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## Lesson 7: One hundred percent

# Rational number word problem: ice

CCSS.Math:

## Video transcript

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.