About this video
Water expands by about 9% when it freezes. Starting with 1/3 gallon, the video writes the ice volume as 1/3 + 9/100 x 1/3, simplifies 9/100 x 1/3 to 3/100, and adds using a common denominator of 300 to get 109/300 gallon.
You'll be able to
- write a percent increase as original + percent x original.
- write a percent as a fraction over 100.
- add fractions with different denominators using the least common multiple.
Key words
- percent
- Per 100; 9% means 9 out of 100, or 9/100.
- volume
- How much space something takes up, here measured in gallons.
- expand
- To get bigger, taking up more space.
- least common multiple
- The smallest number that two numbers both divide into; for 3 and 100 it is 300.
- common denominator
- A shared bottom number that lets you add fractions.
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.
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