Adding Integers How to Add Positive and Negative Integers

Welcome to Math with Mr. In this video, I'm going to cover how to add integers. Now, when it comes to adding integers, there are different strategies you can use in order to solve these. So, as we go through the four examples, I'll give you couple of different ways to think through these problems and get to that final answer. So, let's jump into number one where we have -5 + 7. And the strategy we're going to use first is at the top of the screen. So, the first thing we need to do is see if we have different signs or the same signs. In the case of number one, we have -5 and positive seven. So, we have different signs. So, we're going to look right here. So, what we need to do, we need to find the absolute value of our integers. And then we'll take the greater absolute value and subtract the smaller absolute value. That's going to give us our answer. We'll use the sign of the greater absolute value for that final answer. So, let's find our absolute values. And remember, absolute value is the distance from zero. The absolute value of -5 is five. And the absolute value of seven, positive seven, is seven. So, we take the greater absolute value, which would be seven, and subtract the smaller absolute value, which is five. 7 - 5 is 2. Now, we need to use the sign of the greater absolute value. So, the greater absolute value would be the seven here. And in the original problem, the seven, it's positive seven. So, that means our answer is going to be positive two. Now, the other strategy we can use would be using our overall number sense and knowledge of integers in order to solve this using mental math. So, let me rewrite the problem. We have -5 + 7. So, one way to think through this problem using mental math would be thinking, "Okay, we're starting at -5 and we're adding positive seven. So, we are increasing in value." Well, -5 + positive five gets us to zero, but we have seven, which is two more than that positive five. So, let's go two more than zero and we land on positive two. Now, do want to mention have video that goes through how to add integers using number line, and this really helps visualize what's going on within these problems, and it's going to help with mental math when it comes to adding integers. I'll drop that link down in the description. So, let's move on to number two where we have positive 20 + -12. So, again, we have different signs. So, let's find the absolute value of our integers here. So, the absolute value of 20 is 20, and the absolute value of -12 is 12. So, we need to do the greater absolute value, 20, minus the smaller absolute value of 12, and we get eight. So, we need to use the sign of the greater absolute value. So, the greater absolute value is 20, and in the original problem, it was positive 20. So, our answer is positive eight. Let's think through this using mental math as well. So, I'll rewrite the problem. 20 + -12. So, we are starting at positive 20 and we're adding -12. So, we are decreasing in value by 12 from 20. So, we can almost think of this as 20 and we are taking away or subtracting 12 because we are decreasing in value. So, we would end up at positive eight. Again, we are going from positive 20 and we are decreasing in value by 12, so we would land on positive eight for our answer. On to number three where we have -13 + -4. So, we have the same signs here. So, we will look right here. So, we need to add the absolute values and use the same sign from the problem. So, let's find our absolute values here. So, the absolute value of -13 would be 13. And the absolute value of -4 would be four. So, we need to add the absolute values there. So, 13 + 4 is 17. And we use the sign from the problem. So, the sign from the problem, well, -13 and -4 both negative, so our answer is negative 17. Now, using mental math, well, let's think. -13 + -4. We are starting at negative number, -13, right? And we are adding -4. So, we are decreasing in value, or going down in value by four. So, if we start at -13 and decrease in value by four, go down the number line to the left by four, we end up at -17. And lastly, number four, we have -25 + -8. So, same signs again. So, we need to add the absolute values. -25 has an absolute value of 25. And -8 has an absolute value of eight. So, add those and we get 33. And use the same sign from the problem, which they're both negative, so our answer is negative. So, negative 33. Mental math, same thing as number three, we are starting at -25 and we're adding -8. So, we are decreasing in value, going further left on the number line, and we end up at -33. So, there you have it. There are couple of different strategies that you can use in order to add integers. hope that helped. Thanks so much for watching. Until next time, peace.