This table shows the number of people living in various towns in England. What is the total of the numbers of people living in Formby and in Telford? What is the difference between the numbers of people living in Bedford and in Dover?
This problem is based around a table of information that we’re given. We’re told that the table shows the number of people that live in different towns. And another word for the number of people that live somewhere is population. And we can see the population of each town in the second column.
Bedford has a population of 82448. The town of Carlton has a population of 48493. The population of Dover is 34087. 24478 people live in Formby. And we can see that the town of Telford has a population of 166640. So this table of information is going to help us to solve these problems.
Let’s think about the first one. What is the total of the numbers of people living in Formby and in Telford? The question asks us to find the total. So we know that this is an addition problem, and we need to add to find the answer.
First, we can locate Formby and Telford in our table. And we can see what the populations are. So to find the answer, we need to add 24478 and 166640. Is this the sort of calculation we could do in our heads? Oh, perhaps we could. But we’d have to hold a lot of digits and make sure that we exchange a number of times. These are not nice round numbers that we can add quickly in our heads. So let’s use vertical addition and make sure that we get the correct answer.
First of all, write the numbers out vertically. We make sure that we’ve lined up each of the digits so the ones digits are in line, the tens digits, and so on. It’s often useful to start with a larger number too. But we’d still get the same answer if we added the numbers in the other order.
We need to start by adding the ones and move from right to left. Zero ones add eight ones equals eight ones. Four tens plus seven tens equals 11 tens. And we can exchange 10 of those 11 tens for 100. So let’s write a one underneath in the hundreds column. Six hundreds plus four hundreds equals 10 hundreds, not forgetting the one hundred underneath which gives us 11 hundreds. We can exchange 10 of those 11 hundreds for one thousands. We’ll put a one in the thousands column, 11 hundreds or 1100.
We need to do a similar calculation in the thousands column. Six thousands plus four thousands equals 10 thousands. Don’t forget the extra one thousand that we exchanged, which gives us 11 thousands. We can exchange 10 of those 11 thousands for one lot of 10000. Six ten thousands plus two ten thousands or 60000 plus 20000 equals eight ten thousands or 80000. And we have one ten thousand underneath. So that gives us a nine in the ten thousands column, 90000. And finally, one hundred thousand plus no hundred thousands gives us one hundred thousand. And so the answer to the first part of our problem “What is the total of the numbers of people living in Formby and in Telford?” is 191118.
Let’s think about our second part of the problem. What is the difference between the numbers of people living in Bedford and in Dover? When we’re asked to find the difference between two numbers, we can sometimes count on and use addition. But usually, we have to subtract to find the answer. So this is a subtraction problem.
First, let’s locate Bedford and Dover in our table. So the question is asking us to subtract 34087 from 82448. This doesn’t look like the sort of calculation that we can work out quickly mentally. So let’s use vertical subtraction just like we used vertical addition for the first part.
First, set out the calculation vertically, making sure that we’ve lined up all the digits correctly and also making sure that the larger number is on the top. Unlike addition, with subtraction, we have to have the larger number first. And starting with the ones, let’s subtract each column. Eight ones take away seven ones leaves us with one one. Four tens take away eight tens, looks like we can’t do this because eight is greater than four. But what we can do is exchange one hundred for 10 tens. Instead of four hundreds, we now have three hundreds. And instead of four tens, we now have 14 tens.
Remember that when we exchange like this, we don’t change the value of that first number at all. It’s still worth 82448. We’ve just partitioned it slightly differently. Let’s subtract these tens. 14 tens take away eight tens leaves us with six tens.
Remember, we now have three hundreds in our hundreds column. Three hundreds take away zero hundreds equals three hundreds. 2000 take away 4000 is not possible at the moment, so we need to exchange one lot of 10000 for 10 one thousands. So instead of 80000, we now have 70000. And instead of 2000, we now have 12000. 12 thousands take away four thousands equals eight thousands. And finally, seven ten thousands take away three ten thousands leaves us with four ten thousands, or 40000.
And so what is the difference between the numbers of people living in Bedford and in Dover? 48361. It would have been difficult to hold the numbers in our head. And that’s why we used vertical addition and vertical subtraction to find both answers.