Video Transcript
Multiplying Multiples of 10
In this video, we’re going to learn
how to multiply together a pair of multiples of 10. Now, before we start, let’s remind
ourselves what is a multiple of 10. Multiples of 10 are what we get
when we multiply 10 by any whole numbers, so numbers like 50, 30, 90, and so on. These are all multiples of 10. And they’re all the sorts of
numbers that we’re going to be multiplying in this video.
We can always spot a multiple of 10
because it has a zero in the ones place. Let’s choose two multiples of 10 to
use as an example. Let’s have 60 and 30. If we want to multiply these two
multiples of 10 together, how can we calculate 60 times 30? In this video, we’re going to look
at three strategies we could use in particular. And what we’ll do is we’ll keep
coming back to 60 times 30 to show that we can answer the same question but in
different ways.
The first thing we could do is to
use basic facts and patterns to help us. And this strategy is all about
looking at our multiplication and saying to ourselves, “Well, I might not know the
answer to this, but do I know another multiplication fact that maybe I could use to
help?” So let’s think about 60 times 30
then. What fact do we already know that
might help us multiply 60 by 30? Well, if we ignore the zeroes for a
moment, what about six times three? This is a fact we already know. Six groups of three equals 18. Now, if we know this basic fact,
what else do we know?
Well, we know what six lots of 30
is going to be worth. 30 is 10 times larger than
three. So six groups of 30 is going to be
worth 10 times more than 18. It’s 180. By making one of the factors 10
times greater, we’ve made the answer 10 times greater. Now what can we use six times 30 to
solve? 60 times 30, we could keep the 30
as it is, but we need to make our six 10 times larger. And because again we’ve made one of
the factors 10 times larger, the answer’s going to be 10 times larger again. Instead of 180, it’s going to be
1,800.
To find the answer to 60 times 30,
we first looked for a basic fact that we already knew to help us. If we know that six times three
equals 18, we can use this to help us see that six times 30 is 180. And then we can use that fact to
help us find that 60 times 30 equals 1,800.
Now, as we said a moment ago, we’re
going to keep coming back to this calculation. So we’re going to keep finding that
the answer’s 1,800, but we’re going to find it in different ways. But for now, let’s try a question
where we have to use basic facts and patterns to multiply two multiples of 10
together.
What is the result of seven times
three? What is the result of seven times
30? What is the result of 70 times
30?
We’ve got three multiplication
questions to answer here. Do you notice anything similar
about them? The digits seven and three keep
cropping up again and again, don’t they? The reason for this is because this
question is all about using a fact like seven times three to help us find the answer
to related facts. And so when finally we arrive at
multiplying these two multiples of 10 together, we’ll see that 70 times 30 has got a
lot to do with seven times three.
So let’s start off with the most
basic of these multiplication facts. What is the result of seven times
three? Three, six, nine, 12, 15, 18,
21. Seven threes are 21. Now if we look at the second
question we’ve got here, we can see that one of our numbers has changed. What is the result of seven times
30. Now if we write out this
calculation, we can see how it’s linked with the first one. Instead of finding the answer to
seven times three, we need to find the answer to seven times 10 lots of three, seven
times 30. And because one of our factors has
become 10 times larger, we’d expect the answer to become 10 times larger, too. So instead of 21, we get the answer
210. When we multiply a number by 10,
the digits shift one place to the left. And that’s why 21 becomes 210.
Finally then, we need to find the
result of 70 times 30. Now at the start, we probably
looked at this question and thought we’re multiplying two multiples of 10 here. This is really tricky. But because we’re working through
this step by step, it doesn’t seem so difficult anymore. We know what seven times three is,
and we know what seven times 30 is. So it’s not such a big step,
really, to move to 70 times 30. All we’ve done really is make the
number seven 10 times larger. And again, if we make one of the
factors 10 times greater, the answer’s going to be 10 times greater, too. So instead of 210, we’re going to
need to shift those digits one more place to the left. The answer’s 2,100.
This question has taken us through
some multiplications step by step. And it’s taught us that if we want
to multiply two multiples of 10 together, we could use a fact we already know to
help us. Seven times three equals 21. And if we know that, we know that
seven times 30 equals 210. And if we know that, then we also
know that 70 times 30 equals 2,100.
So that’s the first way we could
multiply two multiples of 10 together, taking a fact we already know and using it to
help. Something else we could do is to
use what we know about place value to help us. So if we come back to 60 times 30
for a moment, we could look at one of our factors and think about the place value
behind it. Let’s take our second factor
30. What is 30? Well, to write 30 we write the
digit three in the tens place. It’s the same as three 10s. So if we want to find out the
answer to 60 times 30, this is the same as 60 times three 10s.
