Lesson Video: Dividing by 3 | Nagwa Lesson Video: Dividing by 3 | Nagwa

# Lesson Video: Dividing by 3 Mathematics

In this video, we will learn how to use various strategies to divide by 3 within the known times tables, including using models and times table facts.

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### Video Transcript

Dividing by Three

In this video, we’re going to learn how to use different strategies to help us divide by three. Some of the strategies we’re going to use are models and also using times tables facts to help.

Each of these monsters has three eyes. Now let’s imagine that we turn the light off, and then we noticed 12 eyes looking back at us. How many monsters is this? We can find the answer by dividing 12 into groups of three. This is one thing that dividing by three can mean. And so the answer to our division, this is what we call the quotient, is going to be the number of equal groups that we’ve made.

So what strategy could be used to divide 12 by three? Let’s draw a model. We could sketch 12 counters like this and the way that we’ve drawn them is going to help us split this number into equal groups of three. We can see one, two, three, four groups of three. 12 divided by three equals four. We divided 12 into equal groups of three. And the quotient or the answer to our division shows us the number of equal groups that we can make. And in this problem, it’s the number of monsters that there are. Shall we check that there are four? It’s time to turn that light switch back on. We were right. There are four monsters in the room. 12 divided by three equals four.

So we used a model to help us solve that problem. Let’s try a different strategy for dividing by three. And let’s turn the lights off again. And let’s imagine we can now see 30 eyes looking back at us. To find out how many monsters there are, we’re going to need to divide by three again to split these 30 eyes into equal groups of three. And just like before, the quotient or the answer to this division is going to be the number of equal groups that we can make or the number of monsters that there are. And last time we used our model to find the answer. This time, let’s try a different method. We could use a number line to help.

To see how many threes fit into 30, we could start with 30 and count back three each time. This is very similar to something called repeated subtraction. This is when we start with 30 and we keep taking away three and then another three and so on until we’ve got no more to take away. So let’s see how many threes fit into 30. We’ll count back three from 30. 30, 29, 28, 27 and then 26, 25, 24 and then 23, 22, 21, 20, 19, 18 then 17, 16, 15. So far, we’ve subtracted five lots of three. 14, 13, 12, 11, 10, nine and then eight, seven, six, then five, four, three. And this means we’ve got one more lot of three we can subtract. Two, one, zero.

So in total, we’ve made one, two, three, four, five, six, seven, eight, nine, 10 jumps backwards of three, or we’ve subtracted three 10 times. And we’ve gone from 30 all the way back to zero. So we can say there must be 10 threes in 30. 30 divided by three equals 10. We used a number line to help us find the answer, and it looks like there’s going to be 10 monsters. Let’s turn the light back on. What a lot of monsters. And there are 10 of them. 30 divided by three equals 10. Now so far, we’ve looked at dividing by three where we have to make equal groups of three, and the answer or the quotient is the number of equal groups we can make.

But you know, we can think of division another way. Let’s imagine there are six monsters. And they’ve been asked to divide themselves into three equal groups. This is the same as six divided by three. You know, we can also write this another way: six divided by three. And we’d write the answer up here. As we learn to divide bigger and bigger numbers, we’ll use this sort of division more often. But we could write our division like this. Now the idea of dividing by three in this problem is slightly different. We’re not splitting the monsters up into equal groups of three. We’re splitting them up in three equal groups. It’s almost like there are three tables in the classroom and your teacher says, “go and split yourselves up so that there’s an equal number in each group.”

This time, the quotient or the answer isn’t going to be the number of groups; it’s going to be the number in each group. So far, we’ve used a model. We’ve counted back on a number line or used repeated subtraction to help. What else could we do? Well, because division and multiplication are linked, we could use times tables facts to help. Can you think of a three times table fact that might be able to help us here? Well, we know that two lots of three make six; two times three equals six. And we can use this to help. If two times three is six, we know that six divided by three must equal two.

Let’s share out our monsters into three equal groups and see whether we’re right. One, two, three; one, two, three. We divided six monsters into three equal groups. And we found that there were two monsters in each group. Six divided by three equals two. And we used a times tables fact this time to help us. Let’s have a go at answering some questions now where we have to divide by three. And perhaps we’ll try drawing a model, counting back on a number line, and maybe even use our knowledge of times tables to help.

Find 18 divided by three using the cubes shown.

In this question, we need to practice our skills at dividing by three. And we know that we need to use a model to help us because we’re given a picture of some cubes. And we’re told that we need to find the answer using the cubes shown. Now when you see the calculation 18 divided by three, what do you think of? We could think of it as 18 split into groups of three. And we try to find how many groups. Or we could think of it as 18 shared into three equal groups. And then we’d be trying to find out how many in each group. In the picture, we’re given 18 cubes. And you know, it doesn’t really matter which way we think of 18 divided by three. We can find the answer in both ways. And both ways involve drawing the lines on our model.

