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.