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Most liquids, when cooled, will simply shrink.
Water, on the other hand, actually
expands when it is frozen.
Its volume will increase by about 9%.
Suppose you have 1/3 of a gallon of water that gets frozen.
What is the volume of the ice that you now have?
So you're starting with 1/3 of a gallon of water.
They tell us that when it gets frozen, when it turns into ice,
its volume is going to expand by 9%.
So the new volume is going to be your existing volume.
So this is the original volume, 1/3 of a gallon,
and it's going to expand by 9%.
So your frozen volume is going to be your original volume
plus 9% of your original volume.
So you could say it's 9% times 1/3.
So this right over here is going to be the expanded volume.
Now, there's a bunch of ways we can figure it out.
We could turn things to decimals or whatever else,
but they tell us to express your answer as a fraction.
So let's make sure that everything here is a fraction,
and then we'll just try to simplify.
So the one thing that's sitting here that is not a fraction
is our 9%.
Well, what does 9% actually represent?
Well, 9% literally means 9 per 100.
So we could rewrite this as-- so this
is going to be equal to 1/3 plus, instead of writing 9%,
I'll write that as 9 per 100, and then once again times 1/3.
And we can simplify this expression right over here.
We have a 9 in the numerator, a 3 in the denominator.
If we divide both of them by 3, we get a 3 and a 1.
And so we're left with 1/3 plus 300 times 1/1.
Well, that's just going to be 3/100.
So this is just going to be equal to 1/3 plus-- I'll
write this in orange still, or maybe I'll
do it in a new color-- plus 3/100.
And now we have to add something, or two numbers that
have different denominators.
So let's find a common denominator.
So this is going to be equal to, well, the least common multiple
of 3 and 100.
And they share no common factor, so it's really just going
to be the product of 3 and 100-- the least common multiple is
300.
So it's going to be something over 300
plus something over 300.
Now to go from 3 to 300, in the denominator you multiply
by 100, so you have to multiply the numerator by 100 as well.
So 1/3 is the same thing as 100/300.
And to go from 100 to 300, we have
to multiply by 3 in the denominator,
so we have to multiply by 3 in the numerator as well.
So 3/100 is the same thing as 9/300.
And now we're ready to add.
This is going to be 100 plus 9/300, which is 109/300.
So this is the volume of ice that I now
have expressed as a fraction.