You are filling up trays to make ice cubes.
You notice that each tray holds the exact same amount of water
but has a different number of ice cubes that it makes.
The blue tray makes 8 equally sized ice cubes.
The pink tray makes 16 equally sized ice cubes.
So let me draw the blue tray here.
The blue tray, I'll draw it like this.
That is not blue.
Let me draw it in blue.
So the blue tray makes 8.
So this is the blue tray right over here.
And let me draw it and divide it into 8 sections
to represent the 8 equally sized ice cubes.
And I'll try to do it.
So, let's see.
That's about in half, and then I'm
going to put each of those in half, and then each
of those in half.
So there we go.
This is pretty close to 8 equally sized cubes,
except for this one there.
Let me actually make it a little bit cleaner.
So there's the half, half, half, half, half.
All right, so this is looking a little bit better,
so 8 equally sized ice cubes.
This is the blue tray.
Now, the pink tray takes the same amount of water,
so I'm going to make it the exact same length.
So the pink tray is the exact same length,
but it has 16 equally sized ice cubes.
So what I'm going to do is I'm going
to make these same sections here,
but then I'm going to cut these sections in two.
So that's 8, and to 16, I got to divide these into two.
So almost done.
This is the hard part.
That last one wasn't that neat.
Almost done.
All right.
There we go.
Set up the problem.
Now, you put 3 ice cubes from the blue tray into your drink.
So, let's do that.
So, 1, 2, 3 ice cubes from the blue tray into your drink.
How many ice cubes from the pink tray
would you need to equal the same exact amount of ice?
So there's a bunch of ways to do it.
We can think about it with numbers,
or we can think about it visually.
Let's first think about it with numbers.
So how much of this tray have I pulled out?
Well, I have 8 equally sized cubes and I took 3 of them out,
so this literally represents 3/8.
So the question is 3 over 8, if I
take 3 out of 8 equally sized cubes, that's
the same quantity as taking what?
I want to do that in white.
That's the same quantity as taking
how many cubes out of 16, out of 16 equally sized cubes?
Well, let's look at it over here visually.
So if we want the exact same amount of ice,
so we're gonna have 1, 2, 3, 4, 5, 6.
We have 6/16, so this is equal to 6/16.
Now, does that make actual sense?
Well, sure.
To go from 3/8 to 6/16, you multiply the numerator by 2,
and you multiply the denominator by 2.
Now, does that actually make sense?
Well, sure it does.
Because for the pink ice tray, you
have 2 ice cubes for every 1 that you have in the blue ice
tray.
So the blue ice tray, you have 8 equally sized cubes.
Well, for each of those, you're going
to have 2 in the pink ice tray, so you multiply
by 2 to have 16 equally sized cubes.
And out of the blue tray, if you take 3, well,
that equivalent amount for each of those cubes,
you would get 2 from the pink ice tray.
So you're multiplying by 2 right over there.
So the answer to the question, how many
ice cubes from the pink tray would you
need to equal the same amount of ice?
Well, that is you would need 6 cubes.