Lesson Video: Column Subtraction of Three-Digit Numbers: Regrouping Hundreds Mathematics • 2nd Grade

In this video, we will learn how to subtract from three-digit numbers when we have to regroup a hundred and record the calculation in columns.


Video Transcript

Column Subtraction of Three-Digit Numbers: Regrouping Hundreds

In this video, we’re going to learn how to subtract from three-digit numbers. And we’re going to do this where we have to regroup 100. Each time we’re going to record the calculation using column subtraction.

Before we begin calculating, there’s a fact we’re going to find useful in this video. It’s a fact you probably already know, but it’s worth reminding yourself of. This fact is that we can represent the same number, using hundreds, tens, and ones, in different ways. Just as a quick example, we could show 429 as four 100s, two 10s, and nine ones or, in other words, 400 plus 20 plus nine. But we could take one of our hundreds and exchange it for 10 10s because 10 10s are the same as 100. So now we’d only have three 100s blocks, and we’d have to show that fourth 100 using 10 10s blocks. Then we’ve got our two 10s from before and our nine ones.

This time, we’ve modeled that 300 plus 12 10s, or 120, plus nine also equals 429. And you know, the most important part of this important fact are these three words here. Although we’ve modeled the number in different ways, we’ve regrouped our 100, it represents the same number. If I have this collection of blocks and you have this collection of blocks, we both have exactly the same value. But the fact that numbers can be regrouped and partitioned in different ways is really going to help us when we’re faced with some tricky subtractions. Let’s see how.

Now, at first glance, this might not look like a tricky subtraction. The two three-digit numbers have been written in columns for us, so we know that we can use column subtraction to find the answer. It’s always useful to know what method to use, isn’t it? The second number, 241, is smaller than the first number, 536, so we know that we can take it away. Everything’s being set out correctly. What could go wrong? We just need to subtract the ones and the tens and the hundreds. Six ones subtract one one leaves us with five ones. Onto the tens. Three 10s subtract four 10s equals — wait a moment. How can we subtract four 10s if our first number only has three 10s in it?

As we’ve said already, we can definitely take away 241 from 536 because it’s a smaller number, so it definitely can be done. But this tens column is a bit of a problem. What do we do if we need to subtract more 10s than we have? Let’s use place value blocks to help solve this little problem. Our starting number, that’s the number that we’re going to subtract 241 from, is made up of five 100s, three 10s, and six ones. And this is a much bigger number than 241, so we know we can definitely subtract 241 from it. It’s just that we don’t have enough 10s. What can we do about this? Is there a way that we could show the number 536, but with more tens than we have already? This is where that important fact that we went over at the start of this video comes in useful.

We know that we can show numbers in different ways, but they can be still worth the same value. And one way we could do this with the number 536 and increase our number of tens is if we took one of our 100s blocks and swapped it for 10 10s because we know that 10 lots of 10 is 100. Let’s regroup our number in this different way then. First, we’ll take one 100s block. We now have four 100s, but we need to regroup this 100 as 10 10s. Here are our 10 10s. So at the moment, we can see the number 500 modeled out of base 10 blocks. It’s just been modeled in a different way. Here are our three 10s that we already had in the number, and here are our six ones. Let’s show exactly what we’ve done with these place value blocks in our column subtraction at the top.

We know we needed to regroup the number so that we saw more tens in the tens column, so we looked to the hundreds place. We took one of our hundreds, so we now have four 100s, and we exchanged that 100 for 10 10s. So instead of three 10s, we now have 13 10s. And four 100s, 13 10s, and six ones is exactly the same number as 536. We’ve just regrouped it in a way that will help us subtract those tens. So we’ve already subtract the ones. Six ones subtract one one leaves us with five ones. We’ve got plenty of tens to subtract those four 10s from. 13 10s take away four 10s leaves us with nine 10s. And in the hundreds column, we need to subtract two 100s from four 100s, which leaves us with two 100s.

