates a positive number. (Two negatives make a positive!)
-4 ÷ (-2) = --(4 ÷ 2) = +(4 ÷ 2) = +2 = 2

##### Interactive Test
show

Here's a second test on negative numbers.
Here's a third test on negative numbers.

# What Do Negative Numbers Mean?

It can be hard to think what a negative number means.

A positive number can be used to count things: 1 apple, 2 people, ½ a cake...

What can negative numbers describe?
• A negative amount of money can represent a debit, a debt or a loss.
• If \$100 leaves your bank account, it might show up as -\$100 on your bank statement.

• A balance of -\$100 would mean you owe the bank \$100.

• A profit of -\$100 would mean the company spent \$100 more than it earned.
• A negative temperature means the temperature is below 0.
• -2°C is 2°C below 0°C

• -10°F is 10°F below 0°F

• Electrons have a negative charge. (Protons have a positive charge).

• A decrease can be thought of as a negative increase. If economic growth is -3%, the economy has shrunk by 3%.

# Different Types of Negative Numbers

Any number less than 0 is a negative number, whether the number is an integer or a fraction.

# Positive Numbers

A positive number is a number greater than zero.

# 0 Is Not a Negative Number

0 is not a negative. Nor is it a positive number.