ANTHONY VARELA: Hi. My name is Anthony Varela, and today I'm going to talk about adding and subtracting positive and negative numbers. So we're going to take a look at a number and its opposite. Then we're going to talk about positive and negative numbers in a context. And then we're going to practice adding a negative and subtracting a positive, and see that's the same thing.
So to start, let's talk about a number and its opposite. So I'm going to use a number line to illustrate this idea. So let's plop a number on our number line, like 2. Well, what's the opposite of 2?
Well, we see that 2 is 2 units away from 0 in the positive direction. So the opposite of that is going to be 2 units away from 0 in the negative direction. So negative 2 is the opposite of positive 2.
So we notice that when we're talking about a number and its opposite, we're really taking that same digit, but turning a positive into a negative, or a negative into a positive. And then one thing to note about a number and it's opposite is that when you add those two values together, you'll get 0. So negative 2 plus 2 equals 0. Negative 5 plus 5 equals 0. So a number and its opposite sum to 0.
So now let's talk about positive and negative numbers in a context. So let's say I've gone out grocery shopping, and here's my receipt. I purchase cereal, juice, coffee, and soup, and there are all the prices for that.
Well, if I add all of these prices together, I get my total. So let's take a look at what this is like on a number line. So I'm starting at 0, and I'm going to add my cereal, juice, coffee, and soup, and that's going to give me a total of $15.78.
So we can imagine we're starting at 0. I'm adding $3.59, adding $2.88, adding $7.64, and then adding $1.67 to get that $15.78. So when we're adding positive numbers together, that's going to increase our sum.
So let's write that down. Adding positive numbers increases the sum. So now let's introduce a negative number. So here I have a coupon for $2 off my entire purchase. How is this going to affect my total?
Well, my total, then, is not going to be $15.78. It's going to be $13.78. So let's represent this sum on the number line. So here's $13.78. And we can imagine starting at 0, going up $3.59, up $2.88, up $7.64, up $1.67, and then down $2 to get to $13.78.
So when we add a negative number, this decreases the sum. So we're going to write that down-- that adding negative numbers decreases the sum. So then there's this whole idea, then, that adding a negative number is the same thing as subtracting a positive number. So let's take a look at that.
Here's our situation-- that a package of oatmeal costs $7. You have a coupon for $3 off the oatmeal. How much do you need to buy the oatmeal? So we can write this out as 7 plus negative 3, because we're interpreting our cost for our oatmeal as a positive 7, and then we are interpreting our coupon for $3 off as a negative 3. And we're going to combine these two together with addition.
So doing this on the number line, we start at 0, and then we're going to find our positive 7. And then we're going to add negative 3. So we're going to be going in the negative direction 1, 2, 3 units. So 7 plus negative 3 is a positive 4.
Now, this was showing how to add a positive and a negative number. We're going to represent this as subtracting a positive. So is this the same, then, as saying 7 minus 3? Let's go ahead and take a look.
We're starting at 0. We're going to go to positive 7 on our number line, and subtracting 3. So we're going to go in the negative direction 1, 2, 3 units. So 7 minus 3 also equals 4.
So this is a big idea. Adding a negative is the same as subtracting a positive. Well, we're going to take a look at a final example here. Our situation reads as follows.
I am looking into buying a new computer. The computer costs $800, which includes a warranty. I'd like to add extra storage, which is going to cost me $200 more. But I'm not interested in the warranty package, so that's going to save me $120.
There's an instant rebate of $50 for buying during the back-to-school season. So what I want to know is, what is the total cost of the computer with extra storage, no warranty, and the instant back-to-school rebate?
Well, the first thing I'm going to do is highlight some of my numbers, and I'm really going to think about the context-- if they represent positive numbers, or negative numbers. So here I've highlighted my positive numbers. These are things that are going to contribute or add to my cost-- the $800 for the computer-- that includes the warranty-- and my extra storage space that I'm going to be charged $200 more to have.
So now let's highlight what we can interpret as negative numbers. I highlighted the $120, because that's what I'm going to save by opting out of the warranty package. And then I'm going to save $50 for this instant rebate for buying during back-to-school season. So now I can write this, then, as an addition problem.
My total cost is going to be $800 plus $200, and I'm also going to add my negative $120 and my negative $50. Now, I know that adding a negative can also be written as subtracting a positive, so I'm actually going to rewrite this, and I'm going to interpret my negative numbers as a subtraction-- so $800 plus $200 minus $120 minus $50.
So this, then, all evaluates to $830. That's going to be the total cost for my computer with extra storage, no warranty, and that instant rebate. So let's review what we talked about today.
We talked about a number and its opposite. That's just changing the sign from positive to negative, or negative to positive. And we also talked about opposites summing to 0. So a negative 10 plus a positive 10 gives me 0.
We talked about positive and negative numbers in context. When you're adding negative numbers, that's going to decrease your sum. And when you're adding positive numbers, that's going to increase your sum.
And then finally, we talked about how adding a negative is the same thing as subtracting a positive. And we saw this in example of purchasing a computer. The cost could be expressed as $800 plus $200 plus negative $20 plus negative $50. And we can rewrite this involving some subtraction too-- $800 plus $200 minus positive $120 minus positive $50. So thanks for watching this tutorial on adding and subtracting positive and negative numbers. Hope to catch you next time.