Lesson Video: Dividing a Two-Digit Number by a One-Digit Number: Breaking Apart Tens and Ones | Nagwa Lesson Video: Dividing a Two-Digit Number by a One-Digit Number: Breaking Apart Tens and Ones | Nagwa

Lesson Video: Dividing a Two-Digit Number by a One-Digit Number: Breaking Apart Tens and Ones Mathematics • 4th Grade

In this video, we will learn how to divide a two-digit number by a one-digit number by using models and breaking apart the numbers.


Video Transcript

Dividing a Two-Digit Number by a One-Digit Number: Breaking Apart Tens and Ones

In this video, we’re going to divide two-digit numbers by single digits. And we’re going to do this by using models and by breaking apart the numbers. One of the methods that we can use to divide by a one-digit number is taking multiplication facts we already know and using these to help. So, for example, if we want to find the answer to 16 divided by two, we just need to recall that eight twos are 16. And then we can say that 16 divided by two equals eight.

But what if we need to divide a larger two-digit number by a single digit? What if we can’t think of a multiplication fact straight away to help us? Let’s imagine that we want to find the number of twos in 48. 48 divided by two equals what. Even though we can use multiplication facts to help, what if we’ve only learned our times tables up to 10 times two is 20 or 12 times two is 24? We need to know how many twos there are in 48. What are we going to do? Well, as we see in maths again and again, we don’t need to use numbers as they are. We can break them up into smaller pieces to help us. And that’s exactly what we’re going to be doing in this video.

We’re going to be partitioning or breaking apart the two-digit numbers to make them easier to divide. In this calculation, the number we’re dividing is 48. Now if we want to split up the number 48 into smaller parts to make it easier to divide, what’s a quick way we could do it? Splitting it into its tens and ones is pretty quick, isn’t it? Let’s see if this helps us. 48 is made up of four 10s or 40 and eight ones. So one way we could split up 48 is into 40 and eight. Now there’s no point doing this unless it’s going to make our division easier.

But we need to stop at this point and ask ourselves a question. Can we divide both of our parts by two? Are they both multiples of two? Because if they’re not, we need to find another way to split up the calculation. We haven’t made it easier for ourselves at all. Now one thing we know about multiples of two is that they’re always even, and this makes it really easy to spot them. We could see straight away that both 40 and eight are even numbers. So we are going to be able to divide them by two. Let’s use the place value blocks to help us.

If we divide four tens by two, there’ll be two tens in each part. And so we know 40 divided by two equals 20. And if we divide eight ones by two, we’re going to get four ones. Eight divided by two equals four. Now can you see what we need to do to find the overall answer? We need to put our two parts back together again. We said that half of 40 is 20, half of eight is four, and so half of 48 is 24. 48 divided by two equals 24. But what if splitting a number directly into its tens and ones doesn’t help us? A good example of this might be a calculation, something like 45 divided by three. Watch what happens when we try to split it up directly into its tens and ones.

45 can be split into four tens and five ones. But we can see this isn’t going to help us at all. Neither 40 or five are numbers in the three times table. So if we try to divide these parts by three, we’re gonna have bits left over. We haven’t made the division easier at all. We’re going to need to break apart 45 a different way. Now we know there are all sorts of ways to split up the number 45. So what have we got to do? There must be a quicker way than just seeing how we can split 45 up again and again until we just come across an answer where both of the parts are multiples of three.

A good place to start is to keep this idea of tens and ones, but to look for a multiple of 10 that’s also a multiple of the number we’re dividing by. In this example, we look for a number that’s a multiple of 10 and also multiple of three. And three times 10 is 30. So we can split 45 into 30 and 15. And our knowledge of the three times table tells us that both these numbers are multiples of three. We found a way to break apart 45 to make it easier to divide by three. Now we can get on and work out the answer. We know that 10 threes are 30, so 30 divided by three equals 10. And we know that five threes are 15, so 15 divided by three equals five. And if we add our two parts back together, 10 plus five equals 15.

We split up the number so that there were 10 threes in this part and five threes in this part. This is how we know there are 15 threes in the whole amount. 45 divided by three equals 15. The big difference between this question and the last example is that breaking apart our number into its tens and ones didn’t help us here. We needed to give the breaking apart step a little bit more thought and find a way to split up 45 so that both parts were multiples of three. And it’s probably fair to say that in most divisions we’re going to need to do this. Not all divisions split neatly into their tens and ones. In fact, this skill is so important. Let’s practice it on its own for a second.

Here are two more divisions. Now we’re not gonna be answering these, so don’t worry about that. But let’s just ask ourselves a quick question. How would we split up these two-digit numbers to make the division easier? Let’s just practice this skill. In the first calculation, we’re being asked to divide 72 by six, and if we break apart 72 into its tens and ones directly, this is going to give us 70 and two. These aren’t multiples of six, and this hasn’t made the calculation easier for us at all. So let’s try the idea that we talked about earlier. Let’s look for a multiple of 10 that’s also a multiple of six.

We know that six times 10 is 60. So we’ve got a part here that’s quite large, but also quite easy to divide by six. And if one of our parts is 60, we know the other one must be 12 because 60 plus 12 makes 72. And so if we wanted to, we could then get on and answer the question. Probably the most helpful way to spit up 72 is into 60 and 12. Our second example is 96 divided by four. And again, we’re not going to work out the answer here. We’re just going to practice our skill of seeing how we can spit up the number. And again, we can see straightaway that breaking it apart into its 10s and ones isn’t going to help us. 90 and six are not multiples of four.

