# Negative Numbers (Mathematics Lesson)

# 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 and Subtracting**

Adding/subtracting a negative number is subtracting/adding a positive number:

- 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.

##### Note

# 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%.