Equivalent Fractions

U02_L1_T4_we1 Equivalent Fractions

Sarah has $48.

She wants to save 1/3 of
her money for a trip.

How many dollars should
she set aside?

So we essentially want to think
about what 1/3 of 48 is.

Use 48 as the denominator
and find an

equivalent fraction to 1/3.

So what they want us to do in
this problem is they want us

to say, OK, we want 1/3 of her
money, but we want to write

this as an equivalent fraction
where we have 48 in the

denominator.

So this is equal to something,
some blank up here.

This is equal to something
over 48.

So how can we get it to that
something over 48?

So let's think about what
this means for a second.

So 1/3, if we were to draw
1/3, it looks like this.

You could imagine a box
or a pie, I guess.

So let's say that this is my
pie, and I have it split into

three pieces.

So let me split it into
three even pieces.

And 1/3 is one of those
three pieces.

That is what 1/3 means.

Now, if we want express this as
a fraction over 48, how can

we do that?

Well, we're going to
have to split this

thing into 48 pieces.

How can we split something
into 48?

Well, 3 times 16 is 48, so if we
split each of these into 16

pieces-- and it's going
to be hard to draw

here, but you can imagine.

Let's see, you split it into
two, now we've split it into

four, now you split
it into eight.

You're just going to end up with
a bunch of lines here,

but you can imagine, you can
just split each of these.

If you split each of these into
enough, you would have 16

pieces, so those would
be 16 right there.

You would have 16 right there
and you have 16 right there.

And I can just keep doing it.

Let me do it in the
green over here.

So if we just kept splitting
it up, we would get 48,

because you have this first
third would be 16 pieces, the

second third would be 16,
and then this third

third would be 16 pieces.

Altogether, you would
have 48 pieces.

Now, that 1/3, what does
that represent?

Well, that represents
16 of the 48.

It represents these
16 right here.

It represents these 16 right
there, so 1 over 3 is the

exact same thing.

So 1 over 3 is the exact same
thing as 16 over 48.

Now, we did it just by thinking
about it kind of

intuitively what 1/3 of 48 is,
but one way to do it more-- I

guess a process for doing it--
we would say, well, look, to

get the denominator, the bottom
number, from 3 to 48,

we multiply by 16.

3 times 16 is 48.

And that's literally the process
of going from 3 pieces

to 48 pieces.

We have to multiply by 16.

We have to turn each of our
pieces into 16 pieces.

That's what we did.

Now, you can't just multiply
only the denominator by 16.

You have to multiply the
numerator by the same number.

And so if each of my pieces
now become 16 pieces, then

that one piece will
now become 16.

So one way to think about it,
you just say, well, 3 times 16

is 48, so 1 times 16 will be my
numerator, so it'll be 16.

So 1/3 is equal to 16/48.

And another way you could think
about it, which you'll

learn in more detail later on,
is we want 1/3 of 48, right?

That's how much she wants to
save. 1/3 of 48 is equal to

1/3 times 48.

And when you multiply-- let me
write it like this-- 1/3 times

48, and you could rewrite
48 as a fraction 48/1.

It literally represents
48 wholes.

And when you multiply fractions,
you can just

multiply the numerators.

So this is equal to 48 over--
and then you just multiply the

denominators.

48/3, 1 times 48 is 48.

We'll see this in more
detail in the future.

Don't worry about it
if it confuses you.

In the denominator, 3 times 1 is
3, and 48 divided by 3, or

48/3, is equal to 16.

So 1/3 of 48 is 16,
or 16/48 is 1/3.

Hopefully, that make
sense to you.