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Lesson Video: The Division Symbol: Sharing Equally Mathematics • 3rd Grade

In this video, we will learn how to use the division symbol to write equations to find the number of things in each group when we have 2, 3, 4, 5, or 10 equal groups.

11:37

Video Transcript

The Division Symbol: Sharing Equally

In this video, we’re going to learn how to use the division symbol to write number sentences that help us find the number of things in each group when we have two, three, four, five, or 10 equal groups.

Here are 12 fish. At the moment, they’re all spread out. But it’s often safer for small fish like this to swim together in groups. Let’s imagine that these fish are split up into two equal groups. We could say that the 12 fish are being divided by two. How many fish will there be in each group?

We could share our 12 fish one at a time into two separate groups. We could put one group on either side. Let’s get sharing. One for the first group and one for the second group. Another fish for the first group; that’s now two we’ve got. And another fish goes into our second group. And we can keep sharing our fish one at a time into two groups. And with each round of sharing, we need to make sure that we share the same amount into each group.

There we are; we’ve divided all 12 fish into two equal groups. There are six fish in this group, and there are also six fish in this group. 12 divided by two equals six.

Now, so far, we’ve written what we’ve done using numbers and words. But wouldn’t it be good if there was a symbol we could use that meant divide? Then, we could write a number sentence or equation to show what we’ve done. Well, there is such thing as a division symbol. It’s made up of two dots with a straight line in between. We use this symbol when we want to show that a number has been divided by another number. And in this video, we’re using it for sharing into that number of equal groups.

Let’s use this division symbol to write down what’s happened to our fish. We did have 12 fish. This was the whole amount. It was the number that we started with. And then, we split this number into equal groups. And as we’ve said already, another word for “split” is “divide”. So, we can write the division symbol here, two dots and a line in between. This shows that we’ve shared out or split up 12.

How many equal groups did we share the fish into? There were two groups, weren’t there? By the way, how do we know our groups are equal? We know that the word “equal” means the same. And we know our two groups are equal because they contain the same number of fish. So, the final number in our equation is the number of fish in each group. 12 divided by two equals six.

This is exactly the same as what we’ve written at the top. We’ve just used numbers and symbols this time to write it as a number sentence. When we start with a whole amount and we split it into a number of equal groups, the answer will be the number that there are in each group.

Let’s have a go at using the division symbol now. We’re going to answer some questions where we need to divide a number of objects into equal groups.

There are 14 carrots. The carrots will be shared equally between seven rabbits. Each rabbit will get what carrots. Find the missing number: 14 divided by seven equals what.

Our problem begins with 14 carrots. And to help us imagine them, we’re given a picture that shows them. But something’s going to happen to these carrots. We’re told that they’re going to be shared equally. When something is shared equally, it’s divided. This is a question all about division.

So, how many groups will the carrots be shared into? Well, if we look carefully, we can see who’s doing the dividing here. The carrots are going to be shared equally between seven rabbits. So, we need to split our 14 carrots into seven equal groups. To help us do this, let’s sketch the groups.

Here are seven circles to represent the seven rabbits, one circle for each rabbit. Now, we need to make sure that these groups are equal. So, each time we share the carrots, each group needs to get the same amount. Let’s use counters to represent carrots.

To begin with, let’s give each of the seven groups one carrot. So, that’s one, two, three, four, five, six, seven. There are seven groups, and they each now have one carrot. But we’ve got more carrots left. We’re going to need to give each group another carrot. Now, there are no more carrots left to share. We’ve divided all 14 of them. And they’ve been split up into equal groups.

We know that the groups are equal because if we look at them quickly, we can see that they’ve got the same number of counters in them. Remember, we said our counters represented carrots. So, now, we can answer the first part of our question. Each rabbit will get what carrots. Well, we managed to put two counters in each group, didn’t we? So, we know that each rabbit will get two carrots.

In the final part of our question, we’re given a number sentence and we need to fill in the missing number. Our number sentence begins with the number 14. We know this is the whole amount. This was the number of carrots that we began with. But then, we have an interesting symbol, two dots with a line in between them.

Perhaps you were listening carefully when the text of this question was read out at the very start. If so, you’ll know what this symbol means. That’s right. It means divided by. We use the division symbol whenever an amount is shared into equal groups. We started with 14 carrots. They were divided or shared between seven rabbits. And the missing number in our number sentence, that’s the answer to our division, is the number of carrots in each group. Of course, the answer’s two.

If there are 14 carrots and they’re shared equally between seven rabbits, each rabbit will get two carrots. And we can write this using the division symbol as 14 divided by seven equals two. Both of our missing numbers are the number two.

Natalie is preparing breakfast. She made 20 sandwiches and put them on 10 plates. Choose the calculation that is equal to the number of sandwiches on each plate. 20 take away 10, 20 divided by two, 20 plus 10, or 20 divided by 10. How many sandwiches are on each plate?

This problem describes Natalie who’s preparing a really big breakfast. Perhaps she’s made it for her whole class because she’s made 20 sandwiches. But you know, she hasn’t just put them in one big group; she split them up. We know this because we’re told that she’s put the 20 sandwiches on 10 plates. We could say she’s shared them out. And we can see a picture to help us.

In the first part of the problem, we’re told to choose the calculation that is equal to the number of sandwiches on each plate. And we’re given four possible calculations to choose from. Now, we can see in the picture how many sandwiches are on each plate. But if we didn’t have the picture to help us, which of these calculations would we use?

To find the answer, we need to think carefully about what Natalie’s done here. The first thing that she’s done is to make 20 sandwiches. So, this is the number she begins with, 20. But then, what does she do? She puts them on 10 plates, doesn’t she? And if we look at each plate, we can see that they all have an equal number of sandwiches on. These 20 sandwiches have been shared out. And another word for “shared” is “divided.” And the symbol that we use when a number is divided into equal groups is the division symbol, which is a line with two dots either side.

How many equal groups has Natalie made? Well, she shared out her sandwiches onto 10 plates. So, she’s divided 20 by 10. To find out the number of sandwiches on each plate then, we need to find the answer to 20 divided by 10. And if we look at our four calculations, this is one of them.

We might use 20 take away 10 if we wanted to find out how many sandwiches Natalie had left after making 20 and then eating 10 of them. 20 divided by two is a division calculation. But this would be the number of sandwiches in each group if Natalie shared them onto two plates. And we know that adding is to find the total of two numbers. So, 20 plus 10 would be to find the number of sandwiches if Natalie perhaps made 20 sandwiches and then made another 10.

So, that’s how we know the correct answer is 20 divided by 10. And we can use this to calculate the number of sandwiches on each plate. 20 divided by 10 equals two. 10 groups of two make 20. So, if Natalie makes 20 sandwiches and puts them on 10 plates, the calculation that’s equal to the number of sandwiches on each plate is 20 divided by 10. And the number of sandwiches that are on each plate is two.

What have we learned in this video? Firstly, we’ve been introduced to the division symbol. We know that this is a line in between two dots. We’ve also learned how to use the division symbol to write number sentences to find the number of things in each group when we share an amount into equal groups.

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