Adding Signed Numbers - Lesson 101

Adding Signed Numbers - Lesson 101 Hi, I’m Larry. This is the video from Lesson 101 on my website, adding signed numbers. This is one of the most important lessons on my site so make sure that you fully understand it and feel fully comfortable with it. I you have difficulty understanding this lesson you will have trouble with all the materials that follows because it builds up on this lesson especially when we get to Algebra we’re going to be using the skill again and again, so make sure that you don’t have any difficulty with it whatsoever. Up until now I’ve been working with adding positive numbers and we haven’t any trouble with that. In this lesson we’re going to introduce negative numbers and we’re going to have to add them. Now, very often students say something like, “Wow! What’s a negative number? How can you have a negative three ups?” and in a sense they are right, but negative numbers do come up quite a bit in Math, and so we have to know how to work with them and we have to feel comfortable with them. Now, I like to think of negative numbers as a debts or how much money I owe, so if I say negative three I’ll think of that as I owe $3.00. If I say a positive number I’ll think of that as how much money I have, and let me show you how this works. For this example I’d like to add 3 + -5. Now, I know that looks strange especially if you are used to only work with positive numbers, but this is a very common tasks in Math that we’ll have to do. Here’s how I like to teach you. I’m going to look at the 3 as I have $3.00 so a $3.00 on my pocket. This -5 I’m going to look at as a debt, so I owe you $5.00 as in -5. By the way, this three we know it has positive symbol because it doesn’t have a negative sign in front of it. We don’t have to put a plus sign in front of it. Okay, so the situation is I have $3.00 but I owe you $5.00. Now, we know from experience what that means. If I want to pay you back your money I can pay you back the $3.00 that I have, but think about the situation I’ll still owe you money, why? I still owe you $2.00 and the way I will show that is by writing a -2 the negative meaning I owe you money, I still owe you money. Now, how did I know that I still owed you $2.00? Well, first of all I saw right away that I owe you more money than I have, so that’s not a good situation for me, so I know the ends will be negative without a doubt. Now, to figure out the part of it of the actual two part of it all I did was really do 5 - 3 I figure out the difference between how much I have and how much I owe you, and that’s what to really is adding signed numbers. Just think of it in terms of how you have and how much you owe. Let’s take a look at another example. For this example I like to do -4 +7. and by the way just to remind you remember that addition is cumulative that means that we can add the numbers in whatever order we feel like, so if that’s a reason you want to switch the order that these numbers are in, that’s fine. We can also do 7 + -4. Okay, so for this example I’m going to think of this as I owe you $4.00 but I have $7.00. Now right out of the back that’s a good situation for me because I have more money than I owe, so right of the back I know the answer is positive. I don’t have to bother with the plus sign without the plus sign we assumed that the answer is positive. Okay, so I have more money than I owe and what I’ll do is I simply just do 7 – 4 to get three, that’s the difference between how I have and how much I have to pay back, how much I owe you, so the answer is +3. Okay, so let’s do one more example. For this example I like to do -3 + -5, and I think about that for a minute. We said that a negative number we’re going to think of it as a debt or how you owe, so I can think of this problem as I owe $3.00 to one friend and I owe $5.00 to another friend, so what’s my situation there. Well, I’m getting more and more into debt. What I’m going to do is just added my debt. I owe three and I owe five so I owe a total of eight and since I owe alright that is negative, negative eight. So, make sure that you feel fully comfortable doing things like this if you just think of it in terms of how much you have versus how much you owe or in this owing twice you really won’t have any problems at all. One thing I just want to mention is you may see these problems with parentheses written around the numbers. If you see that don’t get confused sometimes they’ll do that just to isolate numbers just to kind and emphasis them so they are easier to see. For example I might do this or you may see it written like that jus to kind to show that we’re dealing with the sum of 3 and -5. It just makes it a little easier to read, but these parentheses are optional, but sometimes you’ll see especially around negative numbers just of them is very clear what our numbers are and what our operation is. And this comes our operation is always addition and we’re just adding the combination of positive and negative numbers. Okay, again make sure that you feel super comfortable with this if you are not comfortable doing problems like this I promise you you’re going to have a lot of difficulties going forward especially when you get to Algebra. Make sure you can do these problems in your sleep. We’ll talk more about this in the upcoming lessons.