# 2.Topic 3-Video 3

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Why don't we have a look at this video
oh how to multiply fractions together?
So, I'm going to start some pretty easy examples,
and I'm going to use these example to explain how to do it.
Then I'm going to bring some harder examples,
and then I can ask someones of you who can try on your own.
So,
we've got much further to do.
And, the other top of thing
you'll be multiplying when you multiply fractions is this
far, you might get to see something like it.
One that looks like this, it is quite simple.
Let's say half
times
three quarters.
Now,
what this actually means is a half of three quarters.
So,
we're going to get it smaller, in the end, here.
So, you might now be thinking what half of three quarters,
and you might me thinking what that is?
I'm going to show you how to do this,
mathematically.
But, why do we do this
is as follows.
I see clearly the top number is here and the bottom number is here.
So,
what we've got is a numerator and a denominator.
So, what we're going to be doing is
we're going to multiply
the 2 top numbers together to get a
first part of the answer.
Then multiply the bottom numbers together
to get the bottom part of the answer.
It says so, 1 times 3
is 3.
2 times 4
is 8.
So, the answer is three eighths.
And, that's how easy they are.
Now,
through another example,
I'll show you how I used to remember this as a kid.
When I wasn't sure of this,
then might be my brother coming home and telling me that
what is half times a half?
They've been telling me what it was and that actually stuck with me.
So, I thought it was pretty strange at the time when you're sort of thinking why that is.
But, if we work it what half times a half is,
1 times 1 is 1,
and 2 times 2 is 4.
I remember this as real little kid think how strange is what's that
half times of half
has given me a quarter.
This is like a
smaller answer.
I am sure that 1 is not.
But, that would be half plus a half.
When you think about this,
half of a half,
if I could imagine sort of a...
a pizza here,
and we've half of this pizza here,
what we have here
is a section which is a half.
But, if we
then cut that half again in a half,
or a half,
we're going to end up with
a quarter.
Okay.
So, hopefully that might be a way
you moreover would have meant if you'd know how to do that.
So, I'm going to give you another example here.
So, you might try this on your own.
Say, let's do,
what is three quarters
times
what about two thirds.
Okay.
You good to go.
All right.
Hopefully, you're going to pause if you're going to steal a bit of a time.
So, I'm going to go for the answer right now.
So, 3 times 2
is 6.
And, 4 times 3 is 12.
And, again to see that we can actually
take this stand even further,
because, there is another number that lies in to both here,
denominator and numerator...
that's the top and the bottom number.
And, this common number that goes into both of them
is 6.
So, 6 goes into 6 once,
and 6 goes into 12 twice.
So, this is assigned
as a half.
Okay,
did you go over there?
Now, that I'm pulling a couple of harder examples out. Okay, so,
there's some example I'm going to put up there...
involving mixed numbers there.
Mixed numbers are numbers that look like this.
So, we've something like this.
Say, it's 2 and a half,
and I'm going to times it by
3
and one quarter.
You have to multiply this.
It's all of a sudden a bit more difficult.
But, not much more difficult
which just requires one extra stick.
And what to do with this... what we have to do is...
we've to actually
change a number here
into a...
it's a mixed number,
so, it hasn't mixed...
it's got a...
a whole number and a part number,
so, it's called a mixed number.
into an improper fraction.
Now, that is a proper fraction.
But, an improper fraction would be
one way that this number appears.
How the top number appears with the bottom number.
So, I'll show you how to do it. It's most simple.
Because this...
then the easiest way to do this
is...
this is 2,
the bottom number stays the same,
2 times 2 plus 1
is 5.
Now, I'm just going to show you conceptually why this works.
When I do it, it always works.
Let's just draw 2 and a half.
So, this is my...
2 and a half.
Okay.
You might be able to count.
How many halves there are?
There's 1,
2, 3, 4, 5.
Okay.
There's 2, lots of 2s there.
2 times 2 part
which is this part.
Plus 1,
which is on this side.
This is giving you, say the top number.
And, there's
5.
It's okay.
I have got the denominator that's a 2.
These are halves, okay, so...
This is where we end up with a 5
divided by 2.
The easiest way to do this
is you keep the bottom numbers the same.
So, here the 2 stays the same.
And, then we go...
2
time 2, because, this is 2.
Lots of these.
Plus 1.
Okay.
So, it's 1, 2, 3, 4, 5.
Okay, so.
Using that same idea,
so, we're going to get 5 over 2.
Now, I'm going to multiply that.
We're going to change this one here,
in the same way.
3 times 4
plus 1.
So, 3 times 4 is 12,
plus 1,
is 13.
The bottom number stays the same.
