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## Arithmetic (all content)

### Course: Arithmetic (all content) > Unit 2

Lesson 1: Basic addition and subtraction# Basic addition

Introduction to addition. Learn multiple visual ways to represent addition. Created by Sal Khan.

## Want to join the conversation?

- Why did you make your number line from left to right? Isn't it more intuitive to make a number line vertically? As you add numbers you move up the page, as you subtract numbers you move down the page. (Like an elevator, or a lego tower. as you add lego's onto your tower, the tower gets taller)(367 votes)
- Awesome question. You could use a vertical number line and when you get further in math you will use a combination of two or more number lines. The most logical explanation seems to be that the horizontal number line makes sense because that is how you read in some languages (such as English which is Sal's language ;-) ). Would be interesting to find out if people who use languages which are vertical use vertical number lines instead ...(251 votes)

- Is addition used when we grow up?(12 votes)
- Yes, for example, if you want to know how much money you have, you need to add it all to get the total(12 votes)

- Where did the word "addition" come from?(8 votes)
- "Addition" and "add" are English words derived from the Latin verb *"addere",* which is, in turn, a
**compound**of*"ad (to)" and "dare (to give)",*from the**Proto-Indo-European**root**deh₃- "to give"; thus to add is to give to. Using the gerundive suffix "-nd" results in "addend", "thing to be added". Likewise from**)", one gets*"augere*(to increase*"augend"*, "**thing to be increased**".(10 votes)

- And Basic Addition is?(6 votes)
- Basic addition is "easy addition", with questions like 3+2=
*__ or 1+2=__*(7 votes)

- So If I add 1 with 1 I get 2?(5 votes)
- Yep, you're right! 1 + 1 = 2.

Just picture a number line. If you start at 1 and go 1 hop to the right (you don't want to go to the left because that would be subtracting), you land on 2!(3 votes)

- Ok, i will admit ive done wrong things in life (math wise) now with this website im doing better! LOL * i feel dumb but u guys should stay on this website! *it helps, trust me im a 7th. grader and i should know this stuff by now but. i don't but guess what? NOW I DO BCAUSE OF THIS WEBSITE!!! so i would not leave if i were you :) thanks if you read this post! :D cya'll later!(17 votes)
- Everybody starts somewhere, and some people start later than others. As long as you understand the concepts at the end everybody comes out equal, so I'd say good on you for learning it finally!(4 votes)

- How is arithmetic used in the real world?(3 votes)
- Everywhere, how do you think the internet works? Hamsters? No, arithmetic.(7 votes)

- When did people start using numbers?(4 votes)
- Roman numerals are coming from 500 BC, which is 2500 years ago

And usual numbers (arabic numerals) are coming from no later than V century which is minimum 1500 years ago(3 votes)

- Addition is moving numbers up a number line.(4 votes)
**Absolutely no**

If you add a negative number you would move down the line, if you add a complex number, you'll end up on 2 number lines, one for real numbers and the other for the imaginary, if you add n/0 or any other undefined value, you'll end up not having an exact answer at all.(2 votes)

- how do I finish Dividing(2 votes)
- You don't ever finish dividing. It keeps on going. Forever. It will always be there. In the back of your mind. You will never forget it. It will never forget you.

It

is

always

there.(3 votes)

