# Dividing numbers: long division with remainders | Arithmetic | Khan Academy

It never hurts to get a lot of

practice, so in this video I’m just going to do a bunch more

of essentially, what we call long division problems. And so if you have

4 goes into 2,292. And I don’t know exactly why

they call it long division, and we saw this in the

last video a little bit. I didn’t call it long division

then, but I think the reason why is it takes you a long

time or it takes a long piece of your paper. As you go along, you kind of

have this thing, this long tail that develops on the problem. So all of those are, at least,

reasons in my head why it’s called long division. But we saw in the last video

there’s a way to tackle any division problem while just

knowing your multiplication tables up to maybe 10

times 10 or 12 times 12. But just as a bit of review,

this is the same thing as 2,292 divided by 4. And it’s actually the same

thing, and you probably haven’t seen this notation before,

as 2,292 divided by 4. This, this, and this are

all equivalent statements on some level. And you could say, hey Sal,

that looks like a fraction in case you have seen

fractions already. And that is exactly what it is. It is a fraction. But anyway, I’ll just focus on

this format and in future videos we’ll think about other

ways to represent division. So let’s do this problem. So 4 goes into 2

how many times? It goes into 2 no times,

so let’s move on to– let me just switch colors. So let’s move on to the 22. 4 goes into 22 how many times? Let’s see. 4 times 5 is equal to 20. 4 times 6 is equal to 24. So 6 is too much. So 4 goes into 22 five times. 5 times 4 is 20. There’s going to be a

little bit of a leftover. And then we subtract

22 minus 20. Well that’s just 2. And then you bring down this 9. And you saw in the last video

exactly what this means. When you wrote this 5 up

here– notice we wrote in the 100’s place. So this is really a 500. But in this video I’m just

going to focus more on the process, and you can think more

about what it actually means in terms of where I’m

writing the numbers. But I think the process

is going to be crystal clear hopefully, by

the end of this video. So we brought down the 9. 4 goes into 29 how many times? It goes into at

least six times. What’s 4 times 7? 4 times 7 is 28. So it goes into it at

least seven times. What’s 4 times 8? 4 times 8 is 32, so it can’t go

into it eight times so it’s going to go into it seven. 4 goes into 29

nine seven times. 7 times 4 is 28. 29 minus 28 to get our

remainder for this step in the problem is 1. And now we’re going to

bring down this 2. We’re going to bring it

down and you get a 12. 4 goes into 12? That’s easy. 4 times 3 is 12. 4 goes into 12 three times. 3 times 4 is 12. 12 minus 12 is 0. We have no remainder. So 4 goes into 2,292

exactly 573 times. So this 2,292 divided by 4

we can say is equal to 573. Or we could say that this thing

right here is equal to 573. Let’s do a couple of more. Let’s do a few more problems. So I’ll do that red color. Let’s say we had 7

going into 6,475. Maybe it’s called long division

because you write it nice and long up here and you

have this line. I don’t know. There’s multiple reasons why it

could be called long division. So you say 7 goes

into 6 zero times. So we need to keep

moving forward. So then we go to 64. 7 goes into 64 how many times? Let’s see. 7 times 7 is? Well, that’s way too small. Let me think about

it a little bit. Well 7 times 9 is 63. That’s pretty close. And then 6 times 10 is

going to be too big. 7 times 10 is 70. So that’s too big. So 7 goes into 64 nine times. 9 times 7 is 63. 64 minus 63 to get our

remainder of this stage 1. Bring down the 7. 7 goes into 17 how many times? Well, 7 times 2 is 14. And then 7 times 3 is 21. So 3 is too big. So 7 goes into 17 two times. 2 times 7 is 14. 17 minus 14 is 3. And now we bring down the 5. And 7 goes into 35? That’s in our 7 multiplication

tables, five times. 5 times 7 is 35. And there you go. So the remainder is zero. So all the examples I did

so far had no remainders. Let’s do one that maybe

might have a remainder. And to ensure it has a

remainder I’ll just make up the problem. It’s much easier to make

problems that have remainders than the ones that

don’t have remainders. So let’s say I want to divide 3

into– I’m going to divide it into, let’s say 1,735,092. This will be a nice,

beastly problem. So if we can do this we

can handle everything. So it’s 1,735,092. That’s what we’re

dividing 3 into. And actually, I’m not sure if

this will have a remainder. In the future video I’ll show

you how to figure out whether something is divisible by 3. Actually, we can

do it right now. We can just add up

all these digits. 1 plus 7 is 8. 8 plus 3 is 11. 11 5 five is 16. 16 plus 9 is 25. 25 plus 2 is 27. So actually, this number