Okay, what does this equal?
It's 5 times 13,
we're going to get the top number.
What do you think the answer to that is?
Okay, it'll have to be 65.
Okay, and this is going to go over
to 8.
How did you get to that is equally a question.
We can change this a little bit further there,
because, what you want to look at
is you might say we'll...
65 or 8, you don't want them like that,
because, this number here is bigger than this number here.
So, we can actually change this back into a mixed number.
And, the way we do this is as follows.
This 65 over 8.
Okay, this...
I've been probably pronouncing it the wrong way.
This line here...
I'm pretty sure it's called...
a vinculum,
if I'm not wrong with this.
I actually think that this is just 'divides'.
And, this here...
is, it means...
65 divided by 8.
It's a 65 divided by 8.
What did you get?
What do you get for that?
So,
65
divided by 8,
the answer to that,
is 8...
here's 8 8s are 64.
And, there's 1 left over.
So, this 1 we'll put
over 8.
So, we have one eighth.
Yeah.
Okay, we all now that this bottom number here
stays the same.
And, the 1, the remainder part,
over here.
65 divided by 8,
so, it's here.
Okay.
Let's take another example.
Then, I'm going to give you a whole bunch to do
by yourself.
So, what do we head on to do in this one?
What about I do...
1 and a half,
and, I'm going to times that by...
what do I do... I'll times that by 2 and half.
Okay.
So, first of all we're going to change these into
improper fractions.
These are mixed numbers.
So,
1 times 2 plus 1 is 3,
over 2,
times,
2 times 2 plus 1...
2 times 2 is 4, plus 1, is 5.
Bottom number stays as a 2.
And, then we just multiply straight across it.
So, 3 times 5 is 15.
And, 2 times 2 is 4.
And, we can take that to the next step,
because, 15 divided by 4 we can do.
15 divided by 4,
this goes 3 times,
because, 3 4s are 12.
And,
sorry, that part you might not have come through...
And,
we have 3 left over.
Okay, so, 3.
We're going to put that over 4.
Okay.
So,
I'm going to give you a couple weeks ahead of us to go on with this.
I hope you did pretty good with that.
So, what if you had a couple of examples.
Okay, so, let's give you...
I'm going to give you
3 examples here.
And, these are the
one of those not so easy ones,
which is going to be
what is 2
over 3
times
5
over 7.
We get five seventh.
It's not a commonly used fraction.
Looks like... we tend to prefer to use the quarters, and the halves, and the thirds, and that's what we do.
But, let's get it out there.
So, we want to do another one
which I'm going to do...
which is 1 and a quarter,
and, I'm going to times that by
2
and one third.
So, here you go with that.
And, in the last one we're going to do...
is I'm going to get you to do
2
and a half,
and, I'm going to get you to times it by
3
and 3 over 4.
That's three quarters.
Okay.
Let's see how you go.
So, pause the video.
Give them a go, and then we'll come back.
Okay.
Hopefully, you paused it.
Let's say here you go...
So, I'm going to go through them here.
So,
2 times 5 is 10.
3 times 7 is 21.
And, this is not a number that you guys can do anything about this.
So, that's your answer, 10 over 21.
Okay, this one here,
1...
Look, this is a mixed number, so, we have to change that into an improper fraction.
So, 1 times 4
is 4, plus 1, is 5 over 4.
Plus.
2 times 3, plus 1.
2 times 3 is 6, plus 1, is 7
over 3.
And, then I'll multiply these straight across.
Oops, I've got a plus there.
I don't know why I put it.
This is in fact
a
'times'.
Okay.
That's my little mistake.
So, now then we just have also fixed the numbers, as we go.
So,
5 times 7,
is 35.
And,
this is times, 4 times 3 which is 12.
Okay.
And,
35, this goes in...
2,
this 2 12s is 24.
And, there is 11 left over.
11 over 12.
Okay, how did you go with that?
All right, let's do this last one.
So, let's try to turn these mixed numbers into improper fractions.
2 times 2, plus 2, is 5 over 2.
Now, this one here is going to be
3 times 4, plus 3.
3 times 4 is 12, plus 3,
is 15 over 4.
Let's times these across.
5 times 15.
The answer to that is
What did you get as an answer to this?
Hopefully, you were able to get 5 times 15,
which is 75.
And, then 2 times 4
is 8.
So, 75 divided by 8
equals what?
Okay, so,
or what we can do is
9 8s are 72.
So, it equals 9
and, there is 72 to this.
3 left over.
3 over 8.
So, hopefully, that's the answer you got.
So, let me know how you went with those?
Hopefully, you did really, really good.
And, will see you next time.
Okay.
Bye!