Let’s review a little bit

about what we know so far about subtraction. So if I say 5 minus 3,

what does that mean? Well, there’s a couple of

ways to think about it. I could have 5– let’s

say I had to 5 berries. So 1, 2, 3, 4, 5. So I could have 5 berries, and

when I say minus 3 you’re subtracting 3 from it. I can view that as saying

I’m going to take away 3 of these berries. So if I take away that berry,

that berry, and that berry. So I took away 1, 2, 3 berries. How many berries

do I have left? Well the only berries I have

left are right here– 1, 2. So I have 2 berries

left just like that. Now the other way, the other

way that I could visualize or think about 5 minus 3,

I’ll do it over here. 5 minus 3– is to think

about what the difference between 5 and 3 is. So let me draw this. So let’s say I have 5 berries. 1, 2, 3, 4, 5. And let’s say that

you have 3 berries. Here’s a slightly

different color. You have 3 berries. So another way to think about

5 minus 3 is how many more berries do I have

than you have? And if you look right here,

well, you see, this berry is another– you have

also one berry there. We both have one berry there,

we both have one berry there. But I’ve got 1, 2 berries

that you don’t have. So once again, I have 2 more

berries than you have. Now we can also think of

this from the number line point of view. So let me draw a number

line just like that. It’s my number line. We’ve learned on the

addition videos we can keep going off forever. And actually, we could even go

to the left of 0 and go into negative numbers, which

we’ll see in future videos. But I’ll start at 0. 0, 1, 2, 3, 4, 5–

I’ll just go up to 7. So if we do 5 minus 3, if we

view 3 as being taken away from 5, 5 minus 3 means start at 5. If I did 5 plus 3 I would jump

3 spots to the right because that’s increasing the

number of things I have. But since I’m subtracting 3,

I want to decrease by 3. So I decrease by 1, 2, 3 and

I get to 2 just like that. Now if we visualize it from

this point of view, let me draw another number line. I want to show you. I mean this is, I’m taking away

3 and here I’m saying, how many more is 5 than 3? Even though they’re the exact

same answer, but there are two different ways to

think about it. Let me draw a number

line here again. Let me draw the

same number line. I have 0, 1, 2, 3, 4, 5, 6, 7. So if I were to plot where 5

is on this number line, so this is the 5 right there. I’ll put a little pink

square around it. 5 is right there. Now 3, let me do 3 in

this yellow color. 3 is right here on

the number line. So in this way of thinking

about 5 minus 3 you’re saying, what is the difference–

let me write that down. Here we’re saying, what is the

difference between 5 and 3? And to figure out the

difference you actually have to say, how much do you have to

add to 3 to get to 5? So the difference here, how

different is 5 than 3? Well you have to go up 1

and then up 2 to get to 5. So the difference between 5,

which is all the way over here, and 3, which is just that

far, is 2, just like that. That right there is 2. Let me draw that

in another box. So that’s 2 right here. I want to make this difference

between subtraction and difference– I want to make it

at least reasonably clear to you because these are two

different ways of viewing subtraction, but it ends up

being the exact same operation. You’re going to get the same

answer regardless of which way you think about it. Now, I could view– let me

do different numbers now. Let me do 7 minus 4. So I could view this as,

maybe I have a 7 foot long piece of wood. It’s 7 feet long. If I put a ruler up against

it I would have 0, 1, 2, 3, 4, 5, 6, 7. So I have a 7 foot

long piece of wood. And then I could saw

off 4 of those feet. So if I were to saw off

4 of these feet– so I saw off 1, 2, 3, 4. How much wood do I have left? So all of this stuff right

here, I’m eliminating. I’m sawing it off. I’m sawing it off of the wood. Maybe I should do that in

a darker color to show that I’m sawing it off. So all of this stuff is

going to disappear. I’m grinding it away. I’m sawing that off. So I’m just left with– after I

saw the 4 inches or feet or whatever of the wood, I’m left

with 1, 2, 3 inches of wood. So this is 3. So 7 minus 4 is equal to 3. This is viewing subtraction

as literally taking away. I sawed off the wood,

so I took away wood. Now I could think of it in a

slightly different way of thinking about it, but give

you the exact same answer. We could say 7 minus 4. So once again, I could have

the 7 inch long piece of wood like that. So if I put a ruler here

that’s 1, 2, 3, 4, 5, 6, 7. So once again, a 7 inch

long piece of wood. And now instead of taking 4

away of it I’m comparing it– so that’s a 7– I’m comparing

it to a 4 inch long piece of wood. So I have another 4 inch long

piece of wood right there. That’s my 4 inch long piece of

wood. that’s 7, this is 4. You could view 7 minus 4 as

taking 4 inches away from the long piece of wood. Or you could view seven minus 4

as the difference between the 4 inch piece of wood and the

7 inch piece of wood. So in this case, what’s

the difference? To go from the 4 inch piece of

wood to the 7 inch piece of wood I would have to grow by 3

inches, or I would have to add a 3 inch piece of wood somehow. Or the wood would somehow

have to grow by 3 inches in order to become 7 inches. So these are 2 completely

equivalent ways to view subtraction. That’s all a little bit of a

review from the last video. Now what I also want to do in

this video is start tackling slightly larger problems. But you’ll see that really,

the number line applies just equally as well as to kind

of the simpler problems that we’ve done before. Let’s do 17 minus 9. So just like everything

else, there’s two ways we could’ve done it. You know, the more slow way is

you could draw 17 objects. Let’s say I have 17 chips. 1, 2, 3, 4, 5, 6, 7, 8, 9 10,