is divisible by 3. So if you add up all of

the digits, you get 27. And then you can add up those

digits– 2 plus 7 is 9. So that is divisible by 9. That’s a trick that

only works for 3. So this number actually

is divisible by 3. So let me change it a

little bit, so it’s not divisible by 3. Let me make this into a 1. Now this number will

not be divisible by 3. I definitely want a

number where I’ll end up with a remainder. Just so you see what

it looks like. So let’s do this one. 3 goes into 1 zero times. So we can just move forward. You could write a 0 here and

multiply that out, but that just makes it a little

bit messy in my head. So we just move

one to the right. 3 goes into 17 how many times? Well, 3 times 5 is equal to 15. And 3 times 6 is equal to

18 and that’s too big. So 3 goes into 17 right

here five times. 5 times 3 is 15. And we subtract. 17 minus 15 is 2. And now we bring down this 3. 3 goes into 23 how many times? Well, 3 times 7 is equal to 21. And 3 times 8 is too big. That’s equal to 24. So 3 goes into 23 seven times. 7 times 3 is 21. Then we subtract. 23 minus 21 is 2. Now we bring down

the next number. We bring down the 5. I think you can appreciate why

it’s called long division now. We bring down this 5. 3 goes into 25 how many times? Well, 3 times 8 gets you pretty

close and 3 times 9 is too big. So it goes into it eight times. 8 times 3 is 24. I’m going to run out of space. You subtract, you get 1. 25 minus 24 is 1. Now we can bring down this 0. And you get 3 goes into

10 how many times? That’s easy. It goes into it three times. 3 times 3 is 9. That’s about as close

to 10 as we can get. 3 times 3 is 9. 10 minus 9, I’m going to

have to scroll up and down here a little bit. 10 minus 9 is 1, and then we

can bring down the next number. I’m running out of colors. I can bring down that 9. 3 goes into 19 how many times? Well, 6 is about as

close as we can get. That gets us to 18. 3 goes into 19 six times. 6 times 3– let me scroll down. 6 times 3 is 18. 19 minus 18– we subtract

it up here too. 19 minus 18 is 1 and

then we’re almost done. I can revert back to the pink. We bring down this

1 right there. 3 goes into 11 how many times? Well, that’s three times

because 3 times 4 is too big. 3 times 4 is 12, so

that’s too big. So it goes into it three times. So 3 goes into 11 three times. 3 times 3 is 9. And then we subtract

and we get a 2. And there’s nothing

left to bring down. When we look up here there’s

nothing left to bring down, so we’re done. So we’re left with the

remainder of 2 after doing this entire problem. So the answer, 3 goes into

1,735,091– it goes into it 578,363 remainder 2. And that remainder 2 was what

we got all the way down there. So hopefully you now appreciate

and you can tackle pretty much any division problem. And you also, through this

exercise, can appreciate why it’s called long division.

Thanks so much now i dont have any mistakes on my homeworks or qwiz

Im in grade 5 :/

ยก

what do i do with th remainder >?!!! how do i change it to decimalย

?

Awsomeness!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!:)

I would surely recommend Khan Academy. khanacademy.org

This literally teached me how to divide

Tks

Dumb shit

now this teach me a lot about division

Thank you mr.Khan

Dude, You're the best…..Thank you for teaching me & other youtubers. God bless!

Much helpful. Such thanks.

this is cool i learn more ๐

this help me alot

your the only video I'm going to thanks your the best Mr.khan

thank you

i didnt understand it but now perfect thanx mrs.khan !

me to i had it for home

work

My teacher told me to watch this soooo ok what the heck it taught me alot thanks

( อกยฐ อส อกยฐ) very helpful! Thx a lot!

thx alot mr.knan! this helped me alot! A+ on my test because of you!

thanking you for your great help'"

yo so cool

Omg thx so much for doing this video ! Now I understand ! And I was scared to tell my teacher I needed help but u saved my life thx SO MUCH ! ๐โจ

poooooรฒoooooop๐ฉ๐ฉ๐ฉ๐ฉ๐ฉ๐ฉ๐ฉ๐ฑ๐ฑ๐ ๐ ๐ ๐

I got 100 on my test thank youโบ๐๐๐๐๐๐๐ ๐๐๐๐๐ฏ๐๐๐ ๐ฌ๐ก๐ข๐ด๐ฎ๐ฃ๐ค๐ ๐ฌ๐ก๐ข๐ข๐ด๐ด๐ฎ๐ฃ๐ค๐ฅ๐ฆ๐ง๐จ๐จ๐ฉ๐ฐ๐ฐ๐๐ฑ๐ฒ๐๐ณ๐๐ต๐๐ถ๐ท๐๐๐๐๐๐๐๐

