Video Transcript
Subtracting Ones from Two-Digit
Numbers without Regrouping
In this video, we’re going to learn
how to subtract a one-digit number from a two-digit number without crossing a
10. And to help us understand what’s
happening, we’re going to model what we do using place value equipment.
So let’s start with a two-digit
number. What about 37? As our title told us, we’re going
to be using two-digit numbers like this. And we’re going to be taking away
one-digit numbers from them. Let’s subtract five. What’s five less than this
number? We could write what we’re doing as
a number sentence. 37 subtract five equals what?
Now, as we’ve said already, we’re
going to be modeling questions like this in this video using place value equipment
to help. For this example, let’s use 10
frames. The number that we have to start
with, 37, is a two-digit number, which means it’s made up of some tens and ones. It contains three 10s. And because we can show the number
10 using a full 10 frame, three 10s is the same as three full 10 frames. And three 10s are worth 10, 20,
30.
And in the ones place of the number
37, we have the digit seven. And we can model seven ones by
putting seven counters on a 10 frame. So we’ve got three full 10 frames
and one that has seven counters on it. We’ve made the number 37. And as we’ve said already, the
number that we’re taking away here, five, is a one-digit number. It’s just five ones. We don’t need to model these five
ones using a 10 frame because this is a subtraction. We’re actually going to be taking
counters away that we already have. So all we need to do now is to find
out the answer.
The way we can do this is to
subtract the ones first and then the tens. To subtract the ones, we need to
look at the 10 frame that shows the ones. It’s this one here, isn’t it? The one that isn’t completely
full. Our starting number, 37, has seven
ones. And the number that we’re
subtracting has five ones. Let’s subtract five ones and see
what we have left.
So we’re starting with seven, six,
five, four, three, two. We’ve got two ones left. This means our answer is going to
have the digit two in the ones place. Perhaps you knew this fact already
because you know that seven take away five leaves two.
Now we’ve dealt with the ones; it’s
time to subtract the tens. But wait, there are no tens we need
to take away. We’re subtracting a one-digit
number, and there are no tens in a one-digit number. So we started with three full 10
frames, and we still have three full 10 frames. 30 take away zero is still 30. And so our answer is going to have
a three in the tens place. Our tens digit hasn’t changed at
all. 37 subtract five equals 32.
Let’s have a go at a different
example. Let’s have the two-digit number 98
this time. And this time, our one-digit number
could be seven. We need to find seven less than
98. In other words, 98 subtract seven
equals what?
This time, we could use some
different place value equipment. Let’s use base 10 blocks. And to start with again, we need to
think about the tens and the ones in our first number. 98 is made up of nine 10s: 10, 20,
30, 40, 50, 60, 70, 80, 90. And as well as nine 10s, it also
contains eight ones, which we can model using eight ones blocks. And the number that we’re
subtracting again is a one-digit number, and that’s the number seven, seven
ones.
But once again, we don’t need to
model this number because it’s the number we’re taking away. We’re going to show it as we remove
some of the blocks we’ve already got. In this example, we’re going to
cross them out.
So now we’re ready to work out the
answer. And we start by subtracting the
ones. We know that the number 98 has
eight ones and the number that we’re subtracting has seven ones. Perhaps you can guess how many ones
we’re going to have left after we’d taken seven ones away from our eight ones. Let’s see. We’ve got eight to start with,
seven, six, five, four, three, two, one. We started off with eight ones, we
subtracted seven ones, and now we’re left with only one one. Did you guess that this was all
we’re going to be left with?
We know that eight take away seven
is one. And so we know our answer is going
to contain the digit one in the ones place. And now that we’ve subtracted the
ones, it’s time to look at the tens. 98 contains nine 10s. But because we’re subtracting a
one-digit number, there are no tens to take away from our nine 10s. We have nine 10s or 90 to begin
with. We take away nothing. And we’ve still got nine 10s or
90. In this calculation, the tens digit
hasn’t changed at all.
