I think you’ve probably heard

the word divide before, where someone tells you to

divide something up. Divide the money between you

and your brother or between you and your buddy. And it essentially means

to cut up something. So let me write down

the word divide. Let’s say that I

have 4 quarters. Do my best to draw

the quarters. If I have 4 quarters

just like that. That’s my rendition of George

Washington on the quarters. And let’s say there’s two of

us and we’re going to divide the quarters between us. So this is me right here. Let me try my best to draw me. So that’s me right there. Let’s see, I have

a lot of hair. And then this is

you right there. Do my best. So you’re bald. You have side burns. Maybe you have a little

bit of a beard. I want to get too

focused on the drawing. So that’s you, that’s me, and

we’re going to divide these 4 quarters between the 2 of us. So notice, we have 4 quarters

and we’re going to divide between the 2 of us. There are 2 of us. And I want to stress

the number 2. So we’re going to divide

4 quarters by 2. We’re going to divide it

between the 2 of us. And you’ve probably done

something like this. What happens? Well, each of us are

going to get 2 quarters. So let me divide it. We’re going to

divide it into 2. Essentially what I did do is

I take the 4 quarters and I divide it into 2 equal groups. And that’s what division is. We cut up this group of

quarters into 2 equal groups. So when you divide 4 quarters

into 2 groups, so this was 4 quarters right there. And you want to divide

it into 2 groups. This is group 1. Group 1 right here. And this is group 2 right here. How many numbers

are in each group? Or how many quarters

are in each group? Well, in each group I

have 1, 2 quarters. Let me use a brighter color. I have 1, 2 quarters

in each group. 1 quarter and 2 quarters

in each group. So to write this out

mathematically, I think this is something that you’ve done,

probably as long as you’ve been splitting money between you and

your siblings and your buddies. Actually, let me scroll over

a little bit, so you can see my entire picture. How do we write this

mathematically? We can write that 4

divided by– so this 4. Let me use the right colors. So this 4, which is this 4,

divided by the 2 groups, these are the 2 groups: group 1 and

this is group 2 right here. So divided into 2 groups

or into 2 collections. 4 divided by 2 is equal to–

when you divide 4 into 2 groups, each group is going

to have 2 quarters in it. It’s going to be equal to 2. And I just wanted to use this

example because I want to show you that division is something

that you’ve been using all along. And another important, I guess,

takeaway or thing to realize about this, is on some level

this is the opposite of multiplication. If I said that I had 2 groups

of 2 quarters I would multiply the 2 groups times the 2

quarters each and I would say I would then have 4 quarters. So on some level these are

saying the same thing. But just to make it a little

bit more concrete in our head, let’s do a couple

of more examples. Let’s do a bunch

of more examples. So let’s write down, what is

6 divided by– I’m trying to keep it nice and color coded. 6 divided by 3, what

is that equal to? Let’s just draw 6 objects. They can be anything. Let’s say I have

6 bell peppers. I won’t take too much

trouble to draw them. Well, that’s not what a

bell pepper looks like, but you get the idea. So 1, 2, 3, 4, 5, 6. And I’m going to

divide it by 3. And one way that we can think

about that is that means I want to divide my 6 bell peppers

into 3 equal groups of bell peppers. You could kind of think of it

if 3 people are going to share these bell peppers, how

many do each of them get? So let’s divide it

into 3 groups. So that’s our 6 bell peppers. I’m going to divide

it into 3 groups. So the best way to divide it

into 3 groups is I can have 1 group right there, 2 groups, or

the second group right there, and then, the third group. And then each group will have

exactly how many bell peppers? They’ll have 1, 2. 1, 2. 1, 2 bell peppers. So 6 divided by 3

is equal to 2. So the best way or one way to

think about it is that you divided the 6 into 3 groups. Now you could view that a

slightly different way, although it’s not completely

different, but it’s a good way to think about it. You could also think of

it as 6 divided by 3. And once again, let’s

say I have raspberries now– easier to draw. 1, 2, 3, 4, 5, 6. And here, instead of

dividing it into 3 groups like we did here. This was 1 group, 2

group, 3 groups. Instead of dividing into 3

groups, what I want to do is say well, if I’m dividing

6 divided by 3, I want to divide it into groups of 3. Not into 3 groups. I want to divide it

into groups of 3. So how many groups of

3 am I going to have? Well, let me draw

some groups of 3. So that is one group of 3. And that is two groups of 3. So if I take 6 things and I

