Lesson Video: Dividing by 7 Mathematics • 3rd Grade

In this video, we will learn how to use various strategies to divide by 7 within the known times tables up to 12 × 7, including using models and the times tables facts.

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Video Transcript

Dividing by Seven

In this video, we’re going to learn how to use different strategies to divide by seven. These are going to include things like using models and also applying times tables facts that we already know to help. Let’s begin by thinking about what it means to divide by seven, and we’ll start with the question, “What’s 14 divided by seven?”

Now whenever we’re dividing, it doesn’t matter what number we’re dividing by. We can think of it in one of two ways. We’re either sharing or grouping. Let’s show what we mean by this because it will really help us when it comes to working out the answer to divisions. Here’s our starting number 14 as represented by 14 fish. Now, if we think of 14 divided by seven as sharing, we need to share our 14 fish into seven equal groups. When we divide by sharing, we’re finding the number in each group. This is what the answer represents. Let’s try splitting our fish into seven equal groups then. What’s going to happen.

We could start off by sharing one fish into each group. That would mean seven of our fish were shared out, and if we share another fish into each group, that’s all 14 of them. Two, four, six, eight, 10, 12, 14. So one way to think of our division is us sharing 14 fish into seven equal groups. And we’ve found the number in each group. There are two fish in each group, aren’t there? 14 divided by seven equals two. But you know, we can also think of our division in another way. We call this grouping. Instead of splitting themselves into seven equal groups, our fish could decide to split themselves into groups of seven. This time, we know how many there’ll be in each group; there’ll be seven.

But we need to find the number of equal groups. How many sevens are in 14? And we can find the answer by counting in sevens. One group of seven is seven, and two groups of seven are 14. If the fish split up into groups of seven, they’ll make two equal groups. 14 divided by seven equals two. It’s exactly the same answer we’ve found, but the number two means two different things depending on whether we’re sharing or grouping. With this question, we’ve used pictures to help us, but there are other strategies we could’ve used.

Let’s imagine that we want to find the answer to 42 divided by seven. As we’ve seen already, one way that we can think of dividing by seven is that we’re trying to find out how many sevens there are in the number. So we could ask this division slightly differently. How many sevens are in 42? We could find the answer by counting in sevens. We could start at zero and count forwards in sevens until we eventually get to the number 42. Or we could start with 42 and do the same thing but backwards: keep subtracting seven until we eventually reach zero. Let’s try this second method, repeated subtraction.

Let’s start at 42 and see how many sevens we need to take away to get back down to zero. 42 take away seven equals 35. 35 subtract seven equals 28. If we take away one more lot of seven from 28, we have 21 left. 21 subtract seven equals 14. And we know from our last example how many sevens there are in 14, don’t we? We need to subtract two more lots of seven. And then we’ve reached zero. Did you notice how many sevens we needed to subtract? One, two, three, four, five, six. There are six sevens in 42, and so we can say 42 divided by seven equals six.

Now, to find this answer, we’ve just had to do quite a few subtractions, haven’t we? 42 take away seven, 35 take away seven, and so on. But did you notice something about the numbers that we reached each time? These are all numbers in the seven times table. They’re all multiples of seven. And so, if we know our multiples of seven, we don’t need to subtract. We just need to count backwards and keep making jumps. And we call this skip counting. Let’s skip count six times just to show how many sevens there are in 42. So we can say 42 and then 35, 28, 21, 14, seven, zero. If we know our multiples of seven, skip counting is much quicker than repeated subtraction.

But you know there’s an even quicker method that we could use to find out how many sevens there are in a number. And it’s another strategy that we could use. It’s probably fair to say that it’s actually the quickest way to divide by seven, if we know how to. As I’m sure you know already, addition and subtraction in maths are opposites. They’re what we call inverse operations. But did you know the same is true of multiplication and division? They’re opposite to each other. We could think of multiplication as making lots of equal groups to find out the total. And we could think of division as starting with the total and splitting it up into equal groups. And this means that when we’re faced with a division question like this, we can use multiplication facts we already know to help us.

And because in this video we’re thinking about dividing by seven, we need to brush up on our seven times tables facts. Let’s stick with the same question where we’re dividing 42 by seven. And if we want to use multiplication facts to help, we need to ask ourselves something. It’s a similar question to the one the blue fish is asking, how many sevens are in 42? Except this question mentions multiplication. What can I multiply by seven to give the answer 42? Something times seven is 42. And if we know this fact, we can solve the division. Now perhaps you know this fact straightaway, but even if you don’t, we could start at one times seven and keep working through until we get an answer of 42.

One times seven is seven, two sevens are 14, three times seven equals 21, four times seven is 28, five times seven is 35, and six times seven equals 42. Now that we’ve reminded ourselves about this multiplication fact, let’s think what it means. If six times seven equals 42, this means there are six lots of seven in 42. And if we want to start with 42 and split it up into groups of seven, there’ll be six of them. What a quick way to find the answer! If we know six times seven equals 42, then we know 42 divided by seven equals six. Now so far, we’ve just been thinking about finding out how many sevens there are in 42. This is grouping.

But what if we were thinking of our division as sharing. Well, we can use what we know about multiplication here as well. If we know that six times seven equals 42, we also know that seven times six equals 42. Because we can think of this as seven groups of six, we know that if we share 42 into seven equal groups, there’ll be six in each group.

We’re going to answer some questions now where we need to put into practice everything we’ve learned about dividing by seven. And let’s try some of the different strategies we’ve learned too. We’ve learned how to divide by seven by using repeated subtraction, also, how we can do this a little more quickly if we skip count. We’ve used models to help us like these arrays. And finally, we’ve seen how important it is to know our seven times tables because we can use these multiplication facts we already know to help us divide by seven. Let’s try some questions then.