He's really good ๐๐๐๐๐ค๐๐๐๐ค๐๐๐๐๐๐ ๐๐๐๐๐๐ค๐ค๐๐๐ฌ๐๐๐โบ๏ธ๐๐๐๐ค๐๐๐ค๐๐๐๐๐๐๐๐๐๐ถ๐

can you help me

Thanks ….

thank you because i,m the smartest person in my classroom

that was as clear as mud

Tysm! This helped me a lot, but can you make a video on how to present the remainder as a decimal? If you have already can someone link me the video..

im the smartest kid in the world

this guy is good and it helped me a lot

what did you do to get the colors

i have the app

Why don't they teach why you pull down the numbers instead of just giving you a rule to by. Noone learns anything from that…

Thanks

they call it long division because it is a another to say big

Panga Chonga

Thank you because now i know how to divide with remainder๐๐๐๐

thanks for helping me.

he sounds like a murderer when he speaks

nooooooooooooooooooooooooooooooooooooooooo

this sucks

i kid

U ARE AMAZING TYSM!!!!! I DID NOT UNDERSTAND LONG DIVISION UNTIL NOW!! I USED TO GET D'S!! TYSM

good

thanks i needed this im doing math pssa's and i forgot how to do long division

great know i no how๐โบ๐ผ๐๐โ๐

Its funny how you learn a bit of this during grade 4 math class then it comes back at highschool, being more complicated

thank you

What is this????

I suck at dis

Thank u

This is gross I'm to smart 4 this crap

This is very helpful

This helped so much, I totally had that moment of, "OMG, I get it!

This really helped my class

In the video itโs so easy but when you try this in school itโs so hard. But anyways thanks a lot khan

booooooooooooooooooooooooooooooooooooooooooooooooooooooooooo

I am Study Khanacademy too

Lol my math online course told me to watch this xD

what do you use for that

I am so happy I watched this because now I am going to college because of you ๐๐๐๐

i need help with division with 4 or more dividends! help!!!!!!!!

great

You explain stuff way better then my teacher. Whenever I need help with math I just look at your videos and it all makes sense.

helping so much for homework!

This is amazing my forth grader learned a lot for her exam from your channel.

I love this guy's work!

i will pass the fsa test

thanks for explaining this helped me in my test Mr.khan

Does 4 go into 4?๐

Ok

thank you this really helped me keep doing what you do

Is the remainder 2 a point 2 at the end????? Thats what Im trying to figure out. Is the answer 578363.2?

I am terrible at Multu-digit division

Youโre so smart

Youโre so smart #sosmart keep it up dude

Do you think heโs smart like if you agree

yo you are so bad

Thank you my teacher makes me watch you in school

All I learnd is he likes colers

Or LONG DIVISION BEACUSE THE NUMBER is LONG ps THXXXXXXXXX (thx means thank you) you helped me with my homworkkkkkkkk๐๐I watch you in class on computer

thank you for the video! My students were very entertained; however, you changed the division between frames 6:36 and 6:42–which confused them greatly and made the difference between the remainder and no remainder =)

Cool

this really helped me i followed it step by step doing my math sheets and i got the right awnsers every time ๐

Umm who else listened to this in 4th grade

Thanks Khan Academy you've helped me out a lot over the years

THANK YOU MY KID GETS IT SO MUCH THANK YOU YOUR THE BEST

Thanks I needed this

Yay I learned to edit

Thanks sooooooo much!

Thanks u so much for helping to solved this problem ๐

thanks for helping me i was scared to ask much teacher you a life saver Khans academy ๐

1:12 It does bloody look like a fraction though, but I've never seen a fraction that big so I dont know!

6:15 Why did he just skip zero!?

Every example being a single digit number limits the helpfulness of this. It's like every math lesson ever uses the simplest examples. Single digits, 10's, 100's, 2's or 5's. ect.

Ok it kinda of help me๐๐ฎ but the million was not understandable can you explain it more please๐ญ๐จ๐ฐ๐.

Thank you

This is easy