In this lesson, we're going to look at how we can add integers. Now, the strategies that we're going to use will work for any kind of real number, not just integers. But for these examples, we're going to focus on integers. Say if we want to add the numbers negative two and positive five, as we see here, negative two plus five. One strategy is to use counters. Now, you may have seen counters being used in your math class in school. They look like little round chips that are used for counting. So if we want to use counters to add negative two and five, we first start with two negative counters, and this will represent the negative two. And then we'll add five positive counters. Now, each positive counter will cancel out one of the negative counters. So this positive will cancel out that negative, and this positive can cancel out the other negative. So now we just take a look and see what's left, what did not get canceled out. And we can see that we're left with three positive counters. And that's what our answer is, positive three. So negative two plus five equals positive three. Now let's look at the same problem, but solving it using a number line. So here we have a number line. We can see that we have both positive and negative numbers. Here, when we use the number line, first, mark off the very first number that we see on the number line. So we start with negative two. We're going to mark off negative two, mark off that spot on the number line. And since we're adding five to it, addition tells us that we're going to move to the right on the number line. So we're going to move to the right five places and see where we end up. So here we go - 12345. And we can see that we end up at positive three. Wherever you end up, that's your answer. So once again, we can see that the negative two plus five will equal positive three. The third way is just by using reasoning, which means that you're going to think your way through the problem rather than using tools like counters or number lines. So one way that you can think your way through this problem is to first just look at the numbers and ignore their signs. So we're not worried about whether the numbers are positive and negative yet. So we'll just look at the two and the five. Don't worry about the negative and the plus sign. And we want to find the difference between those two numbers. So the difference between two and five is three. To see what sign the answer will be, we find the sign of the larger number. Now, since our numbers are two and five, five is larger. So you can think of it like the larger number is like the boss, it's in control. It's going to determine what the sign of the answer is. Five is the larger number, and it's positive, so that means that our answer is positive. So we figured out that the difference between the two numbers is three and that it will be a positive three because the larger number five was positive. So once again, we still get the same answer negative two plus five equals three. So, just to summarize, we saw three different strategies that we can use for adding integers. We can use counters, a number line, or reason our way, which means just thinking our way through the problem. Another way is to use a calculator if you have one available or if you're allowed to use them in class. Now, when you use a calculator, you just have to be very careful to enter the signs correctly. So just make sure that you pay attention to the negatives and subtraction signs and don't get those mixed up. And it just comes with practice to get more comfortable with it. And keep in mind that these methods do work for all real numbers, not just for integers. In these examples that we just looked at together, it was a little easier to work with integers so that you can see the counters and the number line, see how they work with those more easily. But these strategies can work for any real numbers, whether they're fractions or decimals or anything. The further along you move along in algebra class and get more comfortable, you'll probably come to rely on a calculator or even reasoning your way through these problems more than using counters or number lines, but they are still perfectly fine to use. All right, so now you know how you can add integers.