# 2.Topic 1-Video 2

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In this video,
we're going to take a look at equivalent fractions.
And, if you understand equivalent fractions,
working with fractions is pretty easy.
For what are they?
So, here you have two fractions.
One half and two fourth.
And, they're naming same part of that circle.
One half,
two fourth,
are equivalent fractions.
They are naming the same thing.
...which states
that any number times 1
will give you that same number.
It's identity doesn't change.
For example,
if you multiply 6 times 1,
you're still going to get 6.
The 6 doesn't change.
If you multiply one half
times 1,
you're going to get one half.
If you multiply anything by 1,
it's identity
won't change.
You'll end up with the original number.
Well, that's real important.
All of these fractions here,
are equal to 1.
Eleven elevenths and five fifths, and so on.
All of these equal 1,
which means if we multiply
something
times these fractions,
it won't change the identity
of that number.
For example,
if we took two thirds,
all of these fractions right here
are the same, and is 1.
It's like you're multiplying times 1
which means you're not changing
the identity of the original number.
Two thirds is equal
to 22 over 33.
Two thirds is equal
to
fourteen twenty firsts.
2 times 7 is 14,
3 times 7 is 21.
These are equivalent fractions.
If you multiply
2 times 5 and get 10,
3 times 5 and get 15,
two thirds and ten fifteenths
are equivalent fractions.
And, that last example,
when you're multiplying by three thirds,
it's like you're multiplying by 1.
You're really not changing the identity
of two thirds.
Two thirds is equal
to six ninths.
In fact,
all these fractions,
down here,
that we have created,
they're all equivalent fractions.
They are naming the same thing.
So, if your teacher asks you
to write four different equivalent fractions for three eighths,
it'd be easy.
We could multiply it, three eighths times 2 over 2,
which is just like multiplying by 1.
We're not changing three eighths' value.
3 times 2 is 6.
8 times 2 is 16.
Six sixteenths
is an equivalent fraction to three eighths.
What about if we multiply it times 4 over 4?
3 times 4 would be 12.
8 times 4 would be 32.
Twelve thirty seconds
is an equivalent fraction to three eighths.
What if we did
10 over 10?
...which is the same as 1.
That would be 30
over 80.
Three eighths and thirty eightieths
are equivalent fractions.
Now, what about if we did...how about 10,000 over 10,000?
...which is equivalent to 1.
It's like multiplying times 1.
That would give us 30,000
over 80,000.
That's an equivalent fraction to three eighths.
So, we just made
four fractions
that are equivalent
to three eighths.
Really easy.
Now, let's take a look at these equivalent fractions,
and, see if we can find the missing numerators and denominators.
So, if we look at the first one,
9 times 8 would give you 72.
If you multiply 7 times 8,
that would give you 56.
The missing numerator would be 56.
4 times 5 is 20.
And, 7 times 5
would be 35.
That's your missing denominator.
8 times 7 is 56.
Something times 7 is 21.
It would be 3.
2 times 9
is 18.
Something times 9 is 45.
It would be 5.
Now,
there's a couple of different ways you can tell if...
if two fractions are equivalent.
And, we'll look at both methods.
4 times 3 will give you 12.
Is 7 times 3, 28?
No.
Those are not equivalent fractions.
5 times 8 is 40.
Is 6 times 8, 48?
Yes, it is.
Those
are equivalent fractions.
The name the same thing.
We'll do a different method on this next one.
First, 7 times 3... 3 times 7 is 21.
Is 10 times 7, 30?
No.
Now, there's another way you could tell if these were equivalent?
If you cross multiply, you should get the same product.
So, 10 times 21
is 210.
30 times 3 is 90.
These are not the same.
That isn't... Those are not equivalent fractions.
I'll solve it... this last example.
6 times 6 is 36.
Is 9 times 6, 54?
Yes, it is.
Those are equivalent fractions.
Now, this is an interesting question..
And, equivalent fractions can help you to answer it.
Are there any numbers between one third and two third?
Wow!
When you first look at that,
you say, no, there is nothing in between one third and two third...
two thirds.
Well, that's... it's not true.
And, we can use equivalent fractions to help us.
If you took one third and you multiplied it
times 8 over 8,
which is like multiplying times 1,
you will get an equivalent fraction
of eight twenty fourths.
If we did the same thing to two thirds,
multiplied it by 8 over 8,
we would end up with 16
over 24
which is...
is also an equivalent fraction to two thirds.
So, instead of asking you,
are there any numbers between one third and two third?
...two thirds?
I asked you,
are there any numbers between
eight twenty fourths
which is the same as one third,
and sixteen twenty fourths
which is the same as
two thirds.
You'll say, yes, sure, there are.
There are quite a few things between
eight twenty fourths and sixteen twenty fourths.
And then...
there's actually a lot more than that
as well, but...
You can use equivalent fractions
that can help you in so many different ways,
when you're working with fractions.