divide them into groups of 3, I will end up with 1, 2 groups. So that’s another way to

think about division. And this is an

interesting thing. When you think about these two

relations, you’ll see a relationship between 6 divided

by 3 and 6 divided by 3. Let me do that right here. What is 6 divided by 2 when

you think of it in this context right here? 6 divided by 2, when you

do it like that– let me draw 1, 2, 3, 4, 5, 6. When we think about 6 divided

by 2 in terms of dividing it into 2 groups, what we can end

up is we could have 1 group like this and then 1 group

like this, and each group will have 3 elements. It’ll have 3 things in it. So 6 divided by 2 is 3. Or you could think of

it the other way. You could say that 6 divided

by 2 is– you’re taking 6 objects: 1, 2, 3, 4, 5, 6. And your dividing it into

groups of 2 where each group has 2 elements. And that on some level is

an easier thing to do. If each group has 2 elements,

well, that’s the 1 right there. They don’t even have

to be nicely ordered. This could be one group right

there and that could be the other group right there. I don’t have to draw

them all stacked up. These are just groups of 2. But how many groups do I have? I have 1, 2, 3. I have 3 groups. But notice something, it’s no

coincidence that 6 divided by 3 is 2 and 6 divided by 2 is 3. Let me write that down. We get 6 divided by 3 is

equal to 2 and 6 divided by 2 is equal to 3. And the reason why you see this

relation where you can kind of swap this 2 and this 3 is

because 2 times 3 is equal to 6. Let’s say I have 2 groups of 3. Let me draw 2 groups of 3. So that’s 1 group of 3 and then

here’s another group of 3. So 2 groups of 3 is equal to 6. 2 times 3 is equal to 6. Or you could think of

it the other way if I have 3 groups of 2. So that’s 1 group

of 2 right there. I have another group

of 2 right there. And then I have a 3

group of 2 right there. What is that equal to? 3 groups of 2– 3 times 2. That’s also equal to 6. So 2 times 3 is equal to 6. 3 times 2 is equal to 6. We saw this in the

multiplication video that the order doesn’t matter. But that’s the reason why if

you want to divide it, if you want to go the other way– if

you have 6 things and you want to divide it into

groups of 2, you get 3. If you have 6 and you want

to divide into groups of 3, you get 2. Let’s do a couple

of more problems. I think it’ll really

make sense about what division is all about. Let’s do an interesting one. Let’s do 9 divided by 4. So if we think about 9 divided

by 4, let me draw 9 objects. 1, 2, 3, 4, 5, 6, 7, 8, 9. Now when you divide by 4, for

this problem, I’m thinking about dividing it

into groups of 4. So if I want to divide it

into groups of 4, let me try doing that. So here is one group of 4. I just picked any of

them right like that. That’s one group of 4. Then here’s another

group of 4 right there. And then I have this

left over thing. Maybe we could call it a

remainder, where I can’t put this one into a group of 4. When I’m dividing by 4

I can only cut up the 9 into groups of 4. So the answer here, and this is

a new concept for you maybe, 9 divided by 4 is going

to be 2 groups. I have one group here and

another group here, and then I have a remainder of 1. I have 1 left over that I

wasn’t able to do with. Remainder– that

says remainder 1. 9 divided by 4 is

2 remainder 1. If I asked you what 12 divided

by 4 is, so let me do 12. 1, 2, 3, 4, 5, 6, 7,

8, 9, 10, 11, 12. So let me write that down. 12 divided by 4. So I want to divide these

12 objects– maybe they’re apples or plums. And divide them

into groups of 4. So let me see if I can do that. So this is one group

of 4 just like that. This is another group

of 4 just like that. And this is pretty

straightforward. And then I have a third

group of 4 just like that. And there’s nothing left

over like I had before. I can exactly divide 12

objects into 3 groups of 4. 1, 2, 3 groups of 4. So 12 divided by

4 is equal to 3. And we can do the exercise that

we saw on the previous video. What is 12 divided by 3? Let me do a new color. 12 divided by 3. Now based on what we’ve learn

so far we say, that should just be 4 because 3 times 4 is 12. But let’s prove

it to ourselves. So 1, 2, 3, 4, 5, 6,

7, 8, 9, 20, 11, 12. Let’s divide it

into groups of 3. And I’m going to make them a

little strange looking just so you see that you don’t

always have to do it into nice, clean columns. So that’s a group

of 3 right there. 12 divided by 3. Let’s see, here is another

group of 3 just like that. And then, maybe I’ll take

this group of 3 like that. And I’ll take this group of 3. There was obviously a much

