Video Transcript
Dividing a Two-Digit Number by a
One-Digit Number: Breaking Apart Tens and Ones
In this video, we’re going to
divide two-digit numbers by single digits. And we’re going to do this by using
models and by breaking apart the numbers. One of the methods that we can use
to divide by a one-digit number is taking multiplication facts we already know and
using these to help. So, for example, if we want to find
the answer to 16 divided by two, we just need to recall that eight twos are 16. And then we can say that 16 divided
by two equals eight.
But what if we need to divide a
larger two-digit number by a single digit? What if we can’t think of a
multiplication fact straight away to help us? Let’s imagine that we want to find
the number of twos in 48. 48 divided by two equals what. Even though we can use
multiplication facts to help, what if we’ve only learned our times tables up to 10
times two is 20 or 12 times two is 24? We need to know how many twos there
are in 48. What are we going to do? Well, as we see in maths again and
again, we don’t need to use numbers as they are. We can break them up into smaller
pieces to help us. And that’s exactly what we’re going
to be doing in this video.
We’re going to be partitioning or
breaking apart the two-digit numbers to make them easier to divide. In this calculation, the number
we’re dividing is 48. Now if we want to split up the
number 48 into smaller parts to make it easier to divide, what’s a quick way we
could do it? Splitting it into its tens and ones
is pretty quick, isn’t it? Let’s see if this helps us. 48 is made up of four 10s or 40 and
eight ones. So one way we could split up 48 is
into 40 and eight. Now there’s no point doing this
unless it’s going to make our division easier.
But we need to stop at this point
and ask ourselves a question. Can we divide both of our parts by
two? Are they both multiples of two? Because if they’re not, we need to
find another way to split up the calculation. We haven’t made it easier for
ourselves at all. Now one thing we know about
multiples of two is that they’re always even, and this makes it really easy to spot
them. We could see straight away that
both 40 and eight are even numbers. So we are going to be able to
divide them by two. Let’s use the place value blocks to
help us.
If we divide four tens by two,
there’ll be two tens in each part. And so we know 40 divided by two
equals 20. And if we divide eight ones by two,
we’re going to get four ones. Eight divided by two equals
four. Now can you see what we need to do
to find the overall answer? We need to put our two parts back
together again. We said that half of 40 is 20, half
of eight is four, and so half of 48 is 24. 48 divided by two equals 24. But what if splitting a number
directly into its tens and ones doesn’t help us? A good example of this might be a
calculation, something like 45 divided by three. Watch what happens when we try to
split it up directly into its tens and ones.
45 can be split into four tens and
five ones. But we can see this isn’t going to
help us at all. Neither 40 or five are numbers in
the three times table. So if we try to divide these parts
by three, we’re gonna have bits left over. We haven’t made the division easier
at all. We’re going to need to break apart
45 a different way. Now we know there are all sorts of
ways to split up the number 45. So what have we got to do? There must be a quicker way than
just seeing how we can split 45 up again and again until we just come across an
answer where both of the parts are multiples of three.
A good place to start is to keep
this idea of tens and ones, but to look for a multiple of 10 that’s also a multiple
of the number we’re dividing by. In this example, we look for a
number that’s a multiple of 10 and also multiple of three. And three times 10 is 30. So we can split 45 into 30 and
15. And our knowledge of the three
times table tells us that both these numbers are multiples of three. We found a way to break apart 45 to
make it easier to divide by three. Now we can get on and work out the
answer. We know that 10 threes are 30, so
30 divided by three equals 10. And we know that five threes are
15, so 15 divided by three equals five. And if we add our two parts back
together, 10 plus five equals 15.
We split up the number so that
there were 10 threes in this part and five threes in this part. This is how we know there are 15
threes in the whole amount. 45 divided by three equals 15. The big difference between this
question and the last example is that breaking apart our number into its tens and
ones didn’t help us here. We needed to give the breaking
apart step a little bit more thought and find a way to split up 45 so that both
parts were multiples of three. And it’s probably fair to say that
in most divisions we’re going to need to do this. Not all divisions split neatly into
their tens and ones. In fact, this skill is so
important. Let’s practice it on its own for a
second.
Here are two more divisions. Now we’re not gonna be answering
these, so don’t worry about that. But let’s just ask ourselves a
quick question. How would we split up these
two-digit numbers to make the division easier? Let’s just practice this skill. In the first calculation, we’re
being asked to divide 72 by six, and if we break apart 72 into its tens and ones
directly, this is going to give us 70 and two. These aren’t multiples of six, and
this hasn’t made the calculation easier for us at all. So let’s try the idea that we
talked about earlier. Let’s look for a multiple of 10
that’s also a multiple of six.
We know that six times 10 is
60. So we’ve got a part here that’s
quite large, but also quite easy to divide by six. And if one of our parts is 60, we
know the other one must be 12 because 60 plus 12 makes 72. And so if we wanted to, we could
then get on and answer the question. Probably the most helpful way to
spit up 72 is into 60 and 12. Our second example is 96 divided by
four. And again, we’re not going to work
out the answer here. We’re just going to practice our
skill of seeing how we can spit up the number. And again, we can see straightaway
that breaking it apart into its 10s and ones isn’t going to help us. 90 and six are not multiples of
four.
Remember that to help us, we can
think of a multiple of 10 that’s also a multiple of four. And four times 10 is 40. And if one of our parts is 40, the
other one is going to have to be 56 because 40 plus 56 is 96. Now both these numbers are
multiples of four, but we haven’t made this calculation a lot easier, have we? We’ve still got to work out 56
divided by four, which is quite a large number. And in an example like this, it
might be easier to split up the number a different way. So we could say to ourselves,
“Well, I know what 40 divided by four is, so it’s going to be pretty easy for me to
find out what double this is, what 80 divided by four is.” So I could split up my number into
80 and whatever is left, which is 16.