Remember that to help us, we can think of a multiple of 10 that’s also a multiple of four. And four times 10 is 40. And if one of our parts is 40, the other one is going to have to be 56 because 40 plus 56 is 96. Now both these numbers are multiples of four, but we haven’t made this calculation a lot easier, have we? We’ve still got to work out 56 divided by four, which is quite a large number. And in an example like this, it might be easier to split up the number a different way. So we could say to ourselves, “Well, I know what 40 divided by four is, so it’s going to be pretty easy for me to find out what double this is, what 80 divided by four is.” So I could split up my number into 80 and whatever is left, which is 16.

These two numbers are also multiples of four, but they’re a little bit easier and a little bit quicker to work with. We’re going to have a go at answering some questions now where we actually have to find out the answers. But hopefully you found what we’ve just done here are useful. We’ve taken a moment not to find out answers, but to think about how we would find those answers. It’s always useful to think about how we can break apart a number to help. So let’s try these questions then.

Divide into three groups. 33 divided by three equals what.

In the picture, we can see a number that’s been modeled out of base 10 blocks. And when we read the instruction, divide into three groups, it’s this number that it’s talking about. It’s a number made from three 10s and three ones. It’s the number 33. And we can write what we need to do here in a number sentence. 33 divided by three equals what. Because our number 33 has been modeled for us in base 10 blocks, it’s already being broken up into its 10s and ones. And because there are three of each, hopefully you can see it’s going to be quite easy to split them up.

Let’s divide our 10s first of all. 10, 20, 30. We’ve got one 10 in each group. 30 divided by three is 10. Now let’s divide our ones blocks. One, two, three. Three divided by three equals one. Each of our groups has one 10 and one one. We’ve divided 33 by three by modeling it using place value blocks, then dividing the tens and the ones separately. 33 divided by three equals 11.

Use the following part–whole model to find 84 divided by three.

Often, we can use times tables facts we already know to help us with a division. But do you know a times tables fact that’s going to help you find 84 divided by three? It’s quite a large two-digit number we need to divide, isn’t it? And that’s why in this question we’re shown how to split it up into smaller parts to help us. The whole amount in the part–whole model that we’re given is 84; it’s the number we’re dividing. And we can see it’s been split into two parts, 60 and 24. Now, often when we break apart two-digit numbers to make them easier to work with, we split them up into their 10s and ones. But with this calculation, it would have meant splitting up the number into eight 10s or 80 and four ones.

But if our part–whole model had shown 80 and four, we’d have found it really difficult to divide by three. Neither of these parts are multiples of three. And that’s why we’ve been given this particular part–whole model to help us. Both 60 and 24 are multiples of three. And they’re also multiples of three that we already know facts for. So we can divide each part by three to help us find the overall answer. First of all, how many threes are in 60? Well, this is still quite a large number, but we know a fact that can help us. We know that 10 threes are in 30. 30 divided by three equals 10. And so, if we double 30 to get 60, we double the number of threes that we have.

60 divided by three equals 20. Now we need to divide the second part by three. How many threes are there in 24? Three, six, nine, 12, 15, 18, 21, 24. There are eight threes in 24. We found out there are 20 threes in 60 and eight threes in 24. And 20 plus eight equals 28. We’ve used the part–whole model to find that 84 divided by three equals 28.

Mason spilled ink over his division homework. What number is the arrow pointing at?

We can see if we look quickly at Mason’s division homework here, he hasn’t just had to do one thing to find out the answer. He’s had to complete several steps. But unfortunately, because he spilled ink over his homework, the final answer and some of the other numbers he uses in his working out have been covered up. Interestingly, our question doesn’t ask us to find a final answer. We need to find the number that the arrows pointed at. This is one of the numbers that Mason uses along the way. Possibly the best way of finding out this missing number is to think as if we were Mason. We could go through the whole calculation step by step as if we were him and find all the missing numbers. Then we can understand what he was trying to do.

To begin with, we can see the division that Mason is trying to work out is 42 divided by three. And underneath the number 42, he’s drawn a part–whole model. And we can imagine the sorts of thoughts that would have gone through his head as he did this. He must have thought to himself, “Well, 42 is quite a large two-digit number.” Perhaps he only knew his three times tables facts up to 10 threes are 30. And so he’s clearly thought to himself, “I need to split up the number 42 into easier parts, parts that I can still divide by three.” Now although one of the parts has been covered over when Mason spilled his ink, we can see that the first part is 30.

And what number goes together with 30 to make 42? 30 and 12 make 42, don’t they? And we know that both 30 and 12 are numbers in the three times table. They’re multiples of three. And they’re a bit easier to divide by three than 42. And Mason knows that if he divides both parts by three and then adds his answers together, he’s going to find the overall answer. In other words, 30 divided by three plus the answer to — Oh dear. Here’s another ink splotch. Can you see what this missing number is? It’s the same as the first one, isn’t it? It’s talking about our second part and dividing it by three. That’s better.

To find his answer, Mason needs to divide 30 by three, 12 by three, and then add the two together. And in the next step, this is what we can see he starts to do. We know that there are 10 threes in 30. That’s where the number 10 comes from here. And now we’ve got another ink splotch. This is going to be the answer that we get when we divide 12 by three. Three, six, nine, 12. There are four threes in 12. So 12 divided by three equals four. Now we found out the answer to this particular question because we found the missing number. But it would be a shame not to complete the calculation, wouldn’t it? 10 plus four equals 14.

So Mason has found out the answer to 42 divided by three by breaking apart 42 into two easier numbers. What made them easier to work with is that they’re both smaller than 42 and they’re both multiples of three. So Mason could just use multiplication facts he already knew to help him. By going through the problems step by step, we knew that the missing number was going to be the answer to one of our parts divided by three. And that part was 12, and because 12 divided by three equals four, we know that’s the number that the arrow is pointing at. The answer is four.

So what have we learned in this video? We’ve learned how to divide a two-digit number by a one-digit number by breaking up the number to help.

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