Integers | Adding, Subtracting, Multiplying & Dividing | Lesson + Practice

Welcome to Math with Mr. J. In this video, I'm going to cover how to add, subtract, multiply, and divide integers. We'll start with addition, then we'll move to subtraction, then multiplication, and then division. Once we go through examples together, I'll give you some practice problems that you can try on your own. Let's start off with addition. 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, 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 8 and adding positive 5. Since we are adding a positive, our value increases. So 8 is increasing by 5. That brings us to our answer of 13. So for number one, 8 plus 5 equals 13. Now, to go off of that, let's take a look at number two. We have 8 plus negative 5. Here, we are starting with 8 again, but we are adding a negative 5. That means our value decreases. 8 is decreasing by 5. That means our answer is 3 here. 8 plus negative 5 equals 3. 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 9 plus negative 3. We are starting at negative 9 and adding negative 3. So we are decreasing in value here. So if we start at negative 9 and we are decreasing in value by 3, that brings us to negative 12. And that's our answer. Think of a number line, and we're starting at negative 9. And if we decrease in value, that means we are moving left on the number line. And since we are adding negative 3, 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 6. So we are starting with negative 14 here. And since we are adding a positive 6, this is increasing in value. Negative 14 is increasing by 6. Our answer here is negative 8. 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 8. Moving on to number five, we have 2 plus negative 7. So we are starting at 2 and we are decreasing in value by 7. Now for this one, we're going to pass 0 and move into the negatives. We can think about it this way. If we start at 2 and decrease by 2, that brings us to 0. And then we still need to decrease by 5 more. That brings us to negative 5. 2 plus negative 7 equals negative 5. For problems like this, where we cross 0, it can be helpful to use 0 as a reference point. Lastly, let's move on to number six, where we have negative 4 plus 10. We're starting at negative 4 and we're adding 10. That means our value increases here. Negative 4 is increasing by 10. Now this is another problem where we cross 0. For this one, we start at negative 4 and we will pass 0 and move into the positives. Let's think through it this way. We start at negative 4 and increase by 4. That brings us to 0. We still need to increase by 6 more though. And that brings us to 6. Negative 4 plus 10 equals 6. So there you have it. There's how to add integers. Let's move on to subtraction. Here's our subtracting integer section. Now when we subtract integers, we need to recognize when we are decreasing in value or increasing in value. And this depends on what we are subtracting. So keep in mind, if we subtract a positive, we decrease in value. And if we subtract a negative, we actually increase in value. Let's jump into our examples, starting with number one, where we have 6 minus 4. So just a basic subtraction problem to start here. And we know the answer is 2. 6 minus 4 equals 2. But let's think through this. That way we can apply this thinking to all of the other problems as well. So we are starting with 6 here and subtracting positive 4. Since we are subtracting a positive, our value decreases. 6 is decreasing by 4. That brings us to our answer of 2. Now to go off of this, let's take a look at number 2, where we have 6 minus negative 4. Here we are starting with 6 again, but we are subtracting a negative. That means our value increases. 6 is actually going to increase by 4, which may sound a little confusing for a subtraction problem. I like to relate this to money. For this example, let's think of the negative as a debt or expense. Think of subtracting a negative as taking away that debt or expense and getting that money back. That's a good thing. So it increases the value of the number we started with. So if we start with 6 here and increase the value by 4, our answer is 10. 6 minus negative 4 equals 10. Now before moving on, we have another important note here. When we subtract integers, we can always rewrite the problem as adding the opposite. And this can make problems simpler to think and work through. So this is a good strategy. For example, we can rewrite 6 minus negative 4 as 6 and then add the opposite. The opposite of negative 4 is positive 4. So we can rewrite this as 6 plus 4. Addition is the opposite of subtraction. And then we take the opposite of the number we are subtracting. So this gives us an equivalent problem. We get the same answer. 6 plus 4 gives us 10. So we get 10 that way as well. Let's actually go back and rewrite number 1 and see what happens. So 6 and then add the opposite. The opposite of positive 4 is negative 4. 6 plus negative 4 equals 2. So we get 2 that way as well. Now looking at number 1, subtracting a positive or adding a negative decreases the value. Looking at number 2, subtracting a negative or adding a positive increases the value. So something to keep in mind when it comes to adding and subtracting integers. Let's move on to number 3 where we have negative 11 minus 2. We are subtracting a positive. So we are decreasing in value by 2. That gives us an answer of negative 13. Negative 11 minus 2 equals negative 13. Now we can also work through this by adding the opposite. So we can rewrite this as negative 11 plus and then the opposite of positive 2 is negative 2. Negative 11 plus negative 2 is negative 13. Moving on to number 4, we have 2 minus 10. So 2 is decreasing in value by 10. We are subtracting a positive here. Now for this problem, we are starting with positive 2. But since we are decreasing by 10, we're going to pass 0 and move into the negatives. We can use 0 as a reference point here to help us. If we start at 2 and decrease by 2, that brings us to 0. We still need to decrease by 8 more and that brings us to negative 8. 