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

Welcome to Math with Mr. J. In this video I'm going to cover how to subtract 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 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 six minus four. So just a basic subtraction problem to start here and we know the answer is two. Six minus four equals two. 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 six here and subtracting positive four. Since we are subtracting a positive our value decreases. Six is decreasing by four. That brings us to our answer of two. Now to go off of this let's take a look at number two where we have six minus negative four. Here we are starting with six again but we are subtracting a negative. That means our value increases. Six is actually going to increase by four 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 six here and increase the value by four our answer is 10. Six minus negative four 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 six minus negative four as six and then add the opposite. The opposite of negative four is positive four. So we can rewrite this as six plus four. 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. Six plus four gives us 10. So we get 10 that way as well. Let's actually go back and rewrite number one and see what happens. So six and then add the opposite. The opposite of positive four is negative four. Six plus negative four equals two. So we get two that way as well. Now looking at number one subtracting a positive or adding a negative decreases the value. Looking at number two 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 three where we have negative 11 minus 2. We are subtracting a positive so we are decreasing in value by two. 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 four 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 five 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 six 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? 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 and I also show what adding the opposite looks like for each problem. For number one negative 16. For number two negative four. For number three negative nine. For number four negative three. For number five 27. And then lastly for number six zero. So there you have it. There's how to subtract integers. I hope that helped. Thanks so much for watching. Until next time, peace.