Video Transcript
Column Addition of Three-Digit
Numbers: Regroup Ones
In this video, we’re going to learn
how to add two three-digit numbers when we have to regroup the ones. And we’re going to record our
calculations in columns.
Let’s begin by practicing a skill
that we’re going to be using a lot during this video. Here are 14 ones. And of course we know that 14 ones
are worth 14. Now, we could model any number out
of ones blocks. But as we learn more and more about
numbers and digits, we realize that there’s a more accurate way to model this number
because each of the place values in a number, the ones, the tens, and the hundreds,
can only hold one digit. And so we can’t represent 14 ones
by writing a one and a four in the ones place. We can only put one digit in the
ones place. So what can we do? What’s a better way of modeling
two-digit numbers like this?
Well, we can regroup this number,
in other words, group the 14 ones in a different way. We could take 10 of our 14 ones and
exchange them for something else. Can you guess what? 10 ones are exactly the same as one
ten. And so we can exchange 10 ones for
one ten. Our model now shows one ten and
four ones. And because we’ve regrouped the
number like this, we can now complete the place value table: one ten and four
ones. And it’s important to note here
that this number hasn’t changed at all. When a number is regrouped, its
value doesn’t change.
So what it’s like if your class is
sitting in the classroom in different groups and your teacher says, “Okay, regroup
now.” And you will get up and move around
and sit down in different groups. The amount of children in the class
hasn’t changed. You just group differently. And by exchanging 10 ones for one
ten, we don’t change the value of the number. It’s still worth 14. It’s just made the number a lot
easier to work with, that’s all.
Imagine if we try to model every
two-digit number out of ones. We’d have to count them all
individually to work out what the number was. One, two, three, and so on. There are 43 of these blocks by the
way, but it’s pretty hard to tell just by looking at them. It’s much easier if we can show a
two-digit number in tens and ones. Now, let’s use this skill to help
us add three-digit numbers together.
Let’s imagine a local football
match where two teams are playing. United are at home, and so they
have 317 supporters cheering them on, and Rovers have brought with them 164
fans. How many supporters are there
altogether?
Well, we know to find the answer,
we need to find the total of 317 and 164. And looking at these two
three-digit numbers side by side isn’t very helpful. What would be much more helpful is
if we could break up these numbers into smaller parts. And to do this, we can write them
on top of each other. And if we make sure the ones
digits, the tens digits, and the hundreds digits are all lined up neatly in the
correct columns, we can add the ones, the tens, and the hundreds separately.
Now, to help us understand what’s
going on in this column addition calculation, let’s also model it using place-value
blocks, 317 plus 164. Now, there’s a slight problem with
the way we’ve set out these blocks. Can you see what it is? The ones in our first number are
actually on top of the tens in our second number. Let’s shift them along so that the
ones, the tens, and the hundreds are all in separate columns. There we go. That’s much better.
So which end are we going to start
with? Do we start by adding the hundreds
digits first and then move from left to right? Or do we start by adding the
smallest-value digits, the ones, and then move from right to left? And the answer to that question is
that we always start with the ones. In a moment, we’ll see why. But for now, let’s just add those
ones.
The number 317 has seven ones, and
the number 164 has four ones. So what’s the total of seven ones
and another four ones? We can use our knowledge of number
bonds here. We know that seven and three go
together to make 10. So seven and four must be worth one
more than 10. The answer is 11. But wait a moment, 11 ones is a
two-digit number. We can’t write two digits in the
ones place. There’s only enough space for one
digit.
This is where that skill that we
talked about at the start of the video comes in. We’re going to need to represent
the number 11 in a different way than by writing 11 ones. We’re going to need to regroup our
ones. How can we regroup the number
11? Well, we can take 10 of our
ones. If you look at our place-value
blocks in particular, can you see that group of 10 that we’ve put a ring around? And we can exchange these 10 ones
for one ten. There we go. Now we have one ten and one one,
which is equal to 11.
