Video Transcript
Multiplying Two-Digit Numbers by
One-Digit Numbers: Breaking Apart Tens and Ones
In this video, we’re going to learn
how to multiply two-digit numbers by one-digit numbers. And we’re going to do this by
breaking apart the larger two-digit numbers into tens and ones.
Let’s imagine that we’re playing a
computer game. We could see that each of these
four gold coins is worth 15 points. How many points could we get if we
collected all four of these coins? Now we could say the answer is
going to be 15 plus 15 plus 15 plus 15 or four lots of 15. But a quicker way to work out a
multiple addition like this is to write it and think of it as a multiplication. Four lots of 15 we could write as
four times 15 or, if we want to think of it the other way around, 15 multiplied by
four.
Now, how well do you know your four
times table? Perhaps you know what four tens
are, maybe even as much as four 12s. But here we’ve got a two-digit
number that’s a little bit beyond the times table facts that we usually learn in
class. How are we going to find out what
four 15s are worth? Let’s start by thinking about the
number 15. It’s made up of one ten and five
ones, isn’t it? Now, one thing we learn in maths is
that breaking up numbers into smaller parts can help us work with them. So instead of thinking of the
number 15 as 15, we could break it up into one ten and five ones. Let’s show four lots of 15 using
these base ten blocks then, one, two, three, four. And rather than thinking of this
calculation as four times 15, we can think of it as four lots of five ones and four
lots of one ten.
First, let’s multiply the ones. We know that five ones are worth
five, and so four lots of five ones are the same as four times five, five, 10, 15,
20. If we multiply the ones by four, we
get 20. What about the tens? We know that one ten is simply
worth 10, and so four lots of one ten is the same as four times 10, 10, 20, 30,
40. Four times 10 is 40. So we’ve multiplied out the ones
and the tens. What do you think we need to do now
to find the overall answer? We just need to add them together
to combine our two parts back together again. We know that two and four make
six. So 20 plus 40 must equal 60. Our score if we managed to collect
all these coins is going to be 60. Let’s see, shall we? Four times 15 or 15 times four
equals 60.
And you know, we can still use this
idea of partitioning a number into tens and ones with larger two-digit numbers. What score are we going to get if
we manage to burst all these bubbles? Well, there’re five bubbles and
each one will score us 36 points. So to find the total score, we’re
going to need to find five lots of 36. Now remember, instead of thinking
of 36 as this large two-digit number, we can partition it into its tens and
ones. 36 is made up of three tens or 30
and six ones or six. And so to find the answer to five
times 36, we can multiply the tens part by five, in other words, find the answer to
five times 30, and also multiply the ones part by five. That’s the same as finding five
lots of six. Now in our first example, we
multiplied the ones and then the tens. But just to show that we can do it
the other way round, let’s do it the other way round.
We know that five times three
equals 15 and so five times three tens equals 15 tens. That’s how we know five times 30 is
150. Now, we can multiply the ones. Five multiplied by six ones is
exactly the same as just saying five times six. And we know five times six is
30. Now that we’ve multiplied out both
parts, we just need to combine them back together again. We have zero in the ones place;
five tens plus another three tens makes eight tens. And we’ve got nothing to add to our
100 in the hundreds place. 150 plus another 30 equals 180. The score that we’ll get if we
burst all five bubbles will be 180.
Let’s have a go now at putting into
practice what we’ve learned so that you can multiply some two-digit numbers by
single digits. Let’s have a go, and remember we’re
going to need to partition those two-digit numbers into tens and ones to help
us.
Find the product 43 multiplied by
two by multiplying the tens followed by the ones and then adding. 43 multiplied by two equals
what?
In this question, we need to find
the product, which is what we get when we multiply two numbers together, of 43 and
two. And perhaps you know your two times
table up to 10 times two, maybe even 12 times two. But what about 43 times two? This is quite a large two-digit
number that we’re dealing with here. How can we multiply this two-digit
number by two? Well, the question tells us. First, we’re to multiply the tens,
then by the ones, and then add. What does this mean? Well, underneath the calculation,
we can see a picture that can help us here. It’s the number 43 modeled out of
place-value blocks. And place-value blocks are really
useful because they help us see numbers in their different parts. 43 can be partitioned or split up
into four tens or 40 and three ones, which of course have a value of three.
Now what this question is telling
us to do is not to look at 43 all in one go, but to first think about the tens and
multiply 40 by two, then think about the ones and multiply three by two. Now, we know that four times two is
eight, and so four tens multiplied by two is worth eight tens or 80. So if we multiply the tens part of
our number by two, we get the answer 80. Now let’s multiply the ones; three
times two equals six. So we’ve got the answers 80 and
six. And to find the overall answer, we
just need to combine these two parts back together again. 80 plus six equals 86. We found the product of 43 and two
by multiplying the tens, then the ones, and then adding the two answers
together. 43 multiplied by two equals 86.
