Video Transcript
Subtracting Tens from Two-Digit
Numbers
In this video, we’re going to learn
how to subtract a multiple of 10 from a two-digit number. We’re also going to find out how we
can model this using place value equipment.
Let’s begin with this two-digit
number, 36. And let’s imagine that we want to
find 20 less than this number. We could write what we need to do
as a subtraction. 36 subtract 20 equals what. Let’s think about the number that
we’re taking away for a moment. What do we know about 20? We know that if we were modeling it
out of place value blocks, we’d need two 10s blocks. If we wanted to show it using place
value counters, we need two 10s counters. And if we used a place value grid
to show our number, we need to write the digit two in the tens place. Of course, we would also need a
zero in the ones place just to show that the two was in the tens place.
All these ways of showing how to
model 20 tell us something very important about this number. 20 is a multiple of 10. It’s what we get when we multiply a
number by 10. Two times 10 is 20, isn’t it? If we start at zero and count in
tens, every number that we say will be a multiple of 10. zero, 10, 20, 30, 40, and
so on. These are all multiples of 10 and
they’re all the sorts of numbers that we’re going to be subtracting in this
video. And it’s important that we remember
what we’ve just learned. Each of these is a number of
tens. It’s really going to help us when
we have to take them away.
Right, let’s get back to our
calculation. Now one way we can subtract a
multiple of 10 from a two-digit number is by using place value blocks to help. What is our starting number 36 look
like if we made it out of place value blocks? Well, it’s a two-digit number, so
all we’re going to need are some tens and ones. It’s made up of three 10s, these
have a value of 30, and six ones because 30 plus six equals 36. And we need to take away the number
20 from this, which we’ve said already is worth two 10s. There aren’t any ones at all. Let’s see how our two-digit number
changes then as we subtract these two 10s. Now, we’ll start as we would do
with any calculation like this, and that’s with the ones.
We’ve got six ones blocks here. But as we’ve said already, we’re
taking away a number of tens. If we look at the number 20,
there’s a zero in the ones place. We aren’t subtracting any ones at
all. So we start with six ones, and
we’re going to end with six ones. Our answer is going to have the
digit six in the ones place because six take away zero equals six. Now it’s time to consider the
tens. We’ve got three 10s blocks here
because there are three 10s in 30. But we know because we need to take
away 20, this is the same as taking away two of these 10s. Let’s cross two 10s blocks out, and
as we do, watch how the digit underneath changes. One, two. We know that three take away two
equals one, and so three 10s subtract two 10s is going to leave us with one 10. We’re left with one 10 and six
ones.
To find 20 less than a number, we
noticed that the ones digit didn’t change at all, but we’ve now got two less
10s. 36 subtract 20 equals 16. But what if we don’t have any place
value blocks to help us? There are other ways we could model
what we’re doing. Let’s try using place value
counters. This time, we could begin with the
number 62 and try to find out what’s going to happen if we subtract 40. 62 subtract 40 equals what. Let’s begin by modeling our
starting number again. The six in 62 is worth six 10s or
60. So we could model this using six
10s counters. And then we’re also going to need
two ones counters. Six 10s and two ones are the same
as 62.
Now as soon as we look at the
number that we’re taking away here, 40, we should be able to see that it’s a
multiple of 10 again. Because it’s made up of the digit
four in the tens place, we know that four 10s make 40. So as soon as it comes to actually
working out the subtraction and looking at our ones column, we know there’s nothing
we need to do. Because we’re taking away a
multiple of 10, we just need to think about the tens. If we start with two ones and we
take away zero ones, we’re going to be left with two ones. There’s been no change to our ones
digit at all. But there will be a change to our
tens digit. We’ve got six 10s counters here,
but we need to take away four 10s. How many tens do you think we’re
going to have left?
