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## Arithmetic (all content)

### Unit 3: Lesson 15

Multi-digit division (remainders)- Intro to long division (remainders)
- Divide by taking out factors of 10
- Basic multi-digit division
- Dividing by 2-digits: 6250÷25
- Dividing by 2-digits: 9815÷65
- Dividing by 2-digits: 7182÷42
- Division by 2-digits
- Partial quotient method of division: introduction
- Partial quotient method of division: example using very large numbers

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# Intro to long division (remainders)

Introduction to long division with remainders. Created by Sal Khan.

## Video transcript

Let's now see if we can
divide into larger numbers. And just as a starting point,
in order to divide into larger numbers, you at least need to
know your multiplication tables from the 1-multiplication
tables all the way to, at least, the 10-multiplication. So all the way up to 10 times
10, which you know is 100. And then, starting at 1 times 1
and going up to 2 times 3, all the way up to 10 times 10. And, at least when I was
in school, we learned through 12 times 12. But 10 times 10 will
probably do the trick. And that's really just
the starting point. Because to do multiplication
problems like this, for example, or division
problems like this. Let's say I'm taking 25 and
I want to divide it by 5. So I could draw 25 objects and
then divide them into groups of 5 or divide them into 5 groups
and see how many elements are in each group. But the quick way to do is
just to think about, well 5 times what is 25, right? 5 times question mark
is equal to 25. And if you know your
multiplication tables, especially your
5-multiplication tables, you know that 5 times 5
is equal to 25. So something like this, you'll
immediately just be able to say, because of your knowledge
of multiplication, that 5 goes into 25 five times. And you'd write the
5 right there. Not over the 2, because you
still want to be careful of the place notation. You want to write the
5 in the ones place. It goes into it 5 ones times,
or exactly five times. And the same thing. If I said 7 goes into 49. That's how many times? Well you say, that's like
saying 7 times what-- you could even, instead of a question
mark, you could put a blank there --7 times what
is equal to 49? And if you know your
multiplication tables, you know that 7 times 7 is equal to 49. All the examples I've
done so far is a number multiplied by itself. Let me do another example. Let me do 9 goes into
54 how many times? Once again, you need to
know your multiplication tables to do this. 9 times what is equal to 54? And sometimes, even if you
don't have it memorized, you could say 9 times 5 is 45. And 9 times 6 would be 9 more
than that, so that would be 54. So 9 goes into 54 six times. So just as a starting point,
you need to have your multiplication tables from 1
times 1 all the way up the 10 times 10 memorized. In order to be able to do at
least some of these more basic problems relatively quickly. Now, with that out of the way,
let's try to do some problems that's might not fit
completely cleanly into your multiplication tables. So let's say I want to
divide-- I am looking to divide 3 into 43. And, once again, this is larger
than 3 times 10 or 3 times 12. Actually, look. Well, let me do
another problem. Let me do 3 into 23. And, if you know your 3-times
tables, you realize that there's 3 times nothing
is exactly 23. I'll do it right now. 3 times 1 is 3. 3 times 2 is 6. Let me just write them all out. 3 times 3 is 9, 12, 15,
18, 21, 24, right? There's no 23 in the
multiples of 3. So how do you do this
division problem? Well what you do is you think
of what is the largest multiple of 3 that does go into 23? And that's 21. And 3 goes into 21
how many times? Well you know that 3
times 7 is equal to 21. So you say, well 3 will
go into 23 seven times. But it doesn't go into
it cleanly because 7 times 3 is 21. So there's a
remainder left over. So if you take 23 minus 21,
you have a remainder of 2. So you could write that 23
divided by 3 is equal to 7 remainder-- maybe I'll just,
well, write the whole word out --remainder 2. So it doesn't have to go
in completely cleanly. And, in the future, we'll learn
about decimals and fractions. But for now, you just say, well
it goes in cleanly 7 times, but that only gets us to 21. But then there's 2 left over. So you can even work with the
division problems where it's not exactly a multiple of the
number that you're dividing into the larger number. But let's do some practice
with even larger numbers. And I think you'll
see a pattern here. So let's do 4 going into--
I'm going to pick a pretty large number here --344. And, immediately when you see
that you might say, hey Sal, I know up to 4 times
10 or 4 times 12. 4 times 12 is 48. This is a much larger number. This is way out of bounds
of what I know in my 4-multiplication tables. And what I'm going to show you
right now is a way of doing this just knowing your
4-multiplication tables. So what you do is you
say 4 goes into this 3 how many times? And you're actually saying