Let’s start with the first idea. We could think of this as 18 split into groups of three. And we’re going to count how many groups we can make. Perhaps this is the way you’d think of the division. Well by looking at our cubes, can you see how to split them into groups of three? If we look carefully, we can see some groups of three already. We can see one, two, three, four, five, six groups of three. So if we think of our division like this, we can split 18 into groups of three and see that we can make six groups. But perhaps you thought of the model another way. Perhaps you thought of it as 18 shared into three equal groups. Let’s show the model again. And we’re going to draw our lines in a different way this time.

Can you see how you draw the lines to share 18 into three equal groups? We could do it like this: one group, two groups, three groups. And they’re all the same size. We can see that they all contain one, two, three, four, five, six. So if we start with 18 cubes and we share them into three equal groups, there’ll be six cubes in each group. So it doesn’t really matter how we think of this division. Whether we want to find the number of groups or the number in each group, the answer is still the same. We’ve used a model in two different ways to find the answer to 18 divided by three. And that answer is six.

Count back to find 15 divided by three.

In this question, we’ve got a division to solve. We need to divide 15 by three. One way of thinking of this is, how many threes are there in 15? And one way we could find out how many threes are in 15 is if we count back, which is what this question tells us to do. We could do this on a number line. So we could start by sketching a number line and labeling zero at one end and 15 at the other. But remember, we’re going to be working backwards, so we’re going to start at 15 and go back toward zero. Now to find out how many threes there are in 15, we could count back in threes. So starting on 15, let’s count back one lot of three. 15, 14, 13, 12.

So we know there’s definitely one lot of three in 15. Let’s take away another lot of three, starting with 12, 11, 10, nine, and another jump of three, starting with nine, eight, seven, six. So we’ve already made three jumps of three and we’ve landed on the number six. Can you see how many more jumps of three we need to make? Six, five, four, three. And then if we take away one more lot of three, it’s going to take us to zero. We’ve made five jumps of three altogether to get from 15 all the way back to zero. This tells us that there are five threes in 15. We’ve used counting backwards or repeated subtraction to help us solve this division. 15 divided by three equals five.

Find the missing quotient. 24 divided by three equals what. Hint: How can solving what times three equals 24 help you?

There’s an interesting word in the first sentence of this problem, “quotient.” Whatever it is, there’s one missing because we’re told to find the missing quotient. And underneath this phrase, we can see a division: 24 divided by three equals what. And the missing number is the answer to the division. And you know, this is what a quotient is. It’s the answer when we’ve divided one number by another. So really, we could say, find the missing answer to this division. What is 24 divided by three? And we’re given a hint to help us. We’re asked, how can solving what times three equals 24 help you? Can you see what number sentence we’re given? It’s a times table fact.

Now there are lots of ways we could solve division questions. But probably the quickest way is to think of a times table fact we already know and use this to help us. Perhaps you already know what number you multiply by three to get 24. But in case you don’t, let’s go through our number facts. One times three is three, two threes are six, three times three is nine, four threes are 12, five times three is 15, six threes are 18, seven threes are 21, and now the important one, eight times three equals 24. Perhaps you didn’t need to go through all those facts; perhaps you knew it already.

Eight multiplied by three equals 24. And let’s think about what that means for a moment. There are eight lots of three in 24. And so if we ask ourselves the question, what’s 24 divided by three, really what we’re asking ourselves is, how many threes are in 24? And we know this because the times tables fact tells us. There are eight threes in 24. We found the answer to this division question or the quotient by using a multiplication fact to help us. We know that eight times three is 24, and so 24 divided by three must be eight.

Which number is missing? What divided by three equals seven.

In this question, we’re given a division calculation, but instead of the quotient or the number we get when we divide two numbers together being missing, we can see that the first number is missing. This is the number that we’re dividing by three. What number if we divide it by three would give us an answer of seven? Let’s think about what this means for a moment. We could think of this in two ways. Firstly, what number if we divide it into three equal groups will give us seven in each group? Or we could think of it as, which number if we divide it into groups of three will give us seven groups?

They’re both ways of thinking about the same division. And if we look at these models we’ve drawn, can you see what we can do to find the answer? In the first model, we’ve got three groups of seven. And so we could find the total amount by thinking of the multiplication fact three times seven. And in the second model, we’ve got seven groups of three. So we could find the total amount here by working out seven times three.

Now if there’s one thing we know about multiplication, it’s that we can switch the numbers around and they’ll still make the same answer. So three times seven is exactly the same as seven times three. Do you remember your three times table? What is seven times three? Seven threes are 21. And so we also know that three times seven is 21 too. And we can use this fact to help us complete the division. 21 divided by three equals seven. Our missing number is 21.

What have we learned in this video? We’ve learned how to divide by three using different strategies to help. These have included using models, number lines, or times tables facts to help.

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