Now we're going to look at subtracting integers. First, we'll solve this example, four minus six, using counters. Now, one thing that's important to understand about subtraction is that subtracting a number is the same as adding the opposite of the number. It might sound kind of strange, but this is one of those little tricks that really, really comes in handy when we start to work with subtraction in more complicated algebra problems. So let's see how it would work for this one. Since we're adding the opposite of six, that means we're adding negative six. So this problem becomes four plus negative six. And now we're going to use that to help us set up our counters. We start with positive four, so we have four positive counters. And then since we're adding negative six, we're going to put six negative counters up. And just like we did before with our counters, each positive counter will cancel out one negative counter. So all of these cancel out and we see that we're left with two negative counters. And whatever we're left with shows us what our answer is. So our final answer is negative two. So four minus six is equal to negative two. Now we're going to look how we can solve the same problem using a number line. So we start with our positive four. And on a number line, we can think of subtraction as moving to the left. So since we're subtracting six, we're going to move to the left six units - 123456. And now we're at negative two. Wherever we end up is our answer. So we get the same answer. Four minus six is negative two. Now, the third way that we can solve these different problems with integers is by using our reasoning, thinking our way through the problem. And one way we can do that is by finding the difference between the numbers. And at this step, we're not worried about the signs. We just want to focus on the numbers themselves, not positive or negative. So just looking at the four and six, the difference between four and six is two. For the next step, we want to find the sign of the larger number. Now, there's two different ways that you can look at this to figure out which the larger the sign of the larger number. When we have subtraction, we can go back to what we saw before and remember that subtraction is the same as adding the opposite. So we can see here that the six is negative. Or if you don't want to go through writing out that step, you can look at the original problem and just look at the symbol that's to the left of the larger number. So six is larger, and the symbol that's in front of it to the left of it is subtraction. And we can just treat that subtraction sign as a negative. So whichever way you decide to look at the problem, we can still see that the six needs to be treated as if it's negative. Since the larger number is six and it is negative, our answer is also going to be negative. So our final answer, once again, it's negative two. Let's look at our next example. This one is negative three minus negative four. And I know it looks kind of strange. We have negative signs and we have a subtraction sign. It can get a little bit confusing. Just remember, whenever you see negative signs and subtraction signs and a math problem, just take your time, don't rush through it to make sure that you're handling those signs properly. So the first thing that we're going to do is handle it just like we did the other problem by reminding ourselves that subtracting a number is the same as adding the opposite of that number. So subtracting negative four is the same as adding positive four. So now we can treat this as an addition problem. We start with negative three on our number line. And since we're adding positive four, we're going to move to the right four places, 1234, and we're left at positive one. So that's our answer. Negative three minus negative four gives us positive one. Now let's look at the same problem, but without relying on the number line. So remember, subtracting a number is the same as adding the opposite of the number. So subtracting negative four is the same as adding positive four. So that's one way that you can approach it is that whenever you see subtraction followed by a negative number, just draw two little vertical lines to make them both plus signs, and then we can treat it as an addition problem. So now we have negative three plus four equals positive one. Let's look at one more example, eight minus negative seven. We see that we have the subtraction and then a negative number right after. You can automatically draw those two little vertical lines so that now we're adding the positive seven. So eight plus positive seven gives us 15. So to review, when we're subtracting integers, we can use any of the same strategies as adding integers, counters, number lines. We can reason our way through it or even use a calculator. But the big thing to remember with subtraction is that subtracting a number is the same as adding the opposite of that number. And of course, these methods work for all real numbers, not just integers, so they'll still work for fractions and decimals and any type of real number. Now you know all the different strategies for subtracting integers.