By the way, this last column shows us exactly why we always start by subtracting the ones. If we’d have seen this calculation to begin with and someone had asked us, “How many hundreds do you think there’ll be in the answer?,” if we’d started off by looking at the hundreds column, we’d have seen five 100s subtract two 100s. And we’d have said to ourselves, “Well, the answer is going to be three hundred and something.” But as it turns out, we needed to regroup one of our hundreds.

So in the end, we only had four. This is why we always start with the ones and move from right to left whenever we’re doing a subtraction, just in case we need to regroup and things change. Now, these place value blocks were quite helpful in helping us to understand what was going on. Let’s try answering a couple of questions now where we’re given some place value blocks to help us understand the regrouping that we’re going to need to do. Here is the first.

Jackson is using place value blocks to help him subtract 30 from 223. Finish the calculation and tell him the answer.

In this question, we’re told that Jackson is wanting to subtract a two-digit number from a three-digit number. He wants to find the answer to 223 subtract 30. And the first thing that we can see about how he’s tried to work this out is that he’s written the calculation vertically. In other words, he’s written both numbers so that the hundreds, the tens, and the ones digits are all in the right columns. He’s using column subtraction. Now, we’re also told that Jackson’s using place value blocks to help him. And we can see these in this place value grid here. Now, why does he need to use place value blocks? Surely, he can just subtract the ones, then the tens, then the hundreds using this column subtraction.

Well, perhaps the best way to understand what Jackson’s done here is to try working out the answer using column subtraction and see how far we get. First, let’s subtract the ones. 223 contains three ones. And there are no ones in 30. So we’ve got nothing to take away here. We started off with three ones, and we’re going to end with three ones. Now moving on to the tens column, 223 has two 10s, but we need to subtract three 10s. And we might think to ourselves, “Well, this isn’t possible. We can’t subtract a number that’s larger than the one we want to subtract from.”

But if we look at the two numbers in the calculation, we can see that this has got to be possible. 223 is a lot larger than 30. So of course, we can take 30 away from it. The problem is that we don’t have enough tens in our tens column; that’s all. And this is where Jackson’s place value blocks come in useful. If we look carefully at the place value grid, we can see what he’s done here. First of all, he’s modeled his starting number. 223 is made up of two 100s, two 10s, and three ones. And as we’ve just said, he hasn’t had to subtract anything from his three ones. And that’s why we can see them here in his place value grid.

But when it came to trying to subtract three 10s from the two 10s in 223, Jackson had a problem. He doesn’t have enough 10s. What can he do about this? Well, if we look closely at his place value grid, we can see what he’s done about this. Jackson has taken one of his 100s, and he’s regrouped it into 10s. He knows that 10 times 10 is 100, and so he could just exchange 100 for 10 10s blocks. Now he does have enough 10s to subtract three 10s from. And his number is still worth 223. It’s just being partitioned differently. Let’s go through his column subtraction and show exactly what he’s done to help himself. So he’s got to the tens column, and he realizes the way the number’s being partitioned at the moment. He can’t subtract three 10s.

So he takes one of his 100s. Now, instead of two 100s, he has 100. And he exchanges it for 10 10s. So instead of two 10s, in the tens column, he now has 12 10s. Now there are different ways of recalling this in a column subtraction, but, in this question, we’ve been given two little boxes at the top. So we’ve completed these. So we still have the number 223. But it’s just been made up of one 100, 12 10s, and three ones. Now we can subtract those tens. 12 10s subtract three 10s leaves us with nine 10s. And in the hundreds column, we’ve got no 100s to take away. So this digit is going to stay the same. But remember, instead of two 100s, we now only have one. So 100 take away no 100s is going to still be 100.

In this question, we found that subtracting 30 from 223 was quite tricky because the number 223 doesn’t have enough 10s in the tens place. We looked at the place value blocks and understood that what we needed to do was to regroup 100 into 10 10s. And by doing this, we just made the number 223 a different way. 223 subtract 30 equals 193.

