All right, in Section two, we're going to be talking about negative numbers here. And we're going to talk about positive and negative numbers and what that means we're going to do addition of negative numbers. We're going to do subtraction of negative numbers, and then we're going to finish up with multiplication, division of negative numbers. So with all that said, let's move on to the next slide. Okay, we're, again, we're talking about negative numbers. And if you look, here's my number line.

And I have my zero on my reference right there. And when I go looking at the number line when I go to the left All right, I am stating that my numbers are positive right here. Okay, when we represent a positive number, we don't usually put a plus sign in front of it. It's just assumed to be positive. So even though these numbers don't have a plus side in front of it, okay? They're assumed to be positive.

Now, if you look here going this way, we have negative numbers, oh, my numbers are negative. Well, we really never get anything less than zero. I mean, how can you get a quantity less than zero? You can't. It's physically impossible. So when we talk about negative numbers, we're kind of talking about which direction so in my number line or no number line No, we're saying, Okay, I've got a number line here.

When I go to the left of zero this way, the numbers are positive, and we go to the right of zero this way the numbers are negative. All right. So that's one way we can think about it. Another way that we can think about it, and I give you a little bit of an example, a person receives $100 compensation, we can consider this as a positive number. He's received some money for something that he's done something that he's easy work or whatever, it doesn't matter at this point. But out of this compensation, he's got to pay his rent.

So whatever his rent is, let's say his rent is $50. He's got to pay rent and 50 bucks, that $50 could be construed as phoric and he's the reference from his point of view, You that $50 is a negative number because it's coming out of his compensation. So we can see that positive negative negative numbers are, are a direction from a reference point of view, even though I forgot to put view here, I'll fix that. Okay, someone's point of view. All right. But we don't have we can't have a quantity less than zero.

All right, that's the point I'm trying to make. All right, if I have $100. All right. And I have a bill for 101. I pay the hundred dollars. I have a negative one left.

But that means I still got to get $1 some way to pay it. All right, doesn't mean that I can have it's less than zero. It's still a while. Dollar quantity that I need to pay back. So when we say plus and minus numbers, it's it's a reference. And that's basically all it is.

So let's stop here. And let's move on to the next one, which is adding positive and negative numbers. Okay? Okay addition of negative numbers and if you look at the the rule I give you right here, it says to add a negative number to a positive number, take the difference between the two numbers and give the answer the sign of the largest number and I give you an example here. Again, eight plus minus five right there, okay equals three. So eight is the largest other number and it's positive and the sign is positive.

Therefore three is positive because I take it Dear friends, all right, the difference between eight and five is three and eight is the larger number. And it is positive, so therefore, my answer is three. Right? So, I show a key here graphically, and again, we're talking about direction. So I have a plus eight. So I go, here's my zero, my reference right there, and I go up eight, right?

So there's my plus eight. But now I've got a minus five or I'm adding a minus five. So I go the opposite direction. 1212345 and I land at three and the reason three is read is I'm emphasizing the three is the answer not that's the only reason for the red there. That's the only significance is to say My answer is plus three. So if you look at this again, to add a negative number to a positive number, take the difference between the two numbers and give the answer to the sign of the larger number.

Okay, let's, let's move on. Okay, on this example it's, it's very similar, but look at what we've done. We've changed the sign. So now I got a minus eight, and a plus five. Again, to add a negative number to a positive number, take the difference between the two numbers and give the answer to the sign of the largest number. Okay, so here we go.

Eight, plus five, we take the difference, it's three, eight is minus, okay, so therefore the sign is minus, also the three is negative. So at the previous example, we went to the left of the decimal point now we're going to the right of the decimal point again, direction. so is my minus eight this way as I show you. All right, that's my minus eight. But now we have a plus five right there. And we go the opposite direction as we show, and again, there's my answer three, but it's a minus three.

And again, the red, the red color to minus three, I'm only trying to highlight the answer. So that's it. That's it. Follow the rule take to add a negative number to a positive number. Take the difference between the two numbers and give the answer the sign of the larger number. You've done.

Good, let's move on. Okay, the other rule is that when when there are two numbers The same sign, the sign does not change. All right and give you an example. A minus eight plus a minus three. All right? Eight and three is 11.

Okay, do you use a calculator if you want, okay, they both have a negative sign. It says minus 11. And again, I can show that graphically. Here we are, here's my zero, and I'm going this way, eight units. And then I add another three units in the same direction. Okay, my reference is zero.

So when I go to go to the right of the zero line, there, that direction we've defined as a negative number. My answer is a minus 11. So again, when there are two numbers with the same sign, the sign does not Change. Now I've showed you negative numbers. In the previous section, we we work with positive numbers. So, I mean, there's only two types of numbers positive and negative.

So when this when the signs are the same, the sign does not change. When we are adding numbers in this case, we're talking about negative numbers. Okay, take a few minutes, stop, stop the presentation. Do the examples here. When you're finished, hit resume and you'll see the answers on the next slide. Okay, here are the answers for you.

11 Plus a minus five is a plus six. Five plus a minus 11 is a minus six and minus five plus or minus 11 is 16. I, this wraps up this section. The next step. The next lecture we're going to talk about subtraction of negative numbers. See you there.