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# Adding & subtracting negative numbers

Learn how to add and subtract negative numbers. The problems solved in this video are 2 - 3 = -1 and -2 - 3 = -5 and -2 + 3 = 1 and 2 - (-3) = 5 and -2 - (-3). Created by Sal Khan.

Video transcript

Let's have some practice adding and subtracting negative numbers. So the first example that I want to look at is 2 minus 3. So right now I am just subtracting a positive number from another positive number, but you might already see that I am subtracting a larger number from a smaller number, so I probably or definitely will end up with a negative number. Let's just think about this a little bit. And I am going to do it with the number line. So there's my number line right over there. Now this is 0, this is 1, this is 2, This is negative1, this is negative 2. We could view this as starting at 2, so this is 2 right over here, and were going to subtract 3 from that 2, so we are going to move 3 to the left on the number line. So were going to move 3 to the left. 1, 2, 3, and that gets us to negative 1. This is equal to negative 1. Now let's mix it up a little bit more. Let's imagine what would happen if we had negative 2 minus 3. So this was positive 2 minus 3, now let's think about negative 2 minus 3. So once again, lets draw our number line and I will put 0 over here. So this is 0, this is 1, this is negative 1, negative 2, negative 3, negative 4, negative 5, negative 6 and I could keep going. but were starting at negative 2, and then were subtracting 3 again, so once again we are going to move 3 to the left. We go 1, 2, 3. We end up at negative 5. This is negative 5. Notice, in both situations we subtracted 3, we moved 3 to the left on the nubmer line, it's just here we started 2 to the right of 0, here we started 2 to the left of 0. This is negative 2. Let's do another example with these same numbers. Let's imagine negative 2 plus 3. And I encourage you to pause this video and try to think about this on your own. We draw the number line again. I could draw a straighter line than that. So draw the number line again and let's say that this is negative 2, negative 1, 0, 1 and 2 again. We're starting at negative 2, we're starting 2 to the left of 0. So we're starting at negative 2 and we're going to add 3, so we're going to go 3 to the right now. 1, 2, 3. And we end up at positive 1. Now let's think about 2, so positive 2, and we're going to subtract a negative 3. In other video we've already talked about this. In fact, here is a video explaining why this actually makes sense. But when you subtract a negative, this is the same thing as adding the positive. So 2 minus negative 3 is the exact same thing as 2 plus positive 3. These two statements are equivalent, and this just boils down to, this right over here is just going to be 5. Now, let's mix it up a little bit more. Let's imagine negative 2, let's imagine negative 2 minus negative 3. And this might seem really intimidating to have all these negatives in place here. You just have to remember: subtracting a negative like this is going to get you a positive. So this is the exact same thing as negative 2 plus 3. And negative 2 plus 3, we've already seen it right over here, You started at negtive 2, you started 2 to the left of 0, and then we're going to go 3 to the right, we're adding 3. 1, 2, 3.