easier way of dividing it up then doing these weird l-shaped

things, but I want to show you it doesn’t matter. You’re just dividing

it into groups of 3. And how many groups do we have? We have one group. Then we have our second

group right here. And then we have our

third group right there. And then we have– let me

do it in a new color. And then we have our

fourth group right there. So we have exactly 4 groups. And when I say there was an

easier way to divide it, the easier way was obviously, maybe

not obviously– if I want to divide these into groups of 3 I

could have just done 1, 2, 3, 4 groups of 3. Either of these I’m

dividing the 12 objects into packets of 3. You can imagine them that way. Let’s do another one that

maybe has a remainder. Let’s see. What is 14 divided by 5? So let’s draw 14 objects. 1, 2, 3, 4, 5, 6, 7, 8,

9, 10, 11, 12, 13 14. 14 objects. And I’m going to divide

it into groups of 5. Well, the easiest thing is

there’s one group right there, two groups right there. But then this last one, I

only have 4 left, so I can’t make another group of 5. So the answer here is I can

make 2 groups of 5 and I’m going to have a remainder–

r for remainder– of 4. 2 remainder 4. Now, once you get enough

practice, you’re not always going to be wanting to draw

these circles and dividing them up like that. Although that would

not be incorrect. So another way to think about

this type of problem is to say, well, 14 divided by 5,

how do I figure that out? Actually, another way

of writing this and no harm in showing you. I could say 14 divided by 5 is

the same thing as 15 divided by– this sign right–

divided by 5. And what you do is you

say, well, let’s see. How many times does

5 go into 14? Well, let’s see. 5 times and you kind

of do multiplication tables in your head. 5 times 1 is equal to 5. 5 times 2 is equal to 10. So that’s still less than 14,

so 5 goes at least two times. 5 times 3 is equal to 15. Well that’s bigger than 14,

so I have to go back here. So 5 only goes two times. So it goes 2 times. 2 times 5 is 10. And then you subtract. You say 14 minus 10 is 4. And that’s the same

remainder as right here. Well, I could divide 5 into

14 exactly two times, which would get us 2 groups of 5. Which is essentially just 10. And we still have

the 4 left over. Let me do a couple of more just

to really make sure you get this stuff really, really,

really, really well. Let me write it in

that notation. Let’s say I do 8 divided by 2. And I could also write

this as 8– so I want to know what that is. That’s a question mark. I could also write this

as 8 divided by 2. And the way I do either of

these, I’ll draw the circles in the second, but the way I do it

without drawing the circles, I say, well, 2 times

1 is equal to 2. So that definitely goes into 8,

but maybe I can think of a larger number that goes into–

that when I multiply it by 2 still goes into 8. 2 times 2 is equal to 4. That’s still less than 8. So 2 times 3 is equal to 6. Still less than 8. 2 times– oh, something

weird happened to my pen. 2 times 4 is exactly

equal to 8. So 2 goes into 8 four times. So I could say 2 goes

into 8 four times. Or 8 divided by 2

is equal to 4. We can even draw our circles. 1, 2, 3, 4, 5, 6, 7, 8. I drew them messy on purpose. Let’s divide them

into groups of 2. I have one group of 2, two

groups of 2, three groups of 2, four groups of 2. So if I have 8 objects, divide

them into groups of 2, you have four groups. So 8 divided by 2 is 4. Hopefully you found

that helpful.

Thanks I got an a on my math test you rock 😊☺️😊☺️😊☺️😊☺️😊☺️

Your a good drawer!!:)

Khan art class!

LOL!!

Sick drawing

What is the name of the software used for drawing?

Thank you Khan Academy, you are so very helpful. I online school my son. He is just learning division. We both have add, I hated division, you have made it so easy.

He said twotwo

I learned division a long time ago but I've always had trouble with it and this really helped me catch on 🙂 all you're videos are very explanatory (unlike most school books) and I love it 🙂

D;< this sucks

your smart and confusing

What software did use to write?

Love this video!

Lol

It's really awesome, I've learned lot from this video and I'm 16 years old.

Where do I get these speakers?

Thanks again for the video! For another exciting way to learn basic math, check out the exciting new card game, Combination!

I learn d it it was good and BY

☺

suck a bich ass lover

Blah blah why I'm watching this??

