Question Video: Dividing 5-Digit Numbers by 2-Digit Numbers

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

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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.

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