Video Transcript
Subtracting 10s from Three-Digit
Numbers
In this video, we’re going to learn
how to use models to subtract a multiple of 10 from a three-digit number. And as we do this, we’re gonna try
to spot which digits in the number change. Now let’s start with a three-digit
number, 367. And let’s imagine that we want to
find 50 less than this number. We’re going to need to find the
answer to a subtraction, aren’t we? 367 subtract 50. Let’s think about this number that
we’re taking away, 50, for a moment. What do we know about it?
Well, we know that if we were
modeling it using base 10 blocks, we’d only need a group of five 10s, wouldn’t
we? We wouldn’t need any hundreds or
ones. If we wanted to model it using a
place value arrow card, we’d only need one card representing tens. Again, we wouldn’t need a hundreds
or a ones card. And if we wanted to write it using
digits, the only digit we’d need that’s greater than zero would be a five in the
tens column. Of course, we’d also need a zero in
the ones place to show that it’s in the tens column.
But by taking a moment to think of
all these different ways to model this number, we can see something special about
the number 50. It’s what we call a multiple of
10. It’s what we get if we count in
tens several times. 10, 20, 30, 40, 50. These numbers all end in a
zero. They’re all multiples of 10. And we said at the start of the
video that we were going to be subtracting multiples of 10 from three-digit
numbers. These were the sorts of numbers we
were talking about. These are the sorts of numbers
we’re going to be taking away.
So with this particular question,
the multiple of 10 that we’re thinking of is 50. Now one way we can find out the
answer to a subtraction like this is by using place value blocks to help. Let’s start by modeling our
three-digit number. 367 is made up of three 100s, six
10s, and seven ones. And we need to take the number 50
from this. And as we’ve said already, 50 is
simply five 10s. So we could just look at our place
value blocks and think to ourselves, “we just need to subtract five 10s.” Let’s cross them through as we
subtract them.
One, two, three, four, five. 10, 20, 30, 40, 50. Look how we haven’t touched the
ones or the hundreds blocks. We started off with six 10s and we
needed to take away five 10s. So it was quite easy to do. Six 10s or 60 take away five 10s or
50 leaves us with one 10. We started off with three 100s, and
we still have three 100s. We started off with seven ones, and
we’ve still got those too. But we’ve taken away five 10s from
the six 10s that we had to begin with, and we’ve now only got one 10. And that’s how we know that 367
take away 50 is 317.
Now what if we don’t have any place
value blocks around when we’re trying to work out the answer to a subtraction like
this? Thankfully, there are some other
methods we could use. For example, we could count back in
tens using a number line. Let’s imagine that we want to find
the answer to 783 take away 30. Again, we’re taking away a multiple
of 10 from a three-digit number here, aren’t we? We know it’s a multiple of 10
because it ends in a zero, and also we can get to it by counting in tens: 10, 20,
30. And so we’re going to subtract this
multiple of 10 by counting backwards in tens. And we’re going to use a number
line to help us. So we’ll start by drawing our
number line.
Because we’re going to be counting
backwards, our starting number, which is 783, is going to be on the right
somewhere. So let’s mark it. About here will do, 783. And then just to show that our
number line continues on and on in that direction, we’ll put an arrow. And we’ll put an arrow at the other
end, just to show this is part of a much longer number line. Now we know that 30 is the same as
three 10s. So we can make three jumps of 10
backwards on our number line. And we know how to find 10 less
than a number, don’t we?
Let’s start at 783 and count back
three 10s. 783 and then 773, 763, 753. Did you notice which digit changed
as we counted back in tens? The number 783 is made up of seven
100s, eight 10s, and three ones. And because this number has eight
10s already, we only need to take away three 10s. It’s only the tens digit that’s
going to change. Our eight 10s became seven 10s,
then six 10s, and finally five 10s. And did you notice as we counted
back, you can actually hear how the digits are changing when you read the
numbers? 783, 773, 763, 753. It’s that middle digit that’s
changing each time, isn’t it?
Now you may be thinking, I could’ve
counted back three 10s in my head. And perhaps you could have. But using a number line is a
helpful method we could use if we needed to. We wanted to find 30 less than
783. And so we counted back three 10s
using our number line. The last number we said was
753. And so we know that 783 take away
30 equals 753.
So what we’re doing in all of these
examples is just thinking about the tens. And you know, it might be worth
just looking at one more method. And this time, it involves
separating out the tens so that we can look at them on their own. Let’s think about the calculation
961 take away 40. And let’s imagine we look at it and
see that 40 is a multiple of 10 again. So we know we’re subtracting a
number of tens from 961. So we can take our whole amount of
961, and we can separate out the tens that we need to subtract from.
Now, we know that 961 has six 10s,
which are worth 60. This leaves us with the rest of our
number, which are the nine 100s and the one one. So you can see by taking our six
10s out of the number 961, we’ve split it up into 901 and 60. Do you understand what we’ve done
here and why we’ve done it? We’ve taken our starting
number. And because we want to take away
four 10s from it — we just need to look at the tens part — we’ve separated it so
that we look at the tens on their own, and we’ve got 901 left. Now we know that 40 is made up of
four 10s, 10, 20, 30, 40. And the number we’re taking away
from is 60 or six 10s.
