In this lesson on algebra negative numbers are covered. Get information and negative numbers practice here.

A **negative number** is any number that is less than zero. For instance, -7 is a number that is **seven less** than 0.

-7

It might seem a little odd to say that a number is **less** **than** 0. After all, we often think of zero as meaning **nothing**. For instance, if you have 0 pieces of chocolate left in your candy bowl, you have **no** candy. There's **nothing** left. It's difficult to imagine having less than nothing in this case.

However, there are instances in real life where you use numbers that are less than zero. For example, have you ever been outside on a really cold winter day when the temperature was below zero? Any temperature below zero is a negative number. For instance, the temperature on this thermometer is **-20**, or twenty degrees **below** zero.

You can also use negative numbers for more abstract ideas. For instance, in finances negative numbers can be used to show **debt**. If I overdraw my account (take out more money than I actually have), my new bank balance will be a** negative number**. Not only will I have no money in the bank—I'll actually have **less** than none because I owe the bank money.

Any number without a minus sign in front of it is considered to be a **positive** number, meaning a number that's **greater than** zero. So while -7 is **negative seven**, 7 is **positive seven**, or simply **seven**.

As you might have noticed, you write negative numbers with the same symbol you use in subtraction: the minus sign ( - ). The minus sign doesn't mean you should think of a number like -4 as **subtract four**. After all, how would you subtract this?

-4

You couldn't—because there's nothing to subtract it from. We can write -4 on its own precisely because it **doesn't** mean **subtract** **4**. It means the **opposite** of four.

Take a look at 4 and -4 on the number line:

You can think of a number line as having three parts: a **positive** direction, a **negative** direction, and **zero**. Everything to the right of zero is **positive** and everything to the left of zero is **negative**. We think of positive and negative numbers as being **opposites** because they are on **opposite** sides of the number line.

Another important thing to know about negative numbers is that they get **smaller** the farther they get from 0. On this number line, the farther **left** a number is, the smaller it is. So **1** is smaller than **3**. **-2** is smaller than **1**, and **-7** is smaller than **-2**.

When we talk about the** absolute value** of a number, we are talking about that number's distance from 0 on the number line. Remember how we said 4 and -4 were the same distance from 0? That means 4 and -4 have the same absolute value. We represent taking the absolute value of a number with two straight vertical lines **| |**. For example, |-3| = 3. This is read "the absolute value of negative three is three."

Something important to remember: even though negative numbers get **smaller** as they get further from 0, their absolute value gets **bigger**. For example, -10 is smaller than -6. However, |-10| is bigger than |-6| because -10 has a greater distance from 0 than -6.