# 6.CI 3-Video 2

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Hi.
Welcome to Math Antics.
This video is all about 'Dividing Fractions'.
But, in order to understand how dividing fractions works,
we first need to learn about something called Reciprocals.
A reciprocal
is just a fancy math term
for what you get
when you switch the top and bottom numbers of a fraction.
For example,
if you have the fraction 1 over 2,
and, then switch the top and bottom numbers,
you'll end up with 2 over 1.
2 over 1
is the reciprocal
of 1 over 2.
And,
1 over 2
is the reciprocal of 2 over 1.
And, an interesting thing about reciprocals is
multiplying a fraction
by its own reciprocal,
will always give you 1.
That's because you have the same multiplication problem,
on the top and bottom,
so, you'll end up with a whole fraction
which is always 1.
Okay, that's nice.
But, what do reciprocals have to do with dividing fractions?
Well,
reciprocals let us do a really cool trick
that makes dividing fractions easy.
Whenever you have to divide something by a fraction,
you can multiply it
by the reciprocal of that fraction, instead.
And, you'll get the correct answer.
And, that's great news,
because, multiplying fractions is so simple.
This trick of multiplying by the reciprocal
because, fractions are really just mainly division problems.
So, when you multiply something by 1 over 2,
it's the same as dividing by 2,
since 2 is below the fraction's division line.
And, dividing by 2
is the same as dividing by 2 over 1,
because, you can turn any number into a fraction
by just writing in a 1 as the bottom number, right.
But look,
reciprocals!
That's why multiplying by 1 over 2
is the same as dividing by 2 over 1.
And, it's true the over way around too.
So, really,
it's like you never have to divide fractions.
You can just rewrite your division problems
so that you're multiplying by the reciprocal instead.
Then when you multiply,
you'll get the answer for the original division problem.
As always,
let's see a couple of examples of how this works
so you really understand.
Let's try this problem.
3 over 4
divided by 2 over 7.
Okay.
So, the first thing we want to do
is rewrite our problem.
Instead of dividing by 2 over 7,
we can multiply
by the reciprocal instead.
The reciprocal of 2 over 7
is 7 over 2.
So, our problem becomes
3 over 4
times 7 over 2.
Oh, I should mention a mistake
that a lot of students make
when they first learn to divide fractions.
Sometimes, students take the reciprocal of the first fraction,
the one that's been divided
or even the reciprocal of both fractions.
But, you'd only want to take the reciprocal
of the second fraction,
the one you're dividing by.
Okay.
Now, that our problem is changed into multiplication,
it's easy.
Just multiply the tops.
3 times 7 equals 21.
And, multiply the bottoms.
4 times 2 equals 8.
And, we have the answer to our fraction division problem.
So, 3 over 4
divided by 2 over 7
is 21 over 8.
So, that's pretty easy.
But, let's try one more example.
Let's try 15 over 16
divided by 9 over 22.
Again,
the first thing we'd want to do is rewrite our problem.
We'll change the 'divided by 9 over 22'
into 'times 22 over 9'.
Now, what we have to do is multiply.
But, since these numbers are kind of big,
I'm going to use my calculator to help.
Let's see here.
So, we have...
all right!
On the top,
we have 15 times 22
equals 330.
And, on the bottom,
we have 16 times 9
equals a 144.
So, the answer to our division problem
is 330 over 144.
Of course, that could be simplified
for your final answer on a test.
But, we'll cover simplifying fractions in another video.
All right!
That's how you divide fractions.
You just multiply by the reciprocal,
and you have your answer.
But, there's one more thing I want to show you.
You already know
that the line between the top and bottom number of a fraction
is just another form of the division symbol.
Well,
that means you'll sometimes see fraction division problems written like this.
This shows the top fraction,
2 over 3
being divided bu the bottom fraction,
4 over 5.
It's really just that we have a fraction
made up from other fractions.
The top number is a fraction,
and the bottom number is a fraction.
It just looks a little confusing,
because, we have all these fraction lines here.
But, we can make it look a lot better.
Let's rewrite this as a multiplication problem
by taking the reciprocal of the bottom number,
the fraction that we are dividing by,
and multiplying it
by the fraction on top.
There!
That looks easier to do.
And, it's really the same problem.
We just need to multiply to get the answer.
So, 2 times 5 equals 10.
And, 3 times 4 equals 12.
Okay.
So, there you have it.
What sounded really hard
turns to be easy as
flipping fractions upside down.
If you can multiply fractions,
then you can divide fractions too.
Don't forget to practice what you have learnt
by doing the exercises for this section.
Thanks for watching.
And, I'll see you next time.