These two numbers are also
multiples of four, but they’re a little bit easier and a little bit quicker to work
with. We’re going to have a go at
answering some questions now where we actually have to find out the answers. But hopefully you found what we’ve
just done here are useful. We’ve taken a moment not to find
out answers, but to think about how we would find those answers. It’s always useful to think about
how we can break apart a number to help. So let’s try these questions
then.
Divide into three groups. 33 divided by three equals
what.
In the picture, we can see a number
that’s been modeled out of base 10 blocks. And when we read the instruction,
divide into three groups, it’s this number that it’s talking about. It’s a number made from three 10s
and three ones. It’s the number 33. And we can write what we need to do
here in a number sentence. 33 divided by three equals
what. Because our number 33 has been
modeled for us in base 10 blocks, it’s already being broken up into its 10s and
ones. And because there are three of
each, hopefully you can see it’s going to be quite easy to split them up.
Let’s divide our 10s first of
all. 10, 20, 30. We’ve got one 10 in each group. 30 divided by three is 10. Now let’s divide our ones
blocks. One, two, three. Three divided by three equals
one. Each of our groups has one 10 and
one one. We’ve divided 33 by three by
modeling it using place value blocks, then dividing the tens and the ones
separately. 33 divided by three equals 11.
Use the following part–whole model
to find 84 divided by three.
Often, we can use times tables
facts we already know to help us with a division. But do you know a times tables fact
that’s going to help you find 84 divided by three? It’s quite a large two-digit number
we need to divide, isn’t it? And that’s why in this question
we’re shown how to split it up into smaller parts to help us. The whole amount in the part–whole
model that we’re given is 84; it’s the number we’re dividing. And we can see it’s been split into
two parts, 60 and 24. Now, often when we break apart
two-digit numbers to make them easier to work with, we split them up into their 10s
and ones. But with this calculation, it would
have meant splitting up the number into eight 10s or 80 and four ones.
But if our part–whole model had
shown 80 and four, we’d have found it really difficult to divide by three. Neither of these parts are
multiples of three. And that’s why we’ve been given
this particular part–whole model to help us. Both 60 and 24 are multiples of
three. And they’re also multiples of three
that we already know facts for. So we can divide each part by three
to help us find the overall answer. First of all, how many threes are
in 60? Well, this is still quite a large
number, but we know a fact that can help us. We know that 10 threes are in
30. 30 divided by three equals 10. And so, if we double 30 to get 60,
we double the number of threes that we have.
60 divided by three equals 20. Now we need to divide the second
part by three. How many threes are there in
24? Three, six, nine, 12, 15, 18, 21,
24. There are eight threes in 24. We found out there are 20 threes in
60 and eight threes in 24. And 20 plus eight equals 28. We’ve used the part–whole model to
find that 84 divided by three equals 28.
Mason spilled ink over his division
homework. What number is the arrow pointing
at?
We can see if we look quickly at
Mason’s division homework here, he hasn’t just had to do one thing to find out the
answer. He’s had to complete several
steps. But unfortunately, because he
spilled ink over his homework, the final answer and some of the other numbers he
uses in his working out have been covered up. Interestingly, our question doesn’t
ask us to find a final answer. We need to find the number that the
arrows pointed at. This is one of the numbers that
Mason uses along the way. Possibly the best way of finding
out this missing number is to think as if we were Mason. We could go through the whole
calculation step by step as if we were him and find all the missing numbers. Then we can understand what he was
trying to do.
To begin with, we can see the
division that Mason is trying to work out is 42 divided by three. And underneath the number 42, he’s
drawn a part–whole model. And we can imagine the sorts of
thoughts that would have gone through his head as he did this. He must have thought to himself,
“Well, 42 is quite a large two-digit number.” Perhaps he only knew his three
times tables facts up to 10 threes are 30. And so he’s clearly thought to
himself, “I need to split up the number 42 into easier parts, parts that I can still
divide by three.” Now although one of the parts has
been covered over when Mason spilled his ink, we can see that the first part is
30.
And what number goes together with
30 to make 42? 30 and 12 make 42, don’t they? And we know that both 30 and 12 are
numbers in the three times table. They’re multiples of three. And they’re a bit easier to divide
by three than 42. And Mason knows that if he divides
both parts by three and then adds his answers together, he’s going to find the
overall answer. In other words, 30 divided by three
plus the answer to — Oh dear. Here’s another ink splotch. Can you see what this missing
number is? It’s the same as the first one,
isn’t it? It’s talking about our second part
and dividing it by three. That’s better.
To find his answer, Mason needs to
divide 30 by three, 12 by three, and then add the two together. And in the next step, this is what
we can see he starts to do. We know that there are 10 threes in
30. That’s where the number 10 comes
from here. And now we’ve got another ink
splotch. This is going to be the answer that
we get when we divide 12 by three. Three, six, nine, 12. There are four threes in 12. So 12 divided by three equals
four. Now we found out the answer to this
particular question because we found the missing number. But it would be a shame not to
complete the calculation, wouldn’t it? 10 plus four equals 14.
So Mason has found out the answer
to 42 divided by three by breaking apart 42 into two easier numbers. What made them easier to work with
is that they’re both smaller than 42 and they’re both multiples of three. So Mason could just use
multiplication facts he already knew to help him. By going through the problems step
by step, we knew that the missing number was going to be the answer to one of our
parts divided by three. And that part was 12, and because
12 divided by three equals four, we know that’s the number that the arrow is
pointing at. The answer is four.
So what have we learned in this
video? We’ve learned how to divide a
two-digit number by a one-digit number by breaking up the number to help.
