Video Transcript
Column Subtraction of Three-Digit
Numbers: No Regrouping
In this lesson, we’re going to
learn how to subtract two three-digit numbers together, and we’re going to be
recording our calculation using columns.
Let’s start by making a three-digit
number using digit cards. Our first card is the digit four;
then we’ve got a seven and an eight. We know how to read this
three-digit number because we understand what the columns that each digit in
mean. The four is in the hundreds column,
so we know that it’s four hundred and something. The seven is in the tens place. This means it has a value of 70, so
we know this is four hundred and seventy something. And on the end, we have eight ones,
and so we know the number is 478. Do you know, this idea of hundreds,
tens, and ones is so useful when it comes to working with three-digit numbers?
For example, let’s imagine that
we’ve been asked to subtract a three-digit number from 478. And the calculation that we’ve been
asked to find out is 478 take away 156. Now the way that we’ve written this
calculation is across the page, from left to right. This is the way we write a lot of
calculations, isn’t it? We’re used to this. But as we’ve said already, thinking
of three-digit numbers in terms of hundreds, tens, and ones can be really helpful to
us. Let’s put the digits in 156 in the
right columns too. One 100, five 10s, which is worth
50, and six ones. Can you see what we’ve done
here? By writing both numbers on top of
each other, each of the digits are in the right columns.
Let’s put some dotted lines in to
show us. We’ve got two digits in the ones
column. Here are the tens digits. And our hundreds digits are on top
of each other too. Now this is a subtraction
calculation, so let’s put in a subtraction symbol: 478 take away 156. And as we complete our column
subtraction, we’re going to need somewhere to put our answer. And so we need to draw a line
underneath the subtraction. It’s going to act as a sort of
equal sign. Our answer is going to appear
underneath that line.
Now to help us see what’s happening
with our column subtraction, we can use place value blocks. And we can start by modeling the
larger number, 478. And this is made up of four 100s,
seven 10s, and eight ones. And as we take away 156, we’re
going to take away each part of 156, the hundreds, the tens, and the ones. And we start with the ones. 478 has eight ones; 156 has six
ones. So we need to take away the six
ones from the eight ones we already have. And eight take away six leaves us
with two. Can you see those two ones blocks
that we have left? Now, if we look at the digits in
the tens column, we might think to ourselves, we need to work out seven take away
five.
And in a way, this is true, but we
need to keep in mind that we are subtracting tens here: seven 10s take away five
10s. But certainly, knowing the answer
to seven take away five is really gonna help us. Seven take away five is two. And so seven 10s take way five 10s
is simply going to be two 10s. So we write the digit two in the
tens column. And again, can you see those two
10s blocks that we have left over? Our final job is to subtract the
hundreds. 478 has four 100s and we need to
take away one 100. Can you see the digits four and one
in this column? And of course, 400 take away 100
leaves us with three 100s. Now we can see our answer
underneath the equal sign, 322. And if we erase all the different
blocks that we’ve crossed out, we can see those three 100s, two 10s, and two
ones. 478 take away 156 equals 322. And this is all we need to do.
And perhaps, the best way to learn
how to use column subtraction is just to practice again and again. So we’re going to try some
questions now where we have to subtract using column subtraction. Maybe we’ll start with one or two
examples where, just like this, we use place value blocks to mirror what we’re doing
in the column subtraction and understand it better. And then we’ll try an example where
we use column subtraction on its own. Okay, here’s question one.
Subtract three 100s from 558. Hint: Use the place value blocks if
you need to.
We’ve got quite a large diagram to
look at here underneath the question, haven’t we? It’s made up of lots of place value
blocks. But can you see on the left we’ve
got a calculation? We’re being asked to subtract or
take away three 100s from 558. And you know, we could find the
answer without using the place value blocks at all. They’re not something that we
absolutely have to have to find the answer. But because we’re given a hint that
says, use the place value blocks if you need to, and because we’re shown a picture
of them in a place value grid, we might as well use them.
Now, can you see what the place
value blocks show? There are five 100s, five 10s, and
eight ones. This is our starting number in the
subtraction, isn’t it, 558. And if we look over at our column
subtraction on the left-hand side, we can see those five 100s, five 10s, and eight
ones. Now we’re asked to take away three
100s from this number. And of course, we know that three
100s are the same as 300. So if we were to write this number
using digits, we’d put a three in the hundreds place and then zeros in the tens
place and the ones place. We’re not subtracting any tens or
ones. All we have to really worry about
in this question is the hundreds.
Now can you see the way that we’ve
written these numbers underneath the place value grid? The digits are all in columns. It’s exactly the same as the column
subtraction on the left-hand side, isn’t it? And by seeing the number of
hundreds, tens, and ones in both numbers, it can help us subtract really
quickly. And in this particular question, as
we’ve said already, we know we don’t need to worry too much about the tens or the
ones. We can complete this part of the
calculation really quickly. Eight ones subtract zero means that
eight ones stays the same. We’re not taking any tens away from
our five 10s, so five take away zero is going to leave us with five 10s still.
