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.
