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## Multi-digit division (no remainders)

# Long division: 280÷5

## Video transcript

Let's tackle a slightly more
interesting division problem. So we're going to take
280 and divide it by 5. And I encourage you
to pause this video and try to apply the
technique that we've seen in a previous video
to try to figure out what 280 divided by 5 is. So let's have our go at it. So we could rewrite this. We've already seen this
as 280 divided by 5. So the first question
we can ask ourselves is, how many times
does 5 go into 2? Well, 5 doesn't
go into 2 at all. It goes 0 times. 0 times 5 is 0. And then we subtract. 2 minus 0 is 2. And now, we can bring
down the next digit, which, in this case, is an 8. And so we can ask
ourselves, how many times does 5 go into 28
without going over it? So we could think, well,
let's see 5 times 5 is 25. 5 times 6 is 30. So 5 times 6 would go over 28. So we want to go
back to 5 times 5. So 5 goes into 28 5 times. 5 times 5 is 25. And you subtract. 28 minus 25 is 3. And now, let's bring
down the next digit. In this case, the digit is a 0. So how many times
does 5 go into 30? Well, it goes exactly 6 times. We've already talked about that. 6 times 5 is 30. We subtract. And we have nothing left over. So we just figured out that 280
divided by 5 is equal to 56. Now, why did this work? Well, the first way to
think about it, this was actually 200. And we were thinking
about, do we put anything in the
hundreds place here? So one way of thinking about
it, how many hundreds of times does 5 go into 200? And it doesn't go
any multiples of 100. And if that's a
little confusing, don't worry too much about it. But I want you to
really think deeply about the place notation. But then we were able
to, again, extend it to instead of just
200 but then 280. This 28 right over here,
if you think about it, this 2 is in the hundreds place. This 8 is in the tens place. So this is really
representing 280. And we said, how many tens
of times does 5 go into 280? Well, it goes 5 tens
times, or it goes 50 times. 50 times 5 is 250. When you subtract 250
from 280, you've got 30. And there were no other
things in the ones place here. So we just have to
figure out how many times does 5 go into 30. So hopefully, that
gives you a sense of what's actually happening
behind this little process. It's not just magic. We're really just keeping
track of place value here. The other thing I
want to show you is that we didn't necessarily
have to write this 0 here. Another way of
computing it, we could have said 280 divided by 5. And we could've said, how
many times does 5 go into 2? Well, it doesn't go any times. So let's just think
about 5 going into 28. Well, 5 goes into 28 5 times. 5 times 5 is 25. Subtract. 28 minus 25 is 3. Bring down the 0. 5 goes into 30 six times. 6 times 5 is 30. And we have nothing left over. And again, what
we're really saying is that 5 doesn't go into
200 any hundreds of times. If this was a 500,
you could say, hey, it's going to go
in it 100 times. But instead, we go, well,
what about 5 going into 280? Well, it goes 50 times. 50 times 5 is 250. 280 minus 250 is 30. 5 goes into 30 six times. So hopefully, that makes
a little bit of sense.