What Does Negative Numbers Mean?

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Up to this point, you have learned about the positive integers, which are the ones to the right of the $0$ in the picture below. Now, you will start learning about the integers to the left of the $0$ in the picture below. These numbers are called negative numbers.

A section of the number line from minus five to plus five

A negative number has a short line in front of it, just like the numbers to the left of the $0$ in the picture. This line tells you that the number is a negative number. For example, the number minus three ( $- 3$ ) is made up of two symbols, one line $-$ and a number $3$ . When you put the line and the number together, you get the negative number $- 3$ . On the real line, the number $- 3$ is just as far from $0$ as the number $3$ . The difference is that they are on opposite sides of $0$ . The line you see in front of negative numbers is called a minus sign. This minus sign tells you that you’re dealing with a negative number. The minus you know from earlier is a subtraction minus. It’s an operator that tells you to subtract one number from another number. It’s really important to know the difference between a subtraction minus and a minus sign.

Example 1

Which of the numbers below are negative numbers?
$1 - 2 8 10 - 15 32 - 21 - 1$

$- 2$ , $- 15$ , $- 21$ and $- 1$ are negative numbers, because they have a minus sign.

Think About This

Is 0 a positive or a negative number? Or is it neither?

The number $0$ sits right between positive and negative numbers on the real line. For example, imagine that you give away $0$ chocolates or receive $0$ chocolates. You have neither more nor less chocolates than what you had before. For that reason, you can say that the number $0$ is both a negative and a positive number!

Example 2

Which of the numbers below are negative and which are positive?

23 190 -22 0 -1111 54 -2 3 104

The negative numbers (the ones to the left of $0$ on the real line) are the ones with a minus sign in front of them. That means that the numbers $- 22$ , $- 1111$ and $- 2$ are negative numbers. $0$ is also a negative number as it is both negative and positive.

The positive numbers (the numbers to the right of $0$ on the real line) don’t have a minus sign in front of them. That means that the numbers $23$ , $190$ , $54$ , $3$ and $104$ are positive numbers. $0$ is also a positive number as it is both negative and positive.

Think About This

How many negative numbers are there?

There are just as many negative numbers as there are positive numbers. But how many are there actually? In fact, there are an infinite number of negative numbers, just like there are an infinite number of positive numbers.

In mathematics we use a specific symbol for infinity. It looks like the number eight lying down: $\infty$ .

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How to Calculate with Negative Numbers

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