Find 28 divided by seven using the cubes shown.

This question tests whether we know how to divide by seven, and we’re told how to find the answer. We need to use the cubes that are shown. Now these cubes, and there are 28 of them, aren’t just set out any way. They’ve been laid out in an array. And we can use arrays like this to help us solve division problems. Let’s think for a moment about what dividing by seven means. We can think of the division in two different ways, and we can use the array to show these two ways. Firstly, we can think of our calculation as 28 shared into seven equal groups. Can you see a way to share our array into seven equal groups? If we look closely, we can see that there are seven columns in our array. So we could think of each column as being one of our seven equal groups. And the answer to our division is going to be the number of cubes in each group. Can you see how many there are?

If we share 28 cubes into seven equal groups, there’ll be four cubes in each group. 28 divided by seven equals four. But you know, we can use our array to find the answer a different way. We can think of it as 28 grouped into sevens. And once again, we can use our array to help us. As we’ve seen already, our array has seven columns, but we could think of this fact a different way. If we concentrate on the rows and not the columns, we can say that each row contains seven cubes. So we can see that there are one, two, three, four groups of seven.

This time, we know the number in each group, but our answer tells us the number of sevens there are in 28. We found the answer to 28 divided by seven by using the array. And we’ve shown that we can think of this division in two different ways but still get the same answer. If we share 28 into seven equal groups, there’ll be four cubes in each group. Or if we group 28 into sevens, there’ll be four equal groups. 28 divided by seven equals four.

Find 56 divided by seven using the given number line.

How can we divide a number by seven? In this question, we need to divide 56 by seven. But we’re also given something to help us because one way we can divide by seven is by using a number line. Where do you think our number line begins? Well, if we’re looking at it from left to right, we could say it begins at zero. But if we’re thinking about what’s happening on our number line, we can see that the action begins at the number 56. We can see that we start at the number 56 and then keep subtracting seven again and again, until eventually we arrive back at zero.

Why might we want to take away lots and lots of sevens from 56? Well, we can think of our question as asking us, how many sevens are there in 56? And we can count these sevens by starting at 56 and keeping subtracting seven. Let’s see how many jumps backwards of seven it takes us to get from 56 to zero. 56 take away seven equals 49. If we take away another lot of seven, we’ll have 42. 42 subtract seven equals 35. 35 subtract seven equals 28. If we take away another lot of seven, we’ll have 21 left. 21 take away seven equals 14. 14 subtract seven equals seven. And this leaves us with one more lot of seven we can take away before we get back to zero.

We’ve subtracted sevens eight times. And this took us from 56 to zero. So we can say that there are eight sevens in 56. We could even make eight jumps in the opposite direction from zero up to 56. So we could say zero and then seven, 14, 21, 28, 35, 42, 49, 56. We’ve used repeated subtraction on the number line to help us find the number of sevens that there are in 56. 56 divided by seven equals eight.

Find the quotient.

This is a really interesting question because although we can see some numbers, we can’t see any of the four symbols we’d often see when we’re doing a calculation. There’s also a tricky word. Find the “quotient.” So before we start, let’s go over what this tricky word means and also why these numbers are being written this way. The word “quotient” means the result when one number is divided by another. You know how we use the word “total” when we add two numbers together, and the answer is the total. Or “product,” when we multiply two numbers together, the answer is the product. Well, if we divide two numbers, the answer to that is the quotient.

So the first thing we can say about this question is that it’s a division calculation. And the way that it’s been written is just a way that we can sometimes write divisions. This is the number we’re starting with, 35. And the number on the left is always the number we’re dividing by. This question is just another way of asking us, what’s 35 divided by seven? Or if you want to read the numbers from left to right, how many sevens are there in 35? We can use our knowledge of multiplication to help us here because division and multiplication are inverse operations. They’re opposites. If we know the number that we multiply by seven to get 35, then we know the number of sevens there are in 35.

Let’s go through our seven times tables facts. One times seven is seven, two sevens are 14, three sevens are 21, four times seven equals 28. And here’s the fact we’re looking for: five sevens are 35. And if we know that five times seven equals 35, we also know that the number of sevens that there are in 35 is five. In this question, we’ve used our knowledge of a seven times tables fact to help us divide by seven. Five times seven equals 35. And so we know 35 divided by seven equals five.

Complete the missing number. What divided by seven equals nine.

In this question, we’re given a number sentence that’s all about dividing by seven. But we don’t have to divide by seven to find the quotient or the answer. We already know it. Our missing number is the dividend; it’s the first number in the division, the number that we divide. What number, if we divide it by seven, will give us nine? To help us, we could use multiplication facts and our knowledge of the seven times table. If we start with a number divided by seven and the answer is nine, can you see how you might find the starting number? Bar models are so useful, aren’t they?

And we can see with this one that to find our starting number or our dividend, we need to find seven lots of nine. What is seven multiplied by nine? Well, we know that seven multiplied by 10 or 10 lots of seven equals 70. And so seven lots of nine or nine lots of seven is going to be seven less than this. And seven less than 70 equals 63. We found our multiplication fact to help us solve the problem. Because we know that nine times seven equals 63, we know that 63 divided by seven equals nine. Our missing number is 63.

What have we learned in this video? We’ve learned different strategies to help us divide by seven. These have included using models, using repeated subtraction or skip counting, and applying multiplication facts we already know to help.

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