How many 10s do we have if we have
60 times three 10s? Well, we could use that basic fact
again six times three is 18, so 60 times three is 180. 60 times three 10s is the same as
180 10s. And what’s the value of 180
10s? Well, we just need to multiply the
number 180 by 10, which means we need to shift the digits one place to the left. 180 10s equals 1,800. We found the answer by taking one
of our factors and thinking about its place value. It just made the multiplication a
little bit easier, didn’t it? Let’s answer a question where we
can practice using this strategy.
What is 60 times 40?
In this question, we’re given two
two-digit numbers to multiply together. And because both numbers end in a
zero, we can say they’re both multiples of 10. And there are some useful
strategies we can use when we multiply two multiples of 10 together. We could use place value to help
us. So we want to find the answer to 60
times 40. Now we could take one of these
factors and think about the place value behind it.
Let’s take the number 40. We know that 40 is the same as four
10s and zero ones. So if we want to find the answer to
60 times 40, it’s really like saying we want to find the answer to 60 times four
10s. Well, here’s where we could use a
basic fact we already know to help us. Six fours are 24. And so 60 fours are worth 240. 60 lots of four 10s is the same as
240 10s. But what are 240 10s worth? We need to multiply 240 by 10 to
find the answer. And we can do this by shifting the
digits one place to the left. 240 10s are the same as 2,400.
We’ve multiplied two multiples of
10 together here and used our knowledge of place value to help. 60 times 40 is the same as 60 times
four 10s. And because we know that six fours
are 24, we know that 60 fours must be worth 240. So 60 times 40 10s has a value of
240 10s. And working out what 240 10s is
gives us our answer. 60 multiplied by 40 equals
2,400.
So as well as using facts we
already know to help us, we can also use our knowledge of place value. And finally, there’s a third
strategy we could use. We could apply some of the
properties of multiplication we know about. Let’s come back one final time to
60 times 30. One of the properties of
multiplication that we know is that we can change the grouping of the factors in a
multiplication. This is called the associative
property. But this isn’t something we really
need to know right now.
But what is helpful to us here is
that we can split up 60 into six times 10 and we can think of 30 as the same as
three times 10. So really this property of
multiplication tells us that 60 times 30 is the same as six times 10 times three
times 10. Now you might be starting to wonder
how this is helpful to us. But there’s another property of
multiplication we could also apply. Perhaps you remember the one that
tells us we can multiply numbers in any order. It’s the commutative property. If we rearrange the numbers in this
long multiplication, it might start to look a little bit easier to us.
We could juggle the factors around
so it now reads six times three times 10 times 10. Now this still might look
complicated, but if we know that six threes are 18, which we do, and if we know that
10 10s are 100, which of course we do, then we know that this long multiplication
six times three times 10 times 10 is the same as 18 times 100. And to multiply 18 by 100, we
simply shift those digits two places to the left. Of course, we knew the answer was
going to be 1,800, didn’t we? We’ve done it three times. Let’s try a different
calculation. And we’re going to apply these
properties of multiplication to help us.
Fill in the blanks: 30 times 30
equals what times 100 equals what.
This question is all about
multiplying together a pair of two-digit numbers. And because both numbers end in
zero, we can say that they’re both multiples of 10. In fact, they’re the same multiple
of 10, aren’t they? Three 10s are 30. Now there are several ways we could
multiply 30 by 30, but in this particular question we can see part of our working
out has been completed for us. We need to change 30 times 30 into
something times 100. And we can do this by applying some
of the properties of multiplication that we already know. So the multiplication that we need
to solve is 30 times 30.
Now we know that one of the
properties of multiplication is that we can change the grouping of the factors in a
multiplication. So if we know that 30 is the same
as three times 10 — of course, the other lot of 30 will be worth the same — then 30
times 30 will be exactly the same as three times 10 times three times 10. Now we still haven’t changed our
multiplication into something times 100, but we’re getting there because now we can
apply another property of multiplication to help us.
And that’s the fact that we can
multiply factors in different orders and they still give us the same product. Can you spot any of these factors
that equal 100? Well, we know that 10 lots of 10 is
100. So if we move these factors to the
end and then move our two threes to the start, we’ve changed our calculation to
three times three times 10 times 10. Now, as we’ve said, 10 times 10
gives us 100, and three threes are nine. And 30 times 30 then is the same as
nine times 100. We can complete our first missing
number. And hopefully you can see it’s not
too difficult to complete our second because we know that nine lots of 100 are
900.
To find the answer to 30 times 30,
we used the properties of multiplication that we know. We changed our calculation into
something multiplied by 100, which made it much easier to work out. 30 times 30 is the same as nine
times 100, which equals 900. Our two missing numbers are nine
and 900.
So what have we learned in this
video? We’ve learned how to use different
strategies to multiply two multiples of 10.