But if we look at our written
calculation for a moment, we’ve written that one ten really large in the tens
place. It looks like our answer is going
to have one ten. But we know that, as well as this
one ten, there’s some more tens that we need to add together. So instead of writing it large like
this, we can write a small one digit just to remind us that we need to add one more
ten to our answer.
Time to add the tens. We can see that the number 317
contains one ten and the number 164 contains six tens. And one plus six equals seven. Now, if we’d have just started by
looking at the tens column on its own, we’d have said one plus six equals seven. But this isn’t accurate. We know there’s an extra ten we
need to remember. It’s the extra ten we made when we
exchanged those 10 ones. So instead of our answer having
seven tens, we need to include that extra ten, and it’s going to have eight
tens. And this is why we always start
with the ones and go from right to left, just in case we have to do some regrouping
or exchanging and our answer is a little bit different to what we expect it to
be. So one ten plus six tens plus
another ten equals eight tens altogether.
Finally, let’s add the
hundreds. And then about 317, we have three
hundreds. And in the number 164, we have one
more hundred. And three hundreds plus one more
hundred equals 400. So by adding the ones, the tens,
and then the hundreds digits, we’ve found that their total number of supporters that
are watching this football match is 481. And as part of the calculation, we
used the skill that we started off this video by practicing. We exchanged 10 ones for one
ten.
Let’s have a go at adding some more
three-digit numbers together now. And as we do so, let’s look at the
ones column really carefully. It could be that we’re going to
need to do some regrouping again.
Add 544 and 438. Use place-value blocks if you need
to. Hint: Do you need to regroup ones
or tens?
In this question, we need to add
together two three-digit numbers, 544 and 438. But writing these two three-digit
numbers side by side in their centers like this isn’t really very helpful to us. What’s much more helpful is if we
write the numbers on top of each other, just like they are underneath. By doing this, we can see that the
ones, the tens, and the hundreds digits are all neat in separate columns. This is going to help us add them
together. And we call this column
addition.
Now, even though we could work out
our answer pretty quickly just by writing our numbers like this, it’s useful that
we’re given a place value table too. And we’re told that we can use
place-value blocks if we need to. And you may know how to work out
the answer without using place-value blocks. But it’s certainly useful though
that there. So why don’t we work out the answer
using what we know about this written method, column addition?
But as we go along, we could work
with the place-value blocks too to show what we’re doing. To begin with then, let’s look at
the digits in the ones column. 544 has four ones, and 438 has
eight ones. We know that eight and four go
together to make 12. But how could we put 12 ones in the
ones place? Each place in a number only has
space for one digit, and the highest digit is nine. How can we represent the number
12?
But only if you noticed that we
read the question, but we’re given a hint to help us. It asked us, do you need to regroup
ones or tens? I don’t know about the tens cause
we haven’t got there yet. But certainly it’d be very helpful
if we could regroup these ones. We don’t want them to change
value. We still want them to be worth 12
ones. But is there another way we could
write this?
Have a look at our place-value
blocks for a minute because this is where they become quite helpful. We know from our knowledge of place
value that 10 ones are the same as one ten. So what if we took 10 ones and
exchange them for one ten? One ten and two ones does make
12. So the value of our answer is
exactly the same. We’ve just regrouped the number to
help us.
So now that we know what to do,
let’s come back over to our written method. How do we regroup when we’re doing
column addition? Well, as we’ve said, we think to
ourselves, four ones plus eight ones equals 12 ones. And we can exchange 10 of those
ones for one ten. So we’re going to write a little
one in the tens column. In other words, when it comes to
adding the tens, we’re not gonna forget we made an extra ten when we added the ones
together. And because 12 is made up of one
ten and two ones, we can write the digit two nice and big in the ones place. So that’s the ones sorted out. On to the tens.
In the number 544, we can see
there’s a digit four in the tens place. And in our second number, we can
see the digit three in the tens place. We know four plus three equals
seven. And so four tens plus three tens
equals seven tens. But don’t forget we made an extra
ten when we exchanged those ones, didn’t we? So instead of our answer going to
have seven tens, we’re going to get a total of eight tens. In the hundreds column, we’ve got
the digits five and four, and we know five plus four equals nine. And so we get a total of nine
hundreds altogether.
