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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 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. So 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. We 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. 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, 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. But 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. 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. I encourage you to
pause this video, and try to think about
this on your own. So 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. 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. And other videos we've
already talked about this. In fact, there's 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 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 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. 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 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.