Adding Integers (Positive & Negative Numbers) | Lesson + Practice

Welcome to Math with Mr. J. In this video, I'm going to cover how to add integers. We'll go through some examples together, and then I'll give you some practice problems that you can try on your own. Now, when we add integers, we need to recognize when we are increasing in value or decreasing in value. And this depends on what we are adding. So keep in mind, if we add a positive, we increase in value. If we add a negative, we decrease in value. Let's jump into our examples, starting with number one, where we have eight plus five, which is going to be 13. But let's think through this. That way, we can apply this thinking to all of the other problems as well. Here, we are starting with eight and adding positive five. Since we are adding a positive, our value increases. So eight is increasing by five. That brings us to our answer of 13. So for number one, eight plus five equals 13. Now, to go off of that, let's take a look at number two. We have eight plus negative five. Here, we are starting with eight again, but we are adding a negative five. That means our value decreases. Eight is decreasing by five. That means our answer is three here. Eight plus negative five equals three. So when adding integers, start with the first number, and then we look at what we are adding. Adding a positive increases the value, and adding a negative decreases the value. Let's move on to number three, where we have negative nine plus negative three. We are starting at negative nine and adding negative three. So we are decreasing in value here. So if we start at negative nine, and we are decreasing in value by three, that brings us to negative 12, and that's our answer. Think of a number line, and we're starting at negative nine. And if we decrease in value, that means we are moving left on the number line. And since we are adding negative three, we are moving three units to the left. That brings us to our answer of negative 12. Moving on to number four, we have negative 14 plus six. So we are starting with negative 14 here, and since we are adding a positive six, this is increasing in value. Negative 14 is increasing by six. Our answer here is negative eight. And if we picture this on a number line, which that can help us think through these, we started at negative 14, and we moved right six units since we are increasing in value. That brings us to our answer of negative eight. Moving on to number five, we have two plus negative seven. So we are starting at two, and we are decreasing in value by seven. Now for this one, we're going to pass zero and move into the negatives. We can think about it this way. If we start at two and decrease by two, that brings us to zero, and then we still need to decrease by five more. That brings us to negative five. Two plus negative seven equals negative five. For problems like this where we cross zero, it can be helpful to use zero as a reference point. Lastly, let's move on to number six, where we have negative four plus 10. We're starting at negative four, and we're adding 10. That means our value increases here. Negative four is increasing by 10. Now this is another problem where we cross zero. For this one, we start at negative four, and we will pass zero and move into the positives. Let's think through it this way. We start at negative four and increase by four. That brings us to zero. We still need to increase by six more, though, and that brings us to six. Negative four plus 10 equals six. So there you have it. There's how to add integers, and now that we've gone through some examples together, it's time for you to try some practice problems on your own. So have paper and a pencil ready. Here are your practice problems. I'll give you three minutes, and then we will go over the answers. Feel free to pause if you need more time or jump ahead to the answers whenever you are ready. Go ahead and start. Okay, so that was three minutes. Let's go over the answers. So here are our answers. For number one, we should have negative three. For number two, negative 30. For number three, six. For number four, four. For number five, negative nine. And then lastly, for number six, negative 19. So there you have it. There's how to add integers. I hope that helped. Thanks so much for watching. Until next time, peace.