We’ve found the answer by using
column addition. But we also used place-value blocks
to help us because we’ve found that when we added the ones, it made a two-digit
number. So we regrouped those ones and took
10 ones and changed them into one ten. This meant that we had one more ten
to add when we added the tens digits. The total of 544 and 438 is
982.
What is the result of the following
operation?
And if we look at the way that this
calculation has been written, we can see that it says 668 plus 212. So the operation that’s mentioned
in our question is an addition. We need to find the total of 668
and 212. And because these two numbers have
been written so that the ones digit, the tens digit, and the hundreds digit are all
in separate columns, we call this column addition. And we need to find the answer by
adding each column separately.
Let’s begin with the ones. Eight ones and two ones are quite
nice numbers to add because they make a pair that we should know already. Eight and two go together to make
10. And so the total of our ones is 10
ones. But we can’t write two digits in
the ones place. How can we show 10 ones? Well, one thing we know about place
value is that 10 ones are worth exactly the same as one ten. So we can take our 10 ones and
exchange them for one ten.
Now, sometimes when we record our
one extra ten that we need to add on, we might write it underneath the equal sign
here, very small, just to remind us not to forget it when we add the tens. But can you see the way that this
calculation has been written? There’s a little box for it at the
top. So that’s right, our one extra ten
in that box. And we know that 10 is made up of
one ten and zero ones. So we’ve still made a total of
10. We’ve just regrouped it in a
different way.
Now, let’s add the tens digits. Six tens plus one more ten makes
seven tens. But don’t forget the extra ten we
made when we added those ones. Our total is going to not be seven
tens, but eight tens. Finally, let’s add the
hundreds. 600 plus two more hundreds equals
eight hundreds. We’ve added these two three-digit
numbers simply by adding the ones, then the tens, and then the hundreds. And the only part we really needed
to be careful about was when we had to regroup those 10 ones and also when we had to
remember to add that extra 10. The result of the operation 668
plus 212 is 880.
Find the following: 236 plus
148.
Did you know in this question we’ve
already been given a hint to help us? Perhaps you find it difficult to
recognize. But if the calculation had been
written like this, we might have found it trickier to work out. The way that our calculation has
been written, with the ones, the tens, and the hundreds digits in neat separate
columns, gives us a bit of a clue. Perhaps we need to add each column
separately.
Now, we always start by adding the
ones digits first, and we’ll explain why in a moment. Six ones plus eight ones makes a
total of 14 ones. Now, we know we can only write a
one-digit number in the ones place. So how can we represent the number
14? We can take 10 of our ones and
exchange them for one ten. And we write that little one ten in
the tens place. This is just to remind us when it
comes to adding the tens, we need to include this extra ten. So 14 is now one ten and four
ones. Can you see how this is still the
same as 14 ones? We’ve just regrouped the
number. It’s important to remember that
when we regroup a number like this, it doesn’t change its value.
On to the tens. Now, when we first looked at our
calculation, we might say three tens plus four more tens equals seven tens. So surely, the answer is going to
have seven tens in it. And, you know, if we’d have started
with the hundreds digit and work from left to right, we might well have written the
digit seven in the tens place. But don’t forget we exchanged 10
ones in the number 14, and we’ve got an extra ten to think about. Good job we started by adding the
ones, isn’t it? Our answer is not gonna have seven
tens, but eight tens.
Finally, if we add the digits in
the hundreds column, 200 plus another 100 equals three hundreds altogether. We’ve used column addition to add
these two three-digit numbers together. We even regrouped some ones where
we needed to. We exchanged 10 ones for one
ten. And so we’ve worked out that 236
plus 148 equals 384.
What have we learned in this
video? We’ve practiced regrouping a number
of ones into tens and ones. And we’ve learned how to regroup
ones when adding two three-digit numbers using column addition.
