Lesson Video: Multiplying a Two-Digit Number by a One-Digit Number: Column Method without Regrouping Mathematics • 4th Grade

In this video, we will learn how to use the standard algorithm to multiply a two-digit number by a one-digit number for calculations where there is no regrouping.

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Video Transcript

Multiplying a Two-Digit Number by a One-Digit Number: Column Method without Regrouping

In this video, we’re going to learn how to use the column method to multiply a two-digit number by a one-digit number. And we’re going to do this for calculations where we don’t need to regroup.

How many times tables facts do you know off by heart? If we take the two times tables as an example, you’ve probably learned up to 10 times two, maybe even gone as far as 12 times two. But what happens if we want to multiply larger numbers by two? What if we start to go into the teens like 13 times two or 14 times two? What if we go beyond the teens numbers into other two-digit numbers like 21 times two or 43 times two? Do we have to memorize every single fact? Well, thankfully not. We can use something called the column method or short multiplication to help.

Let’s imagine that we’ve been asked to multiply 14 by two. We know that 14 is a two-digit number, and it’s slightly beyond the facts we usually memorize. Let’s start by modeling the number 14 in a place value table. It’s made up of one ten and four ones. Now, to multiply 14 by two, we can think of these two parts, the ten and the ones, separately. In other words, we can take the ones and multiply them by two, and we can take the ten and multiply it by two. And by breaking up the number into its tens and ones, it makes it a little bit easier to multiply.

And now we’re able to multiply each part in turn using facts that we already know. First, let’s multiply the ones. We have four ones, and we know that four times two is eight. So we know our answer is going to have eight ones in it. And now the tens, we only have one ten, so this is worth 10. And 10 times two is 20. Can you see the two facts that we already know that we used to help us? We found the answer by using four times two and also 10 times two. And our answer has got two tens and eight ones. It’s 28. And so we can say that 14 times two equals 28.

Now we wouldn’t call this the column method, so let’s have a go at another multiplication. This time we’ll carry on using place value blocks, but we’ll start to set out our work using the column method. This time let’s imagine we’ve been asked to find the answer to 23 times three. Again, this is a little bit larger than the times tables facts we’ve memorized for our three times table. So we’re going to need to use the column method to help us. And just like using the place value blocks in our first example, using the column method to write out the calculation helps us to see the tens and the ones separately.

We know that 23 is made up of two tens and three ones, and we’re being asked to multiply this number by three. And what you can see over here is what the column method looks like. We’ve got our two-digit number, then we got a multiplication sign to tell us that we’re multiplying. And then we’ve got our one-digit number that we’re multiplying it by, and then of course this line, which acts as the equals sign, underneath which we put our answer. Do you know why we call this the column method? Well, it’s because by writing our numbers on top of each other like this, it helps us to think of them in columns, the ones and the tens. And normally, we wouldn’t draw dotted lines like this, but maybe they’ll help. So let’s keep them for this example.

Now just like when we were working with the place value blocks, we’re going to start by multiplying the ones. 23 has a three in the ones place, so we need to start by multiplying three by three. And we know that three times three equals nine, so we can write the digit nine in the ones place of our answer. It’s going to have nine ones in it.

Now, if we look at the tens digit, we can see that 23 has a two in the tens place. Can you see we’re working column by column, aren’t we? So what are two 10s multiplied by three? Well, again, we can use facts we already know to help us. We know that two times three is six, and so two 10s times three is the same as six 10s or 60. So we need to write a six in the tens place, and that’s all we have to do. We’ve multiplied the ones by three and then the tens by three, and we can read our answer along the bottom. 23 times three is 69.

Let’s have a go at answering some questions now where we have to multiply two-digit numbers by a one-digit number. Each time, we’re going to use the column method. Perhaps for the first question what we’ll do is we’ll use some more maths equipment to help model what we’re doing. But then, for the next couple of questions, we’ll try using the column method all on its own. Ready? Here we go.

Solve the following: 23 times two equals what.

Now, perhaps you’ve learned your two times tables facts up to 10 times two or maybe even 12 times two. But what happens when we need to multiply larger numbers by two? Well, in this question, we’ve got a two-digit number, 23, and we need to multiply this by two. And we can see, first of all, that the way that these numbers have been written they’re on top of each other. And by writing the numbers in columns like this, it helps us to see the tens and the ones digit separately. Let’s begin by thinking about the tens and the ones in our first number. The number 23 is made up of two tens and three ones. And to solve the problem, we can multiply these two parts of our two-digit number separately.

We can start by looking at the ones. What are three ones multiplied by two? Well, we know that three times two is six. So in our column addition, we can write the digit six in the ones place of our answer underneath the equal sign. Our answer is going to have six ones in it. Now that we’ve multiplied the ones part of our number, we can multiply the tens part. And if we look at the tens column in the number 23, we can see the digit two. And we must always remember, although it looks like we’re multiplying two by two, what we’re really multiplying is two 10s by two because the two is in the tens place.