11, 12, 13, 14, 15, 16, 17. And I’m going to take

away 9 of them. So I’m going to take away

1, 2, 3, 4, 5, 6, 7, 8, 9. How many am I left with? I’m left with 1, 2,

3, 4 5, 6, 7, 8. So 17 minus 9 is equal to 8. But that took a long time and

you could imagine, if this number was a lot bigger it

would’ve taken me forever to draw all of these circles and

then scratch out things. And it would’ve wasted

paper and time. And we have other things to do. So another way you could do it,

and maybe this would be easier for you to visualize, is

to draw the number line. You always don’t

have to start at 0. So if we draw the number line,

if we say that’s 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8,

7– you could imagine, I could keep going to the left

all the way to 0. But I start at 17. I could start at 17 and

take away 9 from it. So I go 1, 2, 3,

4, 5, 6, 7, 8, 9. And once again, we

are left at 8. Now this was, at least in my

head, a little bit cleaner and faster than this one. But in either case, you don’t

want to do this every time you have to subtract 9 from 17 or

want to find the difference between 17 and 9. And then to realize that’s 8. So this is something that

eventually you want to internalize. You’ll want to know by heart

that, oh, 17 minus 9? I know that is 8. And by the way, 17 minus 8? What’s 17 minus 8? Well, that is 9. And now why does all

of this make sense? Because 8 plus 9

is equal to 17. So 17 minus 9 is 8. Or 17 minus 8 is 9. When I say 17 minus 8, I’m

essentially saying that is equal to some number that if I

were to add to 8 will equal 17. Well, that’s 9. When I say 17 minus 9 that’s

saying, there’s some number, that if I were to add

it to 9, I’ll get 17. And that’s 8. So all of these, all of these

statements, are kind of saying the same thing. That 8 plus 9 are 17. Or the difference

between 17 and 9 is 8. Or the difference

between 17 and 8 is 9. Hopefully I’m not

confusing you. So for most of these

subtraction problems where the answer is a one-digit answer,

you should eventually have them memorized, but in your head

it’s good to be imagining this number line. Let’s do a couple

more of these. And then, once we have these

memorized or at least be able to do a number line if we

forget, I’ll show you have to do any subtraction problem,

arbitrarily for super large numbers. So let’s say we’re going

to do 13 minus 5. So once again, I’m not going

to do the whole circles or the berries this time. I’m just going to draw

the number line. Just draw the number

line like that. Let’s start at 14, 13, 12, 11,

10, 9, 8, 7, 6, 5– and you just can keep going

lower and lower. You can go to 0 or you

can even go past 0. We’ll talk about

that in the future. But we start at 13. We’re starting at 13. And we’re going to

take 5 away from it. So this is the subtraction

view of subtraction; we’re taking away. 1, 2, 3, 4, 5 and we land at 8. So 13 minus 5– let me

do this in a new color. 13 minus 5 is equal to 8. Now another way we could

have thought about that, I plotted where 13 is. I can plot where 5 is. I could say look, this is 5. 5 is right here on

my number line. What do I have to add

to 5 to get to 13? So let’s see. I would have to go 1,

2, 3, 4, 5, 6, 7, 8. I have to add 8 to

5 to get to 13. 5 plus 8 is equal to 13. So that tells me that 13

minus 5 is equal to 8. This also tells me that 13

minus 8 is equal to 5. All of these, are on some

level, telling me the exact same thing. But the difference

between 13 and 5 is 8. The difference between

13 and 8 is 5. 5 plus 8 is 13. So hopefully you have the hang

of that and if you haven’t done so already, it’ll be good

to practice all of these. Taking a teen number and then

subtracting any of the one-digit numbers from

those teen numbers. That’s in general, very,

very good practice for you.

sal.. you should do computer science videos ๐

This video is berry well explained!

THX you so Much For this Video

@vickiormindyb hahahah hvnt laughed like that in days

boooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo u dumb duby dumb weirdo sldadslfaljfdskdslfkjlsdajfajsd

you make no sense at all

How do you just grow your wood by 3 inches?

You just glue the other half 3 inch

Very simple way to learn subtraction, thanks!

what program did you use?

?

Thx khan or sal lol

Hey Andi Likes Jonah Beck

What program?

Hey uhh Khan wood can't grow 3 MORE inches it's not possible

Learning is important

love it

How much "wood" I have left?

I love your video this helps me on the test tomorrow

Thanks so much

wonderful teacher

Thanks

thanks you helped me a lot ๐

You have made me smart

๐๐๐

๐thanks

Hi

Thx for helping me solving a easy math even though i kinda confused in the first

๐