Introduction to negative numbers

In this video, we're going to introduce ourselves to the idea of negative numbers. Now, you're already used to the idea of positive numbers; you just called them numbers, not positive numbers. And just to give you an example, I will draw a number line here, and this should all be review for you.

So let me start at 0, and then this would be 1, this would be 2, this would be 3. You can think of these numbers, which you're used to, which we could call positive numbers, as how far we are above zero. One is one above zero; two is two above zero.

Now, what do you think negative numbers are going to be? If positive numbers are how far we are above zero, then a negative number would be how far we are below zero. So, for example, if I go one to the left on this number line, that would now get us to negative one. Positive one is one to the right; negative one is one to the left. If I were to go another one to the left, I would get to negative two, and I could keep going.

As many positive numbers are there, I can have the negative version of it. However far I am to the right, I could be that far to the left. Now, some of you, especially if you live in very cold parts of the world, might have already experienced negative numbers in some way.

For example, if you look at a thermometer, and this has both a Celsius thermometer right over here and Fahrenheit, we know that you can get temperatures below zero degrees Celsius and temperatures below zero degrees Fahrenheit on this thermometer. They just mark how far we are below zero with these red numbers, but really these are negative numbers.

We specify negative numbers by putting that negative sign right in front of it like that. So, for example, 20 degrees Celsius is positive. 20 degrees Celsius is actually a pretty comfortable temperature, but negative 20 degrees Celsius, that is below 20 degrees Celsius, below the freezing point of water. That is a very, very, very cold temperature.

One is 20 degrees above zero; one is 20 degrees below zero. So, big picture, for any given number, there's a negative version of it. For example, this right over here would be positive six, and then you could have negative six, but negative six is six below zero or six left of the zero on the number line, while positive six is, of course, six above zero.

So I will leave you there. You might be thinking, "Oh wow, this looks a lot like a subtraction sign." Maybe it is related to subtraction somehow, or how can I do addition and subtraction, multiplication, and division with negative numbers? And for that, we will go to future videos.