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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
Read more about arithmetic with negative numbers

Interactive Test
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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%.

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.