We can use base ten blocks to help
us multiply numbers. Follow the steps to multiply 23 by
four. Multiply the ones. Three times four equals what? Multiply the tens. 20 times four equals what? Add the products to find 23 times
four. 20 times four plus three times four
equals what?
Base ten blocks or place-value
blocks are really useful in maths. They help us to model numbers in
different ways. And so if we’re faced with a
question where we need to multiply a two-digit number by a single-digit number like
this one, we can use base ten blocks to help. So in this question, we’re being
asked to multiply 23 by four. And in the first picture, we can
see that the two-digit number, 23, has been modeled using these blocks. Now, why would we do that? Well, because modeling a number in
this way helps us to see the number 23 in two parts. 23 is made up of two tens and three
ones or, in other words, 20 and three. And instead of having to worry
about what 23 fours are worth all in one go, we can just look at each part
separately.
To begin with, we’re told to
multiply the ones. 23 has three ones, which are worth
three, so let’s multiply this part by four. We know that three times four is
12. Now that we’ve multiplied the ones
by four, we need to multiply the tens by four. As we said already, there’re two
tens which are worth 20. Now we know that two multiplied by
four is eight. So two tens multiplied by four must
be worth eight tens or 80. 20 times four is 80. Now that we’ve multiplied both
parts of our number by four, how do we find the overall answer?
Well, in the final step, it tells
us we just need to add the products together. 20 times four is 80 and three times
four is 12. What’s 80 add another 12? Well we know that 80 plus 10 would
be 90 and 12 is two more than 10. The answer is not going to be 90;
it’s going to be 92. We’ve multiplied 23 by four by
multiplying the ones, then the tens, and then adding our two answers together. Three times four equals 12, 20
times four equals 80, and then 80 plus 12 equals 92. So we can say 23 multiplied by four
equals 92.
Use the following part-whole model
to find 12 times six.
How well do you know your six times
table? Perhaps you know it all the way up
to 10 times six. But do you know how to multiply it
by other two-digit numbers? Well, in this question, we need to
find the answer to 12 times six. And we’re given a part-whole model
that we’re told to use to help us. Well, we can’t see the number six
in this part-whole model, but we can see the number 12. Do you think this has got something
to do with the number 12 in our multiplication? Well, it does. What it’s showing us is that
instead of thinking of the number 12 as one number, we can partition it or split it
up because 12 is the same as one ten or 10 and two ones, which have a value of
two.
By including this part-whole model,
we’re being given a really big hint. We can make the multiplication
easier if we think of the tens and the ones separately. Instead of finding the answer to 12
times six, we can multiply the tens by six, then the ones times six, and then use
these two answers to help. We know that 10 times six equals
60, and then two lots of six equals 12. Now that we’ve multiplied both
parts of our number by six, we need to use these answers to help us find the overall
total. We’re gonna have to add our two
parts back together again. First, the ones, zero ones plus two
ones equals two ones. And then the tens, six tens plus
one more 10 equals seven tens. We partition the number 12 into its
tens and ones to help us find the answer to 12 times six. 12 multiplied by six equals 72.
To solve six multiplied by 14,
Jacob and Chloe break apart 14 into 10 and four. Six times 14 equals six times 10
plus four. Who has found the correct
answer? And then we got a picture of both
Jacob and Chloe. Chloe is saying “It is equal to 60
plus 24,” and Jacob is saying “It is equal to 60 plus four.”
This is a really interesting
question because one of these children has made a mistake. In a way, we need to be the teacher
here, and we need to find out which character has found the correct answer. To begin with, we can see that
Jacob and Chloe are trying to solve a multiplication, six multiplied by 14. Now, rather than thinking of the
number 14 all in one go, Jacob and Chloe are obviously using what they know about
numbers to help because we’re told that they break apart 14 into 10 and four. This is the same as splitting it up
into its tens and ones because one ten and four ones makes 14. And by splitting up a two-digit
number like this, Jacob and Chloe know that they can find six times 10 and then add
it to six times four.
But perhaps you can see from now
who’s made the mistake. But let’s multiply each part just
to check. Six lots of 10 equals 60. And we know that six fours are
worth 24. Chloe has found the correct answer,
hasn’t she? And can you see the mistake that
Jacob’s made? He’s multiplied the tens part of 14
correctly; six times 10 does equal 60. But when it comes to the ones part,
he’s just taken the number four. He hasn’t multiplied it by six.
In this question, we’re not told to
work out the actual answer of the calculation, but it’d be a shame if we didn’t. Let’s add Chloe’s numbers
together. Zero ones plus four ones equals
four, and then six tens plus another two tens equals eight tens. So by using Chloe’s method, we
found the answer to six times 14 is 84. Six multiplied by 14 is equal to 60
plus 24. And so the person who’s found the
correct answer is Chloe.
What’ve we learned in this
video? We’ve learned how to multiply
two-digit numbers by one-digit numbers by breaking them apart into tens and
ones.