And then finally, we get to the
part of the subtraction that we really do need to do. And that’s five 100s subtract three
100s: one, two, three. Five 100s take away three 100s
leaves us with two 100s. And we can see the place value
blocks that we’ve ended up with are exactly the same as the number that we found by
using column subtraction. It’s only the hundreds that have
changed. In a way, this is the sort of
calculation we could have done in our heads. But it’s helpful to use as an
introduction to the column subtraction method. We’ve used place value blocks but
also column subtraction to subtract three 100s from 558. 558 take away 300 equals 258.
Subtract two 10s and three ones
from 437. Hint: Use the place value blocks if
you need to.
In this question, we need to
subtract or take away a number from 437. And it’s interesting because the
number that we need to take away isn’t written as a numeral; we’re told it in terms
of the number of tens and ones that make it up. We’re told to take away two 10s and
three ones. Now we know that a number that has
two 10s is going to be twenty something. And if it has three ones, it’s the
number 23. And to help us solve the problem,
we can think about the number 437 like this. In other words, we can think of its
place value. It has four 100s, three 10s, and
seven ones. And can you see that the way that
we’ve written these numbers on top of each other like this, it shows the hundreds,
the tens, and the ones really clearly in separate columns?
That’s why if we write a
subtraction like this, we call it column subtraction. And it’s a method we can use to
find the answer really quickly. Perhaps, you notice over here we’ve
already got our column subtraction written out for us. So let’s use this method to help us
find the answer. And we’re given a hint to use the
place value blocks if we need to. So what we’ll do as we’re working
out the answer using column subtraction, we’ll take away some of the place value
blocks. And we’ll sort of mirror what we’re
doing in the column subtraction with the place value blocks; it’ll help us
understand it.
Now we always start with the
smallest value place when we’re doing column subtraction. So we’re going to start with the
ones. And we’re told that we need to take
away three ones. And we know that 437 has seven
ones, so we’re beginning with seven ones, and we’re taking away three of those
ones. This is where perhaps we could use
our place value blocks to show what goes on. We’re gonna take away one, two,
three. Can you see how many we’re left
with? Seven ones take away three ones
leaves us with four ones. So we know whatever answer we’re
going to get at the end of this, it’s going to have four ones.
Next, we move on to the tens. And we need to take away two
10s. And we can see that 437 has three
10s. If we look across at our place
value blocks, we can see there’s three 10s. So let’s subtract two of them: one,
two. Of course, three 10s take away two
10s is only going to leave us with one 10. So now we can see our answer is
going to have one 10 and four ones. It’s going to be something and
fourteen.
Now if we look at our column
subtraction, we can’t see any hundreds we need to take away. We were only asked to subtract a
number of tens and ones, weren’t we? So we started off with four 100s
and we’re going to end with four 100s too. And you should be able to see that
this three-digit number that we have as our answer is exactly the same as the number
of place value blocks that we have left over. There are four 100s, one 10, and
four ones. We’ve used column subtraction to
take away two 10s and three ones from 437. And we found that 437 subtract 23
equals 414.
Subtract to find the answer. Tip: Use place value blocks if you
need to. 769 subtract 342 equals what.
In this question, we’re given a
subtraction involving two three-digit numbers. And you know, the subtraction could
have been written like this. 769 take away 342 equals what. But, you know, if we’d have written
our calculation across the page like this, it would have been more difficult to work
out. The way that the calculation has
been written is so that each digit is in the correct column. And because it’s been written on
squared paper, we can see these columns really easily, can’t we? The ones, tens, and hundreds. And we can subtract each of these
parts of our three-digit numbers one by one to help us find the overall answer.
So our calculation’s been written
as a column subtraction. But underneath, we’re given a
tip. It says we can use place value
blocks if we need to. Now the question is, do we need
to? If we know how to use column
subtraction to find the answer, then we don’t need place value blocks. Let’s have a go at answering the
question without them. But then maybe we’ll use the blocks
to check our answer at the end. Now, when we work out a subtraction
like this, we always start with the ones and move to the left. We work out the ones, then the
tens, and the hundreds. And if we look down this column, we
can see there are nine ones in the first number and two ones in the second. And nine take away two leaves us
with seven ones. We know that our answer now is
going to end in a seven, isn’t it?
Next, we subtract the tens. 769 has six 10s and 342 has four
10s. Six take away four leaves us with
two. So six 10s take away four 10s is
going to leave us with two 10s. That’s why the digit two is written
in the tens place. Now we can see that our answer is
going to be something hundred and twenty-seven, isn’t it? Finally, the hundreds column, our
first number has seven 100s. And we need to take away three
100s. Seven take away three equals
four. So seven 100s take away three 100s
equals four 100s.
Now let’s check our answer using
place value blocks. First, we’ll make our starting
number. We’re going to need seven 100s, six
10s, and nine ones. And remember, we need to take away
342. So we’ll take away the ones
first. That’s two ones: one, two. Now the tens, we need to take away
four 10s or 40: 10, 20, 30, 40. And finally, we need to take away
our three 100s or 300: 100, 200, 300. We’re left with an answer that’s
made up of four 100s, two 10s, and seven ones. Looks like we didn’t need to use
place value blocks after all, did we? This is the same answer as we got
when we used column subtraction. And column subtraction was a much
quicker method to use, wasn’t it? The same as getting out all those
place value blocks as well. 769 subtract 342 equals 427.
What have we learned in this
video? We’ve learned how to subtract
three-digit numbers and record the calculation in columns.