Now we know six take away four
leaves us with two. So six 10s take away four 10s is
going to leave us with two 10s. So let’s alter our part–whole model
to show two 10s, shall we? And we could also change our arrow
card. Now that we’ve taken away our four
10s, all we need to do is put our two parts back together again to see what we’re
left with. And we can see that our part–whole
model doesn’t make sense, does it? We need to change this whole amount
at the top. 901 and 20 is going to equal
921. And if we put our arrow cards back
together, we get the same answer.
This time we used our heads to find
the answer, but we used a part–whole model to show how we can split up the
three-digit number to take out the tens. And so we can say 961 take away 40
equals 921. Let’s try answering some questions
now where we have to subtract some multiples of 10 from three-digit numbers. And we’re going to use some of the
methods that we’ve talked about.
Which number is 50 less than
386?
Now if we’re being asked to find 50
less than a number, what do we need to do to get to the answer? This is a subtraction question,
isn’t it? And the number that we need to
start with is 386. In other words, what is 386 take
away 50? Now one thing we know about the
number 50 that’s going to make it easier to take away is the fact it’s a multiple of
10. In fact, 50 is what we have if we
count five lots of 10. And you know we can use this fact
to help us because if we know how to find 10 less than a number, we could find 10
less, then another 10 less, and another until we’ve found five lots of 10 less or 50
less.
Well, so we could count back in
tens to find the answer. So let’s have a go at starting with
386 and counting back in tens five times. 10 less than 386 is 376. And 10 less than this is 366, then
comes 356, 346, and then 336. Did you notice which digit changed
each time? We started off with eight 10s in
386. And then as we counted back tens
each time, those eight 10s became seven 10s, then six 10s, five 10s, four 10s, and
finally three 10s. We found the number that’s 50 less
than 386 by counting back in tens five times. And we know that that last number
we said is the answer. 50 less than 386 is 336.
Count back in tens to find the
difference. 751 subtract 40 equals what.
When we’re asked to find the
difference between two numbers, we know it’s a subtraction we need to be doing. And this subtraction is written as
a number sentence for us, 751 take away 40 equals what. So we’ve got a three-digit
number. And we’re taking away a multiple of
10. Four 10s make 40, don’t they? And so one way we could take away
this multiple of 10 from the three-digit number is by thinking of it as a group of
10s. In fact, the question actually
tells us to do this. We need to count back in 10s. And because there are four 10s in
40, we need to count back four 10s.
Let’s complete the number line as
we do this. So we’ll start by saying 751, and
then 741, 731, 721, 711. Our starting number had five
10s. And look how the tens digit changed
as we counted back. We went from five 10s to four 10s
to three 10s, then two 10s, and finally one 10. Five 10s take away four 10s equals
one 10. And so 751 take away 40 equals
711.
Find the difference by first
subtracting tens. 754 take away 20 equals what.
In this question, we need to find
the difference between two numbers or, in other words, subtract them. Now we’re starting here with a
three-digit number, 754. And we’re being asked to take away
20. Now we know that 20 is a multiple
of 10. It’s actually the same as two
10s. And the question gives us a hint as
to find the answer. We’re told to first subtract the
tens. In other words, we can take our
number 754 and all we really need to look at, because there are five 10s in 754, is
the tens part. Now we can see we’ve got a
part–whole model to complete here.
Now as we’ve said already, the
number 754 has five 10s. So we can take those five 10s,
which are worth 50, and we can separate them out. And we’re left with the seven 100s
and the four ones, 704. And we’ll put that to one side. We’ll come back to it at the
end. But to start with, all we need to
think about are our five 10s. Now we know that five take away two
equals three. And so five 10s take away two 10s
is going to leave us with three 10s. Let’s draw a part–whole model to
show our answer. As we’ve just said, five 10s take
away two 10s is going to leave us with three 10s. 50 take away 20 equals 30.
And then we’ve still got our 704
that we haven’t touched yet. And by looking at our two parts, we
can see that our answer is going to have seven 100s, four ones, and of course the
three 10s that we made when we subtracted. Because we’re taking away a
multiple of 10 here, we’ve found the answer by concentrating on the tens. 754 subtract 20 leaves us with
734.
A farmer gathered 892 chicken
eggs. 10 were broken. How many eggs are left?
Can you see what we need to do to
find the answer to this problem? Let’s sketch a bar model to help us
understand. Firstly, we’re told that a farmer
gathered 892 chicken eggs. The next thing we’re told is that
10 of these eggs were broken. And we need to find out the number
of eggs that are left. Can you see what we need to do to
find the answer? We need to take away 10 from
892.
Now we know that our starting
number, 892, is made up of eight 100s, nine 10s, and two ones. And the number that we’re taking
away is a number of tens, isn’t it? It’s a multiple of 10. In fact, it’s one 10. It’s only 10. If we look at the number we’re
starting with, this three-digit number, we can see that there are nine 10s. And this digit, nine, is all we
need to focus on because, as we’ve said, what we’re subtracting is a number of
tens. We have nine 10s. And if we take away one 10, we’re
going to be left with eight 10s. We’ve used our knowledge of place
value to help us answer this question. We could just focus on the tens
digit. If a farmer gathered 892 chicken
eggs and 10 were broken, the number of eggs that are left is 882.
So what have we learned in this
video? We’ve learned how to use models to
subtract a multiple of 10 from a three-digit number. We’ve also investigated which
digits change.
