Video: Solving Word Problems by Dividing 5-Digit Numbers by 2-Digit Numbers

An airport registered 838,500 passengers traveling to Africa over a period of 12 months. Find the average number of passengers that traveled to Africa in one month.

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Video Transcript

An airport registered 838,500 passengers traveling to Africa over a period of 12 months. Find the average number of passengers that traveled to Africa in one month.

This problem is all about the number of people that travel from an airport to Africa. To begin with, we’re told the total number of passengers that the airport registered. And that’s 838,500. But how long did the airport measure this amount for? Is this the number of people in a day, a week? We’re told that the airport registered this amount over a period of a year, 12 months. And the problem asks us to use this information to find the average number of passengers that traveled to Africa in one of those 12 months. So how are we going to calculate this amount?

This is a division problem. We’re going to need to divide 838,500 by 12. And because these numbers are so large, we’re going to need to use long division. How many lots of 12 are there in 838,500? If we just look at the first digit, there are no 12s in eight. So we need to begin by looking at the first two digits. How many 12s are there in 83?

Before we start, it might be worth just jotting down all the multiples of 12 that we know already. These are multiples of 12 that we don’t need to think about. We already know them. Obviously, one times 12 is 12. We can double that to get two lots of 12 are 24. We could double again quickly to find four lots of 12 are 48. Then 10 times a number is always a good one. 10 multiplied by 12 is 120. We can then go backwards and find half of 10 lots of 12 to find what five 12s are worth. Half of 120 is 60. So there are one or two 12 times tables facts there that could help us.

Let’s get back to the question. How many 12s are there in 83? Now instead of starting right at the beginning with 12, because we’ve already written out some number facts that we knew, we can start with five 12s are 60. It looks like we can fit one maybe two lots of 12 into 83. If we add 12 to 60, we’ll find out what six 12s are. 60 plus 12 equals 72.

Let’s just see whether seven 12s fit into our 83. We need to add another lot of 12. 72 plus 12 equals 84. This is too large. We can see that only six lots of 12 fit into 83. So we’ll write the number six at the top. And six lots of 12 as we’ve said are 72. And if we subtract this from 83, we can find the remainder. Three take way two, is one, and eight take away seven is one. We have 11 left. Now there are no lots of 12 in 11. It’s too small. So let’s include an extra digit, and we’re gonna have to bring down this digit from the top number.

The next digit along is an eight. And it’s going to turn our number 11 into 118. How many lots of 12 are there in 118? Again, our facts that we knew already can be helpful here. We know that 10 lots of 12 are 120, which is slightly too much. But if we subtract one lot of 12 from 120, we’ll be left with nine 12s. And this is going to fit into 118. We know that 20 take away 12 leaves us with eight. So 120 take away 12 is 108. So we can write the digit nine at the top as part of our answer.

To calculate the remainder, we need to subtract nine lots of 12, which we said was 108, from the number we were dividing, which was 118. We can work this answer out mentally. The difference between 108 and 118 is 10. Again, 10 is too small to be dividing by 12. So let’s include another digit.

And the next digit along to bring down is going to be the digit five. It’s going to turn our number 10 into 105. How many lots of 12 are there in 105? As we’ve just seen, nine lots of 12 is 108. But this is too large. It’s only too large by three. So we know the answer is going to be eight lots of 12. And to calculate eight lots of 12, we need to subtract another lot of 12 from 108. 108 take away two is 106. And if we take away 10, we have the answer 96.

We could’ve found the same answer by adding 12 to 84. So eight 12s are 96. And this is as close as we’re going to get to 105. To find the remainder, we need to subtract our eight 12s, which is 96, from 105. Again, a quick way to do this would be mentally. We can count up from 96. If we count from 96 to 100, that’s four. And then from 100 onto 105 is another five. And four plus five equals nine. There’s a remainder of nine. Nine is too small to be dividing by 12. So we need to bring down another digit from the top number.

This time, it’s a zero. And it’s going to turn our nine into 90. How many 12s are there in 90? This is where we can see the benefits of writing out all the multiples of 12 that we’ve done as we’ve gone along. We’ve got quite an extensive list now. And we just need to glance across and see how close we can get to 90. The closest multiple of 12 that we can get to 90 without going above 90 is 84. And this is equal to seven 12s. So we can say 90 divided by 12 equals seven. Seven 12s are 84 as we’ve just said. And if we subtract this from 90, we can find the remainder. Again, it’s one we can do in our heads. The difference between 84 and 90 is six.

There are no 12s in six. So we need to bring down our final digit, another zero. And so six becomes 60. Do you recognize the number 60? It’s in one of our facts. There are five 12s in 60. So we can complete our answer by writing the digit five at the top. And we can prove that there’s nothing left over by subtracting five lots of 12, which is 60, from the number that we wanted to divide, which was also 60, to show there’s no remainder.

And so we can see the answer to our problem at the top of the calculation. We used long division to find the answer. If an airport registered 838,500 passengers traveling to Africa over a period of 12 months, we knew that the way to find the average number of passengers that travel to Africa in one month was to divide 838,500 by 12. And so the answer to the problem and the average number of passengers is 69,875.

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