What is 336 subtract 45? Hint: Use place value blocks to help you regroup.

In this problem, we’re asked to subtract 45 from 336. And one of the useful ways that we can subtract from a three-digit number like this is by setting out the calculation as a column subtraction. This allows us to subtract the ones, then the 10s, and the 100s separately. We’ve also been given a place value grid here containing place value blocks. And they show our starting number. 336 is made up of three 100s, three 10s, and six ones. Now we’re given a hint here. We’re told to use our place value blocks to help us regroup. So let’s go through this column subtraction step by step. And as soon as we need to use our place value blocks, we will do so.

First, let’s subtract the ones. 336 contains six ones, and 45 contains five ones. And if we take away five ones from six ones, we’re left with one one. That was simple enough. We didn’t need to use our place value blocks, did we? Let’s take away five of our six ones, though, just to show what we’ve done. There we go. We got one one left. Now it’s time to take away the 10s. 336 contains three 10s, and 45 contains four 10s. But wait a moment. The number of tens that we need to subtract is greater than the number of 10s we have. Doesn’t look like we can do this, does it? But when we stop and look at the two numbers in this subtraction, we can see we definitely can take away four 10s from 336. It’s just that we can’t subtract them at the moment with the way that we’ve modeled this number.

This is where our hint comes in handy. We’re going to need to regroup 336 so that we have enough tens. At the moment, we have three 100s, so we can take one of those 100s. So instead of three 100s, we now have two in the hundreds place. And we can write this digit two in the box above. But we need to do something with that 100 because we want the value to still be worth 336. So we’re going to have to exchange that 100 for 10 10s. 10 10s are the same as 100. There we go. Now instead of three 10s, we’ve got 13 10s. And we’ll write this in the box above too. Our hundreds digit has gone down from three to two. So it might look like our number’s become less.

But when we stop and read it, we can see that it says two 100s, 13 10s, and six ones. And this is exactly the same as 336. It’s just been partitioned in a different way, in a way that allows us to subtract those four 10s that we need to take away. So let’s do that. 13 10s take away four 10s leaves us with nine 10s. And now we don’t have any 100s to take away, but we must remember we have two 100s and not three. So we still have two 100s. To help us subtract the number of 10s that we needed to, we regroup the number 336 to help us. 336 subtract 45 equals 291.

Now we’ve tried a couple of examples where we’ve used place value blocks to help us. Do you think you’re able to regroup without place value blocks? Of course you can. Let’s have a go and see how quick it can be.

Find the result of the following: 865 subtract 384 equals what.

We don’t really need to think about which method we want to use to find the answer to the subtraction. It’s been set out as a column subtraction already for us. So we’ll use the standard written method. First, we subtract the ones. 865 has five ones, and 384 has four ones. And the difference between five ones and four ones is one one. Onto the tens. 865 contains six 10s, and 384 contains eight 10s. At the moment, we can’t subtract eight 10s. We don’t have enough 10s in our tens column. We’re going to need to regroup our starting number. We’ll start by taking one of our 100s. Instead of eight 100s, we now have seven 100s. And we need to regroup this into 10 10s. So instead of six 10s in our tens column, we can put a little one to show we have 16 10s.

We haven’t changed the value of our starting number at all. Seven 100s, 16 10s, and five ones are exactly the same as 865. But by regrouping the number like this, we do have enough 10s to subtract eight 10s. So we have 16 10s; we need to take away eight 10s. We know that eight and eight makes 16, so we’re going to be left with eight 10s. Finally, the hundreds, 865 has eight 100s, and 384 has three 100s. But don’t forget, we’re not subtracting three from eight 100s because we’ve exchanged one of our 100s. We’ve only got seven 100s left in the hundreds place. So seven 100s subtract three 100s leaves us with four 100s. 865 subtract 384 equals 481.

Now what have we learned in this video? We’ve learned how to subtract from three-digit numbers using column subtraction, where we have to regroup 100.

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