Let’s take away four of our 10s
counters and watch how the digit changes. One, two, three, four. We know that six take away four
equals two. And so six 10s subtract four 10s is
going to leave us with two 10s. Although the ones digit hasn’t
changed, our tens digit has decreased by four. 62 subtract 40 equals 22.
Hopefully, you’re getting the hang
of this now and you’re able to spot that what we’re doing each time is concentrating
on the tens digit. You know, we could solve a
calculation like this using a pencil and paper or even just using our heads. Let’s see how quickly we can find
the difference between 50 and the number on the card, which is 85. Do you remember that when we need
to find the difference between two numbers, one way we can do so is by using
subtraction. We start with the larger number,
and we can find the difference between them both by subtracting the smaller.
85 subtract 50 equals what. And there should be no surprise to
see we’re subtracting another number that ends in a zero. It’s a multiple of 10 again. Remember, we’re going to have to
find the answer by focusing on the tens. So we need to think of our
two-digit number in terms of its tens and ones. And we know that 85 is made up of
eight 10s and five ones. And those eight 10s are going to be
really important to us. Now we could just think about these
in our heads. Or if we had a pencil and paper, we
could just quickly sketch eight 10s and five ones. There we are. And the number that we’re
subtracting is simply a number of tens, five 10s and zero ones.
So what do we know about how our
starting number is going to change? Because we’re subtracting a number
of tens, we’re not going to be taking away any ones. And so the number of ones that we
had to start with, which is five ones, is still going to be five ones by the time we
finished. Five subtract zero equals five. But we know that our tens are going
to change. 85 has eight 10s, and if we want to
take away 50, that’s five 10s we need to subtract. Now we could just work out eight
take away five in our heads. If we’ve used a pencil and paper,
perhaps you can see a quick way to spot how to subtract five. The way that we drew our eight 10s,
we’ve actually partitioned them.
There’s a group of five at the top
and then three more underneath. So we can see straightaway that
five and three go together to make eight. If we want to subtract five from
eight, we’re going to be left with three. Eight 10s subtract five 10s leaves
us with three 10s. Our ones digit may not have
changed, but our tens digit has decreased by five 10s. Another way we could have found the
same answer in our heads is by counting back five 10s. We will show what we mean on a
number line, but you could just count backwards in your head. So we’ll start with 85 and then
count back five 10s. 75, 65, 55, 45, 35. Did you notice how each number we
said as we counted had five ones? 85, 75, 65, and so on. Just goes to show how that tens
digit changes, doesn’t it? The difference between 85 and 50 is
35.
Let’s answer some questions now
where we have to put into practice everything that we’ve learned about subtracting
multiples of 10 from two-digit numbers.
63 is six 10s and three ones. Take away one 10 to find 63
subtract 10. What is 63 subtract 30? Think: How many tens should you
take away?
As we read through this question,
did you notice two calculations that we need to work out? We’ve got 63 subtract 10 and then
63 subtract 30. Both of these calculations involve
the number 63. And our question starts off by
showing us how to model this number. We’re told that 63 is six 10s and
three ones. And the place value grid underneath
shows six 10s and three ones, both using place value blocks and also digits in the
correct columns. In the first part of the problem
then, we’re asked to find 63 subtract 10. And we’re told to take away one 10
to do this. Now this might sound obvious.
Of course, we have to take away one
10 if we want to find 63 take away 10. But understanding that the 10 that
we need to subtract is the same as one 10s block is going to help us later on. Let’s see what happens then, when
we take away one 10. Here are our six 10s and three
ones, just like they are in the place value grid. If we’re taking away one 10, we
don’t need to do anything to the ones blocks, but we do need to subtract one of our
six 10s. This leaves us with five 10s. Our answer has five 10s and three
ones. 63 subtract 10 equals 53.
