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.