Adding & subtracting negative numbers

0:00Let's have some practice adding and subtracting negative numbers. So the first example I want to look at is 2 minus 3. So right now I'm just subtracting a positive number from another positive number, but you might already see that I'm subtracting a larger number from a smaller number.

0:16So I'm probably, or I will, definitely end up with a negative number. But let's just think about this a little bit. And I'm going to do it with a number line. So there's my number line right over there. Now this is 0, this is 1, this is 2, this is negative 1, this is negative 2.

0:34We could view this as starting at 2. So this is 2 right over here, and then we're going to subtract 3 from that 2. So we're going to move 3 to the left on the number line. So we're going to move 3 to the left, 1, 2, 3. And that gets us to negative 1. This is equal to negative 1.

0:52Now 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, let's draw our number line. And I'll 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.

1:24But we're starting at negative 2, and then we're subtracting 3 again. So once again, we're going to move three to the left of negative 2. So we go 1, 2, 3. We end up at negative 5. So this is negative 5. So notice in both situations we subtracted 3, we moved 3 to the left on the number line.

1:44It'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. I encourage you to pause this video, and try to think about this on your own.

2:10So we could draw the number line-- I could draw a straighter number 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 zero. So we're starting at negative 2, and we're going to add 3.

2:30So 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. And other videos we've already talked about this. In fact, there's a video explaining why this actually makes sense.

2:59But 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 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.

3:21Now, let's mix it up a little bit more. Let's imagine negative 2 minus negative 3. Now, this might seem really intimidating to have all of these negatives in place here, but you just have to remember subtracting a negative, like this, is going to get you a positive.

3:45So 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 start at negative 2, you start 2 to the left of 0, and then we're going to go 3 to the right, we're adding 3, 1, 2, 3.