You know, as long as we understand that we’re multiplying two 10s, we can use the fact two times two to help us. We know that two times two is four. So two 10s times two equals four 10s. And we can show this by writing the digit four in the tens place. And if we look at both our place value counters that we’ve used to help us but also the column multiplication, we can see the same answer. It has four tens and six ones. We’ve found the answer to 23 times two by using the column method. Although we used place value counters to help us model what we’re doing, we didn’t have to. 23 multiplied by two equals 46.

This robot multiplies any number by three to get an answer. What would the answer in the following case be? 32 times three.

In the picture, we can see a rather colorful robot, can’t we? And this robot has been programmed to do something quite special. If you give it any number at all, it’ll multiply it by three and then give you the answer. Can you see it says times three on its chest? And now, unfortunately, we don’t have a robot to help us here, but we still need to find the answer to our question. Because we can see the number 32 being given to the robot, we know it’s gonna times this number by three. And we’re asked, what’s the answer going to be? So in other words, how can we find the answer to 32 times three without a colorful robot to help us?

Do you know your three times table fact up to 32 times three? Well, we usually stop learning facts around 10 or 12 times something. We don’t usually go as far as 32 times a number. So to help us multiply this two-digit number by a single digit, we can use the column method. To begin with, we can write out our calculation vertically, in other words, with the numbers on top of each other. 32. And then we’re going to be multiplying this, so we’ll draw the multiplication symbol. And we’re going to be multiplying it by three. And then also, before we start, we can draw an equal sign.

Now, as we’ve said already, 32 is a two-digit number. And by writing it like this, we can think about the ones and the tens parts of our number separately. 32 contains the digit two in the ones place. It has two ones. So we can start off by multiplying this part of the number by three. What are two ones times three? Well, this is a fact we already know, isn’t it? Two times three equals six. So we can see our answer is going to have six ones in it.

Now we just need to multiply the tens part of our number. 32 has a three in the tens place. It stands for three 10s. That’s where we get the number 30 from. And once again, we can use a fact we already know to help us here. We know that three times three is nine, and so three 10s times three is simply nine 10s, which just means we need to write the digit nine in the tens place.

Now, there aren’t any more digits in 32. It was only a two-digit number. We’ve multiplied both of our digits by three. Two times three is six, and three 10s times three or 30 times three is nine 10s or 90. We don’t have a robot like this to help us multiply two-digit numbers by three. But then we don’t need a robot like this. We’ve got the column method, and it’s pretty quick to use. 32 times three equals 96.

What is the missing number? 34 times what equals 68.

In this question, we can see a multiplication calculation. Did you know often this multiplication might be written like this? 34 multiplied by something equals 68. We need to find the missing number. Now these are two ways of writing exactly the same multiplication. But can you see how it’s been written in the question? The numbers have been written on top of each other, vertically. They’re all in columns, and we call this way of working the column method. Another way to describe it is short multiplication. And it’s a helpful way of multiplying two-digit numbers, sometimes even three-digit numbers, by a one-digit number, because it helps us to split these two-digit numbers into separate parts.

We know that the number 34 is made up of four ones and three tens. And just by writing our number like this, we can see those tens and those ones, can’t we, in separate columns? Now, often when we’re using the column method, we know what we need to multiply and what we need to multiply by. And we need to find the answer. But with this problem, we know the first number of our multiplication, 34. We know what the answer is going to be, which is 68, but we just don’t know what we’re multiplying by. Perhaps it might be a good idea to imagine we’re going to work out this multiplication using the column method and think about what we need to do to get from our first number to the answer.

So if we’re going to work out this column multiplication, the first thing we do is we look at our ones digit, which is four. And then we’d multiply it by whatever we’re multiplying by. We don’t know. And then we’d write the answer at the bottom. And we can see that the answer is eight. So here’s our first clue as to what our missing number is going to be. What do we multiply four by to get eight? Well, we know that four doubled is eight, isn’t it? Four times two equals eight. So it looks like our missing number might be two. Let’s complete the digit card with a two, and we’ll see whether it works when we multiply our tens digit.

Now in the tens place of our number 34, we have the digit three. Three 10s are 30, aren’t they? And we think that our missing number is two. So what is 30 times two? Well, there is a smaller number fact that we could use to help us here. We know that three times two equals six, and so three 10s times two or 30 equals six 10s or 60. Can you see the digit six is in the tens place in our answer? We’ve used our understanding of how the column method works to find out the missing number. 34 times two equals 68. Our missing number is two.

So what did we learn in this video? We’ve learned how to use the column method or short multiplication to multiply a two-digit number by a one-digit number when we don’t need to regroup.

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