Tell Ian that crainer is in his crundee craft base in minecraft

ur awsome sal!

My teachers name is Mrs. Kahn

U r so good!

y do we have to be bold hade it

my math teacher told me about you I love your video thank you for your helping us

sal is the first 3 letters in my name :O ps i look amazing XD ur vids are helpful keep it up 😀

my mom says that this will help me better on my time test because i'm only in 3rd grade 😀

thanks a lot I am in class 2 and it helped me a lot

My kids are fan of Mr Sal. A great service free of charge for people who love maths! All this free knowledge coming from someone who grew up in a capitalistic world.

It's not a computer it's a pen with a pad linked to a computer

Nice

I'm in third grade, and this really helps me with my math. I didn't know division before so thanks for making this!

I suck so hard at divide 😳

wow Sal, you're good at drawing with computer, it's Super hard 😎

Cool

IM BALD?!?!?!?!?!? IMMA GIRL LOL

i hate division

I am not a boy

I Learned a lot of that thank you 😀

lololo i

SAL your drawing is amazing please tell me where I can learn your tutorials of drawing

I hate division but school is starting again and I need to learn everything all over again! 😂😭 but I'll try ma best lol

great lol

divi is so hard i dontt like it

this is very useful for my grankids

well I am interested 🤔

Why do you do long division instead of short division?

love ur drawing

Your vids are really helpful but I hate division

my son learned a lot

I do not get it

Yes, your on a tablet but at the same time that doesn't mean that you can draw wonderfully like that, in fact, he might have been using whatever this app is on his tablet and been using it for, what? Maybe 5 or 6 years, so he has been doing a lot of practice, although that hardly youtubers use computers. I used to also ask a question to myself how easily he can do numbers and draw so fast in 12 seconds, it made me want to try, I realized that he uses a tablet, with one of those things like a stick, I forgot what they're called. But I just want to say one thing, if you really want to do the same thing but on computer, go to Siri, type in "Paint", and it will give you the app instantly, just press on it, and boom it is set for you, you don't even need to download it.

thank you a lot..

i dont get it?!!!

Your smaller than me for some reason and your thirty years older.

Tanxy Rogue Passing Thru'

Sal what drawing tool are you using?

I am very good at division and I got better

Great video on division. We found it easier to use Beestar to practice these math problems. Also the kids did a lot better after we used Beestar and went on to GT programs.

i can leave yall bc yall nedd help

you rock dude

Nice

I love your video

Thanks I got a 100 on my test

Click it!

I'm a girl but I really like the video. I am 3rd grade I need help in division .But thanks you for the help.

thank you so much i might get an a+ on my math test in 3rd grade

Thanks sir

Surprise men

My sister is so good at drawing when she is drawing it looks like it’s real

Thank you

I LOVE MATHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH THANK YOU KHAN I HATEID MATH BUT NOW I LOVE IT THANK YOU SOO MUCH C; I LOVE MATH NOW

I love your videos it so helpful khan academy

Can you make more math videos

hi I love this video thanks

Since I am not fan of division I am a fan of addictions subtractions and multiplications. But i am still learning divisions

THERE IS GIRLS TO SAL DUHHHH

you thech such goooooooooooooooooooood things

Very helpful videos

I’m ten and I’m not bald and I don’t have a beard.

I love your videos so MUCH

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I love watching this video!!!!!!!!!!!!!!!!!!!

thank u for your help on my math quiz i got a B

i look dumb

Thank you for helping me on my math placement test on Saturday

Hey I’m Sunni I love you’re math solutions

I am in 2 grade but I do 4th and 5th grade math because of you thanks!

Also I got 4s on mathematics

Very much helpful

im not bald 🙁

Very helpful got a b

I'm a girl I'm not bald

I didn't want to leave school be a use I needed help I'm in 5th grade this is to easy

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THANKS SO Much for your interest sweet math videos and it's helping me a hole lot thanks so much Khan aedmy🤗🤗🤗🤗🤗🤗🤗🤗🤗🤗🤗🤗🤗

Hi you may have seen the last comment that i send it was mean but I shan’t to say sorry to be mean to you I was suppose to be nice to every one even boys and girls I’m sooooooooo sorry for being mean to you and I love you r videos to don’t think you video is bad every one likes it even my mom likes the video that you make for every body😉 good job of making the videos thank you sooooooooooo much I love you😉😉😉😉😉

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😀