Video Transcript
Multiplying a One-Digit Number by a
Multiple of 10
In this video, we’re going to learn
how to multiply together single-digit numbers by numbers that are multiples of
10.
We know that multiples of 10 are
what we get if we multiply any number by 10. They’re what we say when we start
at zero and count on in tens. 10, 20, 30, 40, 50, and so on. These are all multiples of 10. And in this video, we’re going to
be taking multiples of 10 like these and multiplying them by one-digit numbers. So the sorts of calculations we’re
going to be thinking about are things like 50 multiplied by three, seven times 20,
or maybe even 80 times four. These are all examples of a
multiple of 10 being multiplied by a single digit.
Let’s imagine that there’s a big
concert and some music fans need to travel to get there. So they’ve booked six taxis and
also six coaches. Obviously, the taxis hold a lot
less people than the coaches. Five people can travel in a taxi,
but 10 times this can travel on a coach. These hold 50 people. So to work out the number of people
that will be traveling by taxi, we need to find the answer to six lots of five. And if we wanted to work out the
number of people that are traveling by coach, we’d need to calculate six multiplied
by 50. And before we start to work out
these numbers, can you see that this calculation here is exactly the sort of
calculation we said we’d be looking at in this video? We’re multiplying a one-digit
number by a multiple of 10.
Let’s use number lines to show how
we can work out both amounts. Let’s start with the taxis. And we’re going to count in fives
six times, one for each taxi. Five, 10, 15, 20, 25, 30. We know that six lots of five ones
equals 30. And so we know that we’ve 30 people
traveling to the concert by taxi. Now let’s work out how many people
are going to travel by coach. And because each of our six coaches
contain 50 people, we can find the answer by counting in fifties six times. 50, 100, 150, 200, 250, 300. By counting in fifties six times,
we found that six lots of five 10s equals 300. 300 people are going to travel to
the concert by coach.
Now what’s all of this got to do
with our video aim of multiplying a one-digit number by a multiple of 10? Well, do you remember we said our
second calculation, which was six multiplied by 50, is exactly the sort of
calculation we’re going to be thinking about. And let’s imagine for a moment that
you’ve been asked to work out the answer to six times 50. Of course, you could count in 50
six times like we’ve done here. But is there a quicker way to find
the answer?
Well, there is, you know. And we can find it by comparing our
two number lines together. With the first number line, we skip
counted in fives or five ones. But with the second calculation, we
skip counted by 10 times this amount, five 10s. And I don’t know if you’ve compared
the jumps we’ve made on both number lines, but if we look at the numbers we’ve
landed on each time, we can see a pattern. The bottom number is 10 times as
large as the top number. One lot of five is five, but one
lot of 50 is 10 times this. It’s 50. Two lots of five are 10, but two
lots of 50 are worth 10 times 10. They’re worth 100.
And we keep on seeing this all the
way down the number line. 150 is 10 times as large as 15. 200 is 10 times as large as 20, and
so on, until we get to the very last answer, where 300 is 10 times as large as
30. If we want to find the answer to
six times 50 or six times five 10s, we can first find the answer to six times five
or six times five ones and then just multiply the answer by 10. Let’s try a couple more examples
and show what we mean.
What if we want to find the answer
to 60 multiplied by four? Can you spot the number fact that
we’re going to use to help us? We know that 60 is worth six
10s. And so if we know the answer to six
times four or six ones times four, we can use this to help us. We know that six times four equals
24. And so six 10s times four equals 24
10s. And to find out what 24 10s are
worth, we just need to multiply 24 by 10. And we know that to multiply any
number by 10, we simply shift all of its digits one place to the left. 24 10s are worth 240. Six times four equals 24, so we
know 60 times four equals 240.
So far, we’ve used place value
blocks quite a lot to help us understand what’s happening. But we can also use what we know
about the properties of multiplication to help. Let’s imagine that we want to find
the answer to three times 50. And of course, we know that 50 is
worth five times 10. And so we know that the properties
of multiplication tell us that three times 50 is going to be the same as three lots
of five times 10. We also know something called the
associative property, which tells us that we can group the factors in a
multiplication in different ways. So if we want to find out the
answer to three times five times 10, we could work out three times five first and
then multiply the answer by 10.
Let’s read that calculation again,
and we’ll model it with place value counters. Watch what happens. So we find three times five, and
then we multiply by 10. And can you see this is going to
give us exactly the same answer as three times 50? So that’s how we’re going to
multiply one-digit numbers by multiples of 10. We’re going to use facts we already
know to help us. To find the answer to 20 times six,
we’ll be using two times six to help us. Three times 60 is made a lot easier
if we know what three times six is. We can find 90 multiplied by five
if we know what nine times five is, and so on. Hopefully, you’re starting to be
able to spot the calculations that can help you. Let’s put into practice what we’ve
learned now. We’re going to try multiplying some
one-digit numbers by multiples of 10.
Find the value of 90 multiplied by
three.
In this question, we’re being asked
to multiply a multiple of 10 by a one-digit number. We know 90 is a multiple of 10
because it ends in a zero. That’s always a good way to spot
them. And multiples of 10 are what we get
when we multiply a number by 10. And 90 is nine 10s, isn’t it? This is a fact that we can use to
help us find out the answer. And we can use place value blocks
to help see how. So firstly, if we think of 90 as
nine 10s, we can write our calculation as nine 10s multiplied by three, or in other
words three lots of nine 10s.