## Video transcript

Welcome to the presentation
on basic addition. I know what you're thinking,
Sal, addition doesn't seem so basic to me. Well, I apologize. Hopefully by the end of this
presentation or in a couple of weeks it will seem basic. So let's get started
with, I guess we could say, some problems. Well let's say I start
with an old classic. 1 plus 1. And I think you already know
how to do this, but I'll kind of show you a way of doing this
in case you don't have this memorized or you haven't
already mastered this. You say, well, if I have 1,
let's call that an avocado. If I have 1 avocado and
then you were to give me another avocado, how many
avocados do I now have? Well, let's see. I have 1, 2 avocados. So 1 plus 1 is equal to 2. Now, I know what
you're thinking. That was too easy, so let
me give you something a little bit more difficult. I like the avocados. I might stick with that theme. What is 3 plus 4? This is, I think, a more
difficult problem. Well, let's stick
with the avocados. And in case you don't know what
an avocado is, it's actually a very delicious fruit. It's actually the fattiest
of all the fruits. You probably didn't even
think it was a fruit, even if you ate one. Let's say I have 3
avocados-- 1, 2, 3. And let's say you were to
give me 4 more avocados. So let me put this 4 in yellow
so you know that these are the ones you're giving me. 1, 2, 3, 4. So how many total
avocados do I have now? That's 1, 2, 3, 4,
5, 6, 7 avocados. So 3 plus 4 is equal to 7. And now I'm going to introduce
you to another way of thinking about this. It's called the number line. And actually, I think this is
how I do it in my head when I forget-- if I don't
have it memorized. So number line, I just write
all the numbers in order. And I go high enough just
so all the numbers I'm using are kind of in it. So you know the first number
is 0, which is nothing. Maybe you don't know,
but now you know. And then you go to 1, 2,
3, 4, 5, 6, 7, 8, 9, 10. Keeps going-- 11. So we're saying 3 plus 4. So let's start at 3. So I have 3 here and we're
going to add 4 to that 3. So all we do is we go up the
number line, or we go to the right on the number
line, 4 more. So we go 1, 2, 3, 4. Notice all we did is we just
increased it by one, by two, by three, by four. And then we ended up at 7. And that was our answer. We can do a couple
of different ones. What if I asked you
what 8 plus 1 is? Well, you might
already know it. You know, plus 1 is
just the next number. But if we look at the
number line you start at 8 and you add 1. 8 plus 1 is equal to 9. Let's do some harder problems. And just so you know, if you're
a little daunted by this initially, you can always
draw the circles. You can always do
the number line. And eventually, over time, the
more practice you do-- you'll hopefully memorize these and
you'll do these problems in like half a second. I promise you. You just got to
keep practicing. I want to draw the number line
again, actually, I have a line tool, so I should give you
all those ugly looking lines that I've been giving you. Look at that. That's amazing. Let me see. Look at that. That's a nice looking line. I'm going to feel bad
to erase it later on. So let me draw a number line. 0, 1, 2, 3, 4, 5, 6, 7, 8,
9, 10, 11, 12, 13, 14, 15. So let's do a hard problem. I'm going to do it in
different colors now. 5 plus 6. So if you want, you could
pause the video and try this. You might already
know the answer. And the reason why I say this
is a hard problem is because the answer has more numbers
than figures, so you can't necessarily do it
on your fingers. So let's get started
with this problem. Actually, my phone is ringing,
but I'm going to ignore the phone because you're
more important. OK, let's start at the 5. So we start at the 5 and
we're going to add 6 to it. So we go 1, 2, 3, 4, 5, 6. And we're at 11. So 5 plus 6 is equal to 11. Now I'm going to ask you a
question, what is 6 plus 5? Well, we're now
going to see that. Can you switch the two numbers
and get the same answer? Well, let's try that. And I'm going to try it in
a different color so we don't get all confused. So let's start at 6. Ignore the yellow for
now and add 5 to it. 1, 2, 3, 4, 5. We get to the same place. And I think you might want
to try this on a bunch of problems and you'll see
it always works out. That it doesn't matter what
order-- 5 plus 6 is the same thing as 6 plus 5. And that makes sense. If I have 5 avocados
and you give me 6, I'm going to have 11. If I have 6 avocados and
you gave me 5, I'm going to have 11 either way. Since this number line is so
nice, I want to do a few more problems using it. Although as I use it I'm sure
I'll just continue to confuse you because I'll write
so much on top of it. But let's see. I'll use white now. What is 8 plus 7? Well, if you can still read
this, 8 is right here. We're going to add 7 to it. 1, 2, 3, 4, 5, 6, 7. We go to 15. 8 plus 7 is 15. So hopefully that gives
you a sense of how to do these types of problems. I guess this and you're going
to learn multiplication in a little bit, but these types of
problems are-- when you're getting started off in
mathematics, these kind of require the most practice and
to some degree, you have to start memorizing them. But over time, when you look
back, I want you to remember how you feel while you're
watching this video right now. And then I want you to watch
this video in like 3 years and remember how you felt when
you're watching it now. And you're going
to be, oh my God. This was so easy because you're
going to learn it so fast. So anyway, I think
you have an idea. If you don't know the answer to
any of the additional problems that we give in the exercises
you can press the hints and it'll draw circles and you can
just count up the circles. Or if you want to do it
on your own so you get the problem right, you
could draw the circles. Or you could draw a number
line like we did in this presentation. I think you might be ready to
tackle the addition problems. Have fun.