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CCSS.Math:

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 one third of a gallon of water that gets frozen what is the volume of the ice that you now have so you're starting with one third of a gallon of water and they tell us that when it when it gets frozen when it turns into ice its volume is going to expand by nine percent so the new volume is going to be your existing volume so this is the original volume original volume one third of a gallon it's going to expand by nine percent so you're frozen volume is going to be original volume plus nine percent of your original volume so plus nine percent of your original volume so you could say it's nine percent times one third 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 express your answer as a fraction so let's make sure that everything here is a fracture then we'll just try to simplify so the one thing that's sitting here that is not a fraction is our nine percent well what does nine percent actually represent well nine percent literally means nine per hundred so we can rewrite this as so this is going to be equal to one-third plus instead of writing nine percent I'll write that as nine per hundred and then once again times one-third times one-third and we can simplify this expression right over here we have a 9 in the numerator a three in the denominator if we divide both of them by three we get a three and a one and so we're left with one third plus three hundreds times one over one well that's just going to be three hundreds so this is just going to be equal to one over three plus I'll write this in orange still or maybe I'll do it anew plus three over 100 plus three over 100 and now we have to add something with have or two two numbers in a different denominator so let's find a common denominator so this is going to be equal to well the least common multiple of three and 100 then they share no common factor so it's really just going to be the product of three 100 the least common multiple is 300 so it's going to be something over 300 plus 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 a hundred as well so 1/3