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

January 3, 2020

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.