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# Adding/subtracting negative numbers

Adding and subtracting negative numbers. Created by Sal Khan.

Video transcript

Welcome to the presentation
on adding and subtracting negative numbers. So let's get started. So what is a negative
number, first of all? Well, let me draw
a number line. Well it's not much of a
line but I think you'll get the picture. So we're used to the positive
numbers, so if that's 0, you have 1, you have 2, you have 3,
you have 4, and you keep going. And if I were to say what's 2
plus 2, you'd start at 2 and then you'd add 2 and
you'd get to 4. I mean most of us
it's second nature. But if you actually drew
it on a number line you'd say 2 plus 2 is 4. And if I asked you what's
2 minus 1 or let's say what's 3 minus 2? If you start at 3 and
you subtracted 2, you would end up at 1. That's 2 plus 2 is equal to 4
and 3 minus 2 is equal to 1. And this is a joke for you. Now what if I were to
say what is 1 minus 3? Huh. Well, it's the same thing. You start at 1 and we're going
to go 1 -- well, now we're going to go below 0 --
what happens below 0? Well then you start going
to the negative numbers. Negative 1, negative 2,
negative 3, and so on. So if I start at 1 right here,
so 1 minus 3, so I go 1, 2, 3, I end up at negative 2. So 1 minus 3 is equal
to negative 2. This is something that you're
probably already doing in your everyday life. If I were to tell you that boy,
it's very cold today, it's 1 degree, but tomorrow it's going
to be 3 degrees colder, you might already know intuitively,
well then we're going to be at a temperature of
negative 2 degrees. So that's all a
negative number means. And just remember when a
negative number is big, so like negative 50, that's actually
colder than negative 20, right? So a negative 50 is actually
even a smaller number than negative 20 because it's even
further to the left of negative 20. That's just something you'll
get an intuitive feel for. Sometimes when you start you
feel like oh, 50's a bigger number than 20, but it's a
negative 50 as opposed to a positive 50. So let's do some problems, and
I'm going to keep using the number line because I
think it's useful. So let's do the
problem 5 minus 12. I think you already might
have an intuition of what this equals. But let me draw a
line, 5 minus 12. So let me start with minus 10,
minus 9, minus 8 --I think I'm going to run out of space --
minus 7, minus 6, minus 5 -- I should have this pre-drawn --
minus 4, minus 3, minus 2, minus 1, 0, 1, 2, 3, 4,
I'll put 5 right here. 5 minus 12. So if we start at 5 -- let me
use a different color -- we start at 5 right here and we're
going to go to the left 12 because we're subtracting 12. So then we go 1, 2, 3, 4,
5, 6, 7, 8, 9, 10, 11, 12. Negative 7. That's pretty interesting. Because it also happens
to be that 12 minus 5 is equal to positive 7. So, I want you to think a
little bit about why that is. Why the difference between 12
and 5 is 7, and the difference between -- well, I
guess it's either way. Because in this situation we're
also saying that the difference between 5 and 12 is negative 7,
but the numbers are that far apart, but now we're starting
with the lower number. I think that last sentence just
completely confused you, but we'll keep moving forward. We just said 5 minus 12
is equal to minus 7. Let's do another one. What's negative 3
plus 5 equals what? Well, let's use the
same number line. Let's go to negative 3 plus 5. So we're going to
go to the right 5. 1, 2, 3, 4, 5. It's a 2. It equals 2. So negative 3 plus
5 is equal to 2. That's interesting because 5
minus 3 is also equal to 2. Well, it turns out that 5 minus
3 is the same thing, it's just another way of writing 5
plus negative 3 or negative 3 plus 5. A general, easy way to always
do negative numbers is it's just like regular subtraction
and addition and subtraction, but now when we subtract we
can go to the left below 0. Let's do another one. So what happens when you get
let's say 2 minus minus 3? Well, if you think about how
it should work out I think this will make sense. But it turns out that the
negative number, the negative signs actually cancel out. So this is the same thing
as 2 plus plus 3, and that just equals 5. Another way you could say is --
let's do another one -- what is negative 7 minus minus 2? Well that's the same thing
as negative 7 plus 2. And remember, so we're doing to
start at negative 7 and we're going to move two to the right. So if we move one to the right
we go to negative 6, and then we move two to the right
we get negative 5. That makes sense because
negative 7 plus 2, that's the same thing as 2 minus 7. If it's 2 degrees and it gets 7
degrees colder, it's minus 5. Let's do a bunch of these. I think the more you do the
more practice you have, and the modules explain it pretty well,
probably better than I do. So let's just do a
ton of problems. So if I said
negative 7 minus 3. Well, now we're going
to go three to the left of negative 7. We're going to get 3 less
than negative 7 so that's negative 10, right? That makes sense, because if we
had positive 7 plus 3 we're at 7 to the right of 0 and we're
going to go three more to the right of 0 and we
get positive 10. So for 7 to the left of 0 and
go three more to the left we're going to get negative 10. Let's do a bunch more. I know I'm probably confusing
you, but practice is what's going to really help us. So say 3 minus minus 3, well,
these negatives cancel out so that just equals 6. What's 3 minus 3? Well, that's easy
that's just 0. What's minus 3 minus 3? Well now we're going to get
three less than minus 3, well that's minus is 6. What's minus 3 minus minus 3? Interesting. Well, the minuses cancel out
so you get minus 3 plus 3. Well, if we start three to the
left of 0 and we move three to the right we end up at 0 again. So that makes sense, right? Let me do that again. Minus 3 minus minus 3. Anything minus itself
should equal 0, right? That's why that equals 0. And that's why it makes sense
that those two negatives cancel out and that's
the same thing as this. Let's do a bunch more. Let's do 12 minus 13. That's pretty easy. Well, 12 minus 12 is 0, so
12 minus 13 is negative 1 because we're going to
go one the left of 0. Let's do 8 minus 5. Well, this one is just a
normal problem, that's 3. What's 5 minus 8? Well, we're going to go all the
way to 0 and then 3 more to the left of zero, so it's minus 3. I could draw a
number line here. If this is 0 this is 5, and now
we're going to go to left 8, then we end up and negative 3. You could do that
for all of these. That actually might
be a good exercise. I think this will give you good
introduction and I recommend that you just do the modules
because the modules actually, especially if you do the hints,
it has a pretty nice graphic that's a lot nicer than
anything I could draw on this chalkboard. So try that out and I'm going
to try to record some more modules that hopefully won't
confuse you as badly. You could also attend the
seminar on adding and subtracting negative numbers. I hope you have fun. Bye.