4 goes into this 3 how many hundred times? So this is-- Because
this is 300, right? This is 344. But 4 goes into 3 no hundred
times, or 4 goes into-- I guess the best way to think of
it --4 goes 3 0 times. So you can just move on. 4 goes into 34. So now we're going
to focus on the 34. So 4 goes into 34
how many times? And here we can use our
4-multiplication tables. 4-- Let's see, 4 times
8 is equal to 32. 4 times 9 is equal to 36. So 4 goes into 34-- 30-- 9
is too many times, right? 36 is larger than 34. So 4 goes into 34 eight times. There's going to be a
little bit left over. 4 goes in the 34 eights times. So let's figure out
what's left over. And really we're saying 4 goes
into 340 how many ten times? We're actually saying 4 goes
into 340 eighty times. Because notice we wrote
this 8 in the tens place. But just for our ability to do
this problem quickly, you just say 4 goes into 34 eight times,
but make sure you write the 8 in the tens place right there. 8 times 4. We already know what that is. 8 times 4 is 32. And then we figure
out the remainder. 34 minus 32. Well, 4 minus 2 is 2. And then these 3's cancel out. So you're just left with a 2. But notice we're in the
tens column, right? This whole column right here,
that's the tens column. So really what we said is 4
goes into 340 eighty times. 80 times 4 is 320, right? Because I wrote the 3 in
the hundreds column. And then there is-- and I don't
want to make this look like a-- I don't want to make this look
like a-- Let me clean this up a little bit. I didn't want to make that line
there look like a-- when I was dividing the columns
--to look like a 1. But then there's a remainder
of 2, but I wrote the 2 in the tens place. So it's actually a
remainder of 20. But let me bring down this 4. Because I didn't want to
just divide into 340. I divided into 344. So you bring down the 4. Let me switch colors. And then-- So another
way to think about it. We just said that 4 goes into
344 eighty times, right? We wrote the 8 in
the tens place. And then 8 times 4 is 320. The remainder is now 24. So how many times
does 4 go into 24? Well we know that. 4 times 6 is equal to 24. So 4 goes into 24 six times. And we put that in
the ones place. 6 times 4 is 24. And then we subtract. 24 minus 24. That's-- We subtract at
that stage, either case. And we get 0. So there's no remainder. So 4 goes into 344 exactly
eighty-six times. So if your took 344 objects and
divided them into groups of 4, you would get 86 groups. Or if you divided them
into groups of 86, you would get 4 groups. Let's do a couple
more problems. I think you're getting
the hang of it. Let me do 7-- I'll
do a simple one. 7 goes into 91. So once again, well, this is
beyond 7 times 12, which is 84, which you know from
our multiplication tables. So we use the same system we
did in the last problem. 7 goes into 9 how many times? 7 goes into 9 one time. 1 times 7 is 7. And you have 9 minus 7 is 2. And then you bring down the 1. 21. And remember, this might seem
like magic, but what we really said was 7 goes into 90 ten
times-- 10 because we wrote the 1 in the tens place --10
times 7 is 70, right? You can almost put a
0 there if you like. And 90 with the remainder--
And 91 minus 70 is 21. So 7 goes into 91 ten
times remainder 21. And then you say 7 goes into
21-- Well you know that. 7 times 3 is 21. So 7 goes into 21 three times. 3 times 7 is 21. You subtract these
from each other. Remainder 0. So 91 divided by 7
is equal to 13. Let's do another one. And I won't take that little
break to explain the places and all of that. I think you understand that. I want, at least, you to get
the process down really really well in this video. So let's do 7-- I keep
using the number 7. Let me do a different number. Let me do 8 goes into
608 how many times? So I go 8 goes into
6 how many times? It goes into it 0 time. So let me keep moving. 8 goes into 60 how many times? Let me write down the 8. Let me draw a line here so
we don't get confused. Let me scroll down
a little bit. I need some space
above the number. So 8 goes into 60
how many times? We know that 8 times
7 is equal to 56. And that 8 times 8
is equal to 64. So 8 goes into-- 64 is too big. So it's not this one. So 8 goes into 60 seven times. And there's going to be
a little bit left over. So 8 goes into 60 seven times. Since we're doing the whole 60,
we put the 7 above the ones place in the 60, which is the
tens place in the whole thing. 7 times 8, we know, is 56. 60 minus 56. That's 4. We could do that in our heads. Or if we wanted, we can borrow. That be a 10. That would be a 5. 10 minus 6 is 4. Then you bring down this 8. 8 goes into 48 how many times? Well what's 8 times 6? Well, 8 times 6 is exactly 48. So 8 times-- 8 goes
into 48 six times. 6 times 8 is 48. And you subtract. We subtracted up here as well. 48 minus 48 is 0. So, once again, we get
a remainder of 0. So hopefully, that gives you
the hang of how to do these larger division problems. And all we really need to know
to be able to do these, to tackle these, is our
multiplication tables up to maybe 10 times 10
or 12 times 12.