Now, before we write the answer in
at the top, let’s just pause a second. So far, we’ve been modeling our
questions using place value equipment. It’s what we said we were going to
do at the start of the video. Although this video is about using
equipment, and there’s a reason for that, hopefully, you’re starting to notice ways
that you can work out the answer in your head too, maybe little subtraction facts
that you can see could help you. In this example, it’s the fact
eight take away seven equals one. It’s a fact we know already, isn’t
it? And if we know that eight subtract
seven equals one, we know that 98 subtract seven equals 91. So although we’re using place value
equipment in this video, let’s remember there are other ways we could find out the
answer too.
Now, what if we don’t have any 10s
frames and counters or base 10 blocks? What if all we have is a pen and
paper? How could we use place value to
find the answer then? Well, all we really need is a way
to think about the tens and the ones separately. Let’s imagine that we want to find
the difference between 58 and four. And we can do this quickly by
starting with 58 and taking away four. Now, remember, all we have is a pen
and paper for this question. But we can still show tens and ones
by drawing lines to represent tens and dots for ones. Let’s see how quickly we can find
the answer.
58 is made up of five 10s. So that’s 10, 20, 30, 40, 50. And it’s also made up of eight
ones: one, two, three, four, five, six, seven, eight. And the number that we’re taking
away is a one-digit number, and it’s the number four, four ones. And we’ll start by subtracting the
ones. 58 has eight ones shown by these
eight dots. And the number that we’re taking
away contains four ones. So we’re going to cross through
four of our dots. We have eight ones to start
with. And then this becomes seven, six,
five, four ones. Eight subtract four leaves us with
four.
We had enough ones ready in our
first number to take away four ones from. We didn’t need to do anything
else. And we don’t need to do anything
when it comes to the tens either. We know the number that we’re
subtracting is a one-digit number, doesn’t have any tens. So we started off with five 10s or
50, we’ve subtracted zero, and we’ve still got five 10s or 50. We know that eight take away four
equals four, and so 58 subtract four equals 54. The difference between our two
numbers is 54.
We’re going to try answering some
questions now where we have to take away a number of ones from some two-digit
numbers. We are going to start off by
modeling the answer using place value equipment. But I would encourage you as you
look at each question, think to yourself, “Can I see an easier subtraction fact that
might help me here?” Because in each of these questions,
there will be one. Here’s the first question then.
Use place value to subtract
numbers. Pick the correct way to break
apart 47 into tens and ones. Subtract five from 47 by taking
away five ones.
The main calculation that we
need to do in this question comes right at the end. We need to subtract five from
47. But before we get to this step,
there’s one or two things we need to do first. The first sentence tells us
that we need to use place value to subtract numbers. Do you remember what these
words “place value” mean? They’re all about how the
digits in a number can have different values depending on where you write them,
depending on their place in a number. And we can see, just by quickly
looking at this question, we’re thinking about two-digit numbers.
In the first part of the
question, we’re asked to start thinking about a two-digit number. We need to pick the correct way
to break apart 47 into tens and ones. We know from later on that 47
is one of the numbers in our subtraction. And it looks like it’s going to
be helpful to us to split up this number into its tens and ones. The diagram shows that two
different place value grids. And each one shows a different
number of tens and ones. But which one of the two is
correct, seven 10s and four ones or four 10s and seven ones?
Hopefully, you can hear the
similarities as we read those out. They both contain seven of
something and four of something else. In other words, they both
represent numbers that contain a seven digit and a four digit. But which way around?
To answer this part of the
question, we need to understand something about the digits in 47 and their place
value. And to help us, we could write
those digits into a place value grid. Our grid shows two spaces, one
for the tens and one for the ones. And we can write our digits in
order. The digit that comes first is a
four, and that’s going to go in the tens place. So 47 has four 10s. We know this because four 10s
are worth 40. And there’s only one place for
us to write our digit seven, and that’s in the ones place. This has a value of seven
ones.