In the second part of the problem,
we need to find the answer to 63 subtract 30. What’s this got to do with
subtracting 10? How is what we’ve just done going
to help us? Well, we’re given a clue
underneath. We’re asked, “How many tens should
you take away?” When we look at the number 30, we
can see a three in the tens place, but a zero in the ones place. This tells us that it’s a multiple
of 10: three 10s are 30, 10, 20, 30. So just like we subtracted one 10
in the first part of the question, we now need to subtract three 10s.
And because we’re only taking away
a number of tens again, we’re going to have three ones when we’re finished. There’s going to be no change
there, but our tens digit is going to change. We need to subtract three 10s from
the six 10s we already have. One, two, three. We know that six take away three
leaves us with three, and so six 10s take away three 10s is going to leave us with
three 10s. Our answer has three 10s and three
ones. It’s the number 33. In this question, we modeled a
two-digit number out of place value blocks. First, we subtracted one 10 and
then, we had a go at subtracting three 10s. 63 take away 10 equals 53. And 63 take away 30 equals 33.
Take away 20 from 68.
In this question, we’ve got a
subtraction we need to work out. We need to start with 68 and then
take away 20 from it. 68 subtract 20 equals what. Can you see that both the numbers
in this calculation have been written in a place value table for us? This allows us to think of the tens
and the ones separately because they’ve been written in separate columns. We can see that the number we’re
starting with, 68, is made up of six 10s and eight ones. But there’s something interesting
about the number that we’re taking away. 20 doesn’t have any ones. It’s a multiple of 10; it’s what we
get when we multiply a number by 10. Can you think how many tens there
are in 20?
Perhaps you can recall the fact two
times 10 equals 20. Or maybe you find the two digit in
the tens place helpful. Whatever you use to help you, we
can see that 20 is the same as two 10s. But because we’re subtracting zero
ones, we can fill in part of our answer already. We started with eight ones in 68
and we’re going to end up with eight ones. We don’t have to take away any
ones. Eight subtract zero equals
eight. But whilst we don’t have any ones
to take away, we do have to take away some tens. 68 has six 10s, and we need to
subtract two of them.
Now there’s a simple number fact
that we could use to help us here. Six take away two equals four. And if we know this, we also know
that six 10s subtract two 10s equals four 10s. Our answer is going to have the
digit four in the tens place. We found the answer by
understanding that to take away 20 from a number is the same as to subtract two of
its 10s. If we take away 20 from 68, we’ll
be left with 48.
Fill in the blank: 93 subtract what
equals 23.
Do you notice anything about the
numbers that we’ve been given in this subtraction? We have the starting number and
also the answer, but we don’t know what we have to take away to get there. To help us work out what’s being
subtracted, let’s look at how our numbers change. We could write our starting number
in a place value table. 93 is made up of nine 10s and three
ones. 90 and three make 93. Now, we don’t know what we’re
subtracting here. This is the number we need to
find. But there is something interesting
about the number that we get when we take it away. Our answer is 23 which is the same
as two 10s and three ones.
What do you notice about these two
numbers if we compare them? Well, they both contain three ones,
don’t they? We’ve started off with three ones
in 93, and we’ve ended up with a number with three ones, 23. The number that we’ve subtracted
can’t contain any ones at all. It must have a zero in the ones
place. But if we look at the number of
tens we have, they do get less. We’re subtracting a number of tens
here. And so the number that we’re taking
away must be a multiple of 10.
Now, if we start with nine 10s and
we end up with two 10s, how many tens have we taken away? Well, we know that two and seven
are two parts that go together to make up nine. And so if we start with nine and we
end up with two, we must have subtract seven. Nine 10s subtract seven 10s equals
two 10s. In this subtraction, we noticed
that the ones digit didn’t change, but the tens digit did. So we knew we were subtracting a
multiple of 10. 93 subtract 70 equals 23. Our missing multiple of 10 is
70.
So what have we learned in this
video? We’ve learned how to subtract a
multiple of 10 from a two-digit number using different strategies to help. These have included things like
modeling using place value blocks, completing place value tables, and working out
the answer in our heads.