Let’s model these using place value
blocks. One, two, three lots of nine
10s. How many 10s blocks have we got
here? Let’s use our knowledge of the
three times table to help. Here we’ve got three lots of nine
ones. And if we know how many ones blocks
we’ve got, we also know how many 10s blocks we’ve got. Let’s count in nines three
times. Nine, 18, 27. We’ve got 27 ones blocks. And because we’ve got nine 10s
multiplied by three, we’ve also got 27 10s blocks.
But they’re not worth 27, are
they? Remember, each of our 10s blocks is
worth 10. And so to solve this problem, we
need to take our answer to nine times three and multiply it by 10. The diagram on the right is 10
times as large as the one on the left because each of the blocks we’ve used is worth
10 times as much. So what’s 27 multiplied by 10? Well, we know when we multiply any
number by 10, each of its digits becomes 10 times as large. And so it shifts one place to the
left. Instead of the two in 27 being
worth two 10s, it shifts one place to the left and is now worth two 100s. Instead of the seven in 27 being
worth seven ones, that also shifts one place to the left and is now worth seven
10s. And we need to include a zero to
show that we’ve got an empty ones column. 27 multiplied by 10 equals 270.
We’ve found the answer to 90
multiplied by three by thinking of the calculation as nine 10s multiplied by
three. We know that nine 10s are 10 times
as large as nine ones. So first, we found the answer to
nine ones multiplied by three, which was a lot easier. Nine times three equals 27. And then we just found the number
that was 10 times as large as this by multiplying 27 by 10. The value of 90 times three equals
270.
Use the number line to find the
value of 20 multiplied by four. Then we’ve got five possible
answers: 24, 60, 80, 100, or 40.
In this question, we’re being asked
to multiply a multiple of 10 by a one-digit number. And we’re told to use the number
line to help us. Let’s take a moment to look at this
number line. We can see that it’s labeled from
zero all the way up to 100. And each interval is worth 10. That’s why each of the numbers
that’s marked is a multiple of 10: zero, 10, 20, and so on.
Now, how can we use this number
line to help us find the answer to 20 times four? Well, we can think of this question
as asking us to find four jumps of 20 on our number line. Now, how many intervals of 10 would
we need to cross to make one jump of 20? How many numbers would we have to
count along our number line? One, two. Because each interval is worth 10,
we move along two numbers for every 20. Now, the reason why we’re saying
this and not just counting along the number line is that we can actually work out
the answer before we start.
If we move along two numbers for
every jump of 20 and we need to find four 20s, then the number of numbers that we’re
going to move along our number line is the same as two times four. We’re going to end up eight numbers
along, which is the same as eight intervals along. And because as we’ve said already
each interval is worth 10, we’re going to arrive at a number that’s worth eight
times 10. We can predict we’re going to end
up at the number 80. Let’s actually use our number line
the way it’s supposed to be used. We’re going to count along in 20s
four times. And let’s see whether we end up at
80.
So we’ll say zero and then 20, 40,
60, 80. We were right! We predicted that we’d need to move
eight numbers along our number line to find the answer. And because our numbers increase by
10 each time, we predicted that the number we’d end on would be worth eight times
10. If two times four equals eight, we
know 20 times four must have a value of 80.
Calculate two times three. Use the answer to the previous
question to help you calculate two times 30. From the answers to the previous
questions, which of the following is equal to two times 30? Two times three, two times three
times zero, two times three times two, two times three times 10, or six plus 10.
This question has three steps to
it. And to start with, you might look
at it and think to yourself, what have all these steps got to do with each
other? They’re asking three different
things, aren’t they? Well, yes, each part does ask us to
do something different, but they’re all related. And hopefully, by the end of this
question, you’ll be able to see how they’re linked and importantly how this very
first, quite easy fact can help us work out something much harder.
So to begin with, we’re asked to
calculate two times three. Hopefully, we don’t have to think
too much about this, do we? Two threes are six. On to the next part. We’re now asked to use the answer
to the previous question, so that’s the number six, to help us calculate two times
30. How can we use the answer to that
simple multiplication to find the answer to this one, which is a lot harder? Well, let’s take a moment to look
at this calculation. We’re being asked to multiply a
single-digit number, two, by a multiple of 10, 30. We know the number 30 is a multiple
of 10 because it’s a number in the 10 times table. It’s worth three 10s. And knowing this is going to help
us.
Two times 30 is the same as saying
two times three 10s. So how many tens is that? Maybe now you can see how the
answer to the previous question can help us. If two times three is six, then two
times three 10s is six 10s. And what are six 10s worth? We just need to multiply our first
answer by 10. Six times 10 equals 60. Our second answer is 10 times as
large as the first one.
In the third part of this question,
we’re asked to use what we’ve done previously in those first two calculations to
help us find a calculation that’s equal to two times 30. So let’s go back right to the start
and talk through what we’ve done. We wanted to find two times 30. We know that 30 is worth three
10s. So first, we found two times
three. This gave us the number of tens in
our answer. And to find the value of our
answer, we then multiplied this by 10. Can you see which one of the
calculations is the same as this? Let’s write it out as we say
it.
First, we found the value of two
times three. As we’ve just said, this gave us
the number of 10s in our answer. And to find the value of our tens
in the answer to our question, we need to multiply this by 10. Two times three times 10 is the
same as two times 30, and we can see why. The number 30 is simply being split
up into three times 10.
In this question, we’ve found how
we could use a fact we already know to help us multiply a one-digit number by a
multiple of 10. If we know two times three, we can
use this to help us find two times 30 because we know our answer will be 10 times
greater. Two times three equals six. And so we know two times 30 must be
equal to 60, which is the same as two times three times 10.
So what have we learned in this
video? We’ve learned how to multiply
one-digit numbers by multiples of 10 using multiplication facts we already know to
help.