Now, we can use this to help us
find the correct answer. We’re looking for the place
value grid that shows four 10s and seven ones. That’s this one here. The other model shows seven 10s
and four ones. It’s the number 74. But we know that the number our
subtraction begins with can be modeled using four 10s and seven ones.
In the final part of the
question then, we’re asked to subtract five from 47 by taking away five
ones. Can you see how the subtraction
has been written in a place value table for us? Now, the calculation could’ve
been written like this. But by writing the numbers in a
place value table like this, we’re really doing what we’ve done in the first
part of the question. We’re splitting them up into
their tens and their ones. We’re using place value to help
us.
Now, we’re told we need to find
the answer by taking away five ones. And this is because the number
that we need to subtract, five, is worth five ones. If you look in our place value
table, can you see the digit five in the ones place? These are the five ones we need
to take away. So why does this question ask
us to take away a number of ones? Why doesn’t it say a number of
tens and some ones?
Well, that’s because we’re only
taking away a one-digit number. The number five doesn’t have
any tens in it. We just need to subtract a
number of ones. And in the number 47, we
already have seven ones. So we know we’ve got enough
ones to take away our five ones without doing anything else. Let’s cross out five of our
ones blocks and see what we have left. So we’ve got seven to start
with, and then six, five, four, three, two. Let’s write what we have left
in our place value grid. We had seven ones, we’ve taken
away five ones, and now we’re left with two ones. And as we’ve said already, we
don’t need to do anything with the tens.
We started off with four
10s. We don’t need to take any
tens. And four take away zero leaves
us with the same number. We still have four 10s. Our answer contains four 10s
and two ones. It’s the number 42.
In this question, we needed to
subtract five from 47. The first thing we were asked
to do was to break 47 apart into its tens and ones. And we know 47 has four 10s and
seven ones. And by modeling it using place
value blocks, we could then take away five ones blocks. And that’s how we know 47 take
away five equals 42.
Take away three from 66.
In this question, we’ve got a
subtraction to work out the answer to. We need to take away three from
66. In other words, we need to find
the answer to 66 subtract three. Can you see that our
subtraction has been written already for us in the place value grid? 66 subtract three. Now, why do you think our
numbers have been written in a place value grid like this? Do you think maybe splitting
our first number up into its tens and ones is going to help us?
Our grid shows us that 66 can
be split into six 10s and six ones. And we need to subtract three
from this number. Now, three is just a one-digit
number. It represents three ones. And we already have six ones to
start with. So we know we can take away our
three ones from the six ones. We don’t need to do anything
else. So, first, let’s subtract our
ones. Six ones take away three ones
leaves us with three ones. So we can write the digit three
in the ones place of our answer.
Now, we can move on to the
tens. 66 contains six 10s. But as we’ve said already, the
number we’re taking away is only a one-digit number. There aren’t any tens to
subtract. And if we subtract zero 10s
from six 10s, we’re still going to have six 10s when we finish. Our answer contains six 10s and
three ones. We found the answer by
subtracting three ones from our number. And because we didn’t have to
take away any tens, the tens digit stayed the same. Because we know that six take
away three equals three, we also know that 66 take away three equals 63.
85 subtract four equals
what?
In this question, we’re
starting off with a two-digit number and we’re subtracting a one-digit number
from it. And we can use what we know
about place value to help. We can think about the tens and
the ones in our numbers. We know that 85 has eight 10s
and five ones. And the number that we’re
subtracting, four, is a one-digit number. There are some ones, but there
are no tens at all. And because we’ve already split
up our two-digit number into its tens and ones, we can start by subtracting the
ones: five ones take away four ones.
We know that five take away
four equals one. And so five ones subtract four
ones equals one one. We also know that because we’re
subtracting a one-digit number, there aren’t any tens to take away. We started with 85, and we
found the answer by simply subtracting four ones. 85 take away four equals
81.
So what have we learned in this
video? We’ve learned how to subtract a
one-digit number from a two-digit number. We’ve also learned how to model the
answer using place value equipment.
