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.
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?
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.