### Video Transcript

A library has 84550 books and 95
shelves. There are the same number of books
on each shelf. How many books are on each
shelf?

We’re told that a library has 84550
books. We’re also told the number of
shelves in this library, and that’s 95. And we can think of these shelves
as being a number of groups. Because by organising the books so
that there are the same number of books on each shelf, what we’re doing is splitting
up 84550 into 95 equal groups. In other words, we’re dividing
84550 by 95. We’re going to have to use division
to solve the problem.

Because we’re using such large
numbers, we’re going to have to use long division. And to do that, we need to set out
the calculation like this. How many 95s are there in
84550? If we look at the first digit, it’s
too small to divide by 95. And if we take the first two
digits, even 84 is too small. So we need to begin by thinking
about the first three digits. How many 95s are there in 845?

Now we might not know our 95 times
table. But rather than going through every
single multiple of 95 until we get near to 845, we could use estimation to help
here. 95 is very close to 100. How many 100s are there in 845? Well, we know there are eight
hundreds in 845. So we can estimate that there could
be eight lots of 95 in 845 too. There could be nine lots of 95. So what we’ll do is we’ll start
with 10 times 95 and work backwards.

We know that when a number is
multiplied by 10, the digits move one place to the left. So 10 lots of 95 is 950. Nine lots of 95 is one lot of 95
less than this. We know that 100 less than 950 is
850. But we don’t wish to take away as
much as this. We need to take away 95. So our answer is going to be five
more than 850. It’s going to be 855.

If we look across at our
calculation, we need to divide 845 by 95. So we can definitely say there
aren’t nine lots of 95 in 845. What about eight? Well, to find eight lots of 95, we
need to subtract another lot of 95. And we can use the same method
again. If we subtract 100 from 855, we get
755. And from this, we can work out what
subtracting 95 will give us. Instead of 755, we’ll have the
answer 760. And we can definitely see that 760
is as near as we’re going to get to 845. We can say that there are eight
lots of 95 in 845.

But we can also see that there’s a
remainder. Eight lots of 95 as we’ve said
already is 760. And if we subtract this from 845,
we can find out what’s left. Five ones take away zero ones
leaves us with five ones. In the tens column, we can’t
subtract six tens from four tens. So we’re going to need to
exchange. We can take 100 — instead of 800,
we now have seven hundreds — and exchange it for 10 tens. Now we have 14 tens that we can
subtract six tens from. And the answer is eight tens. In our hundreds column, seven take
away seven leaves us with nothing. So our remainder is 85.

Now there are no 95s in 85. So just like before, we need to
include another digit. This time, we’re going to bring it
down from the top. And the next digit along is a
five. How many lots of 95 are there in
855? Now sometimes you might sit down
and work out a calculation like this without using a pencil and paper and just write
down the things that we think are important. But in an instance like this,
writing down everything is important.

Earlier on, we wanted to find out
what eight lots of 95 was equal to. And to get there, we started with
10 lots of 95 and then worked out nine lots of 95. Now because we’ve written this out,
all we have to do is to glance across to the left and see the number 855 written
there already. We don’t have to do any working
out. We’ve already done it. Writing things down as we go is a
really useful skill in maths.

So we can look across and say that
there are nine lots of 95 in 855. And this time, there’s no
remainder. Nine lots of 855 is 855. And if we subtract this from the
number we wanted to divide by 95, we get the answer zero. But we still haven’t completed the
calculation. Our final digit is zero, and we
need to include this. Of course, there are no lots of 95
in zero. So we can just write zero as a
placeholder there.

We’ve used long division to find
the answer. If a library has 84550 books and 95
shelves and there are the same number of books on each shelf, to find the number of
books that there are on each shelf, we need to find the answer to 84550 divided by
95. We’ve done this. And so we can say that the number
of books that there are on each shelf is 890.