2 minus 10 equals negative 8. Let's add the opposite as well. So 2 plus and then the opposite of positive 10 is negative 10. So 2 plus negative 10 and adding a negative decreases our value. So we're still starting at 2 and decreasing by 10. So 2 plus negative 10 gives us that correct answer of negative 8. Moving on to number 5, we have negative 7 minus 9. So we are starting at negative 7 and since we are subtracting 9, a positive 9, we are decreasing in value by 9. That gives us an answer of negative 16. So negative 7 minus 9 equals negative 16. Let's also add the opposite. Negative 7 plus negative 9. That gives us that correct answer of negative 16 as well. Lastly, for number 6, we have negative 5 minus negative 20. So we are subtracting a negative, which remember actually means the value increases. Now we are starting at negative 5, but since we are increasing in value by 20, we're going to pass 0 and move into the positives. So let's think here and use 0 as a reference point. Negative 5 increased by 5 gets us to 0. And then we need to increase by 15 more, which brings us to 15. Negative 5 minus negative 20 equals 15. Now let's add the opposite. And adding the opposite here can make this one a little easier. So we have negative 5 plus and then the opposite of negative 20 is positive 20. So we have negative 5 plus 20. That gives us that correct answer of 15. So there you have it. There's how to subtract integers. We can rewrite the problem and add the opposite. Or we can think about whether the value is going to decrease or increase based on the problem. So are we subtracting a positive and the value decreases? Or are we subtracting a negative and the value increases? Let's move on to multiplication and division. Here's our section on multiplying and dividing integers. And we have them in the same section here because they are very similar. Now when it comes to multiplying and dividing integers, we need to keep two things in mind. If the problem has two integers with the same signs, our answer will be positive. If a problem has two integers with different signs, our answer will be negative. Let's jump into our examples starting with number one where we have 8 times negative 2. Well notice we have different signs here. A positive times a negative. That means our product, our answer, will be negative here. So all we need to do is think 8 times 2 is 16. And again, since we have different signs, this is negative 16. So 8 times negative 2 equals negative 16. Moving on to number two, we have negative 5 times negative 5. We have the same signs here. A negative times a negative. That means our product will be positive. So all we need to do is think 5 times 5 is 25. And since we have the same signs, this is a positive 25. Negative 5 times negative 5 equals 25. So keep in mind, a negative times a negative equals a positive. Moving on to number three, we have negative 10 times 7. So we have different signs. That means our product is going to be negative. So we can think 10 times 7 gives us 70. And again, since we have different signs, this is negative. So negative 10 times 7 equals negative 70. So those were a few multiplication examples. Let's move on to division. Taking a look at number four, we have negative 12 divided by 4. And we're going to do the same thing here that we were doing with multiplication, except we are dividing. So looking at this problem, we have different signs, a negative and a positive. That means our quotient, our answer, will be negative. So all we need to do here is think 12 divided by 4 is 3. And again, since we have different signs, this is negative. So our answer here, negative 3. Negative 12 divided by 4 equals negative 3. Moving on to number five, we have negative 48 divided by negative 6. We have the same signs, a negative divided by a negative. So this is going to equal a positive. So let's think, 48 divided by 6 gives us 8. This is a positive 8. Negative 48 divided by negative 6 equals 8. So keep in mind, a negative divided by a negative equals a positive. Lastly, moving on to number six, we have 33 divided by negative 3. So we have different signs here, a positive divided by a negative. So this is going to equal a negative. 33 divided by 3 is 11. So this is negative 11. 33 divided by negative 3 equals negative 11. So there you have it. There's how to add, subtract, multiply, and divide integers. 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 five 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 five minutes. Let's go over the answers. So here are our answers. For number one, negative 8. For number two, negative 12. For number three, negative 1. For number four, 25. For number five, negative 7. For number six, 8. For number seven, negative 56. For number eight, negative 5. For number nine, 27. And then lastly, for number 10, negative 84. So there you have it. There's how to add, subtract, multiply, and divide integers. I hope that helped. Thanks so much for watching. Until next time, peace.