 Okay let's talk about some of the basics. Now one of the things that gives people a lot of problem is dealing with negative numbers. So let's take a look at some simple negative numbers, how you add them and subtract them, multiply them and hopefully they'll clear things up for the exercises you're going to do later. Okay let's start with just subtracting two numbers, five minus two. Now that's, you should know that, that's three, right? Now you can think about this as a number line. If this is your zero, you start at one, two, three, four, five. What you're doing, you're going back two. So you're going one, two. So you got one, two, three. So you end up at three. Simple as that. Now let's try with doing it backwards. So let's go two minus five. Now for some reasons, some people have problems with this, okay? Now if you look at this as a number line, you start off at two, one, two, and you go back from two, five steps. So you're going to go one, two, three, four, five. So that's negative one, negative two, and that's negative three. So the answer is negative three, okay? Now what happens if you add two negative numbers? Now take a look at this. What if this was a negative two minus five? So what you're going to do is, you're going to put your zero there. You're going to start at negative two, and again you're moving backwards five steps. So you're going to go one, two, three, four, five. So right now you're at negative seven equals negative seven. I mean you could think about it this way. If you owe me two bucks and then you owe me another five bucks, you're going to owe me seven bucks. So you're negative seven, okay? Keep in mind sort of quintessential rule, the sign in front of the number always goes with the number. So this guy, you could have actually written as negative two plus negative five, which is equal to negative seven. Now that's the long way of doing it. You never really do that. So this is the way you should look at it, okay? So those are simple numbers, two numbers. Let's try, you know, five or six numbers together. Switching between them. So let's say you had negative ten minus six minus seven plus four minus two. So if you do your number line here, start off at ten. Okay. What you're going to do is go back six. So one, two, three, four, five, six. So you're at four here. So ten minus six is going to be four. And then you're going to go back another seven. So you're going to go one, two, three, four, five, six, seven. So if you go one, two, three, four, three, two, one, zero. So that's zero. So you're at negative three here. So four minus seven is negative three. And then negative three plus four. Now you're moving forwards again. You're going to end up at one. So negative three plus four is one. And then one minus two is going to be negative one. So your answer is just going to be negative one. Okay. Now adding subtracting negative numbers, you need to practice it. Again, I'm going to put some questions on my website. You should go through it. Check your answers one by one. Do not go through the whole sheet. Do it and then check your answers because if you're doing it wrong, then unfortunately you're going to be training yourself how to do it improperly. So what you need to do is check one and do one question. Check the answer. If you get it wrong, retry it. Take a look at the way I did it and then move on to the next one and try to get that. So do it one at a time checking your answers until you get really good at it. Then you won't even have to think about it anymore. It will just be there. Now let's take a look at multiplying and dividing negative numbers. Now multiplying and dividing negative numbers is the same thing. All we're concerned about to know if the value is going to be positive or negative. So all you have to keep in mind is two positive numbers multiplied together give you a positive number. Example, 2 times 4 is going to be 8. So that's positive 8. If you got two negative numbers multiplied together, that's going to give you a positive number. So negative 2 times negative 4 is going to be positive 8 again. If you have a positive number times a negative number, that's going to be a negative number. So 2 times negative 4 is going to give you a negative 8. So the way it works is if you have an even number of negatives multiplied or divided together, they're going to give you positive. If you got all the numbers positive, it's still going to be positive. If you got an odd number of negatives multiplied together, the answer is going to be negative. So before you do any multiplication or division, you should know if the answer is going to be positive or negative. For example, let's do, we've got a little room down here. Let's try that. Let's try negative 2 times 4 times negative 5 divided by negative 2 times negative 3. So right now we have 1, 2, 3, 4 negative numbers. 4 negative numbers is an even number. So this, the answer is going to be positive no matter what it, what it turns out. Now let's just try this simple. Just figure out what it is. Negative 2 kills negative 2. Anything that kills each other becomes 1. And then you just have the numbers up top. When you write negative 3 down here like this, it's really negative 3 over 1. Now 1 times 1 is just 1. You don't have to put 1 in the bottom. 4 times 5 is going to be negative 20 or 20. 20 times 3 is going to be 60. And it was an even number of negatives. So we know it's going to be a positive 60. Simple as that. Now that we talked about multiplication of negative numbers, we can talk about subtracting negative numbers. Just a segment before this, we did something like 2 minus 5. And we got negative 3, right? Doing the number line. Now what if you had 2 minus negative 5? This, if you're trying to do it, you have to consider what we talked about just like 2 seconds ago about multiplying negative numbers. If you multiply 2 negative numbers, you're going to get a positive. And this acts as a multiplication of negative numbers. So negative and a negative makes it positive. So 2 minus negative 5 is really 2 plus 5, which is 7. Let's do a couple more so you get this down path, okay? If you have negative 2 minus 5, we talked about this earlier, that gives you negative 7. If you have negative 2 minus negative 5, again, this becomes negative and a negative becomes positive. So negative 2 plus 5 is 3. Let's do one longer one. Let's say you had negative 2 minus negative 4 minus 5 plus 3 minus 6. Mine is negative 6. What you're going to do is you're going to deal with the negatives, the double negatives first. So negative and a negative makes it positive. Negative and a negative makes it positive. So right now, you got negative 2 plus 4 gives you 2. 2 minus 5 gives you negative 3. Negative 3 plus 3 gives you 0. So the final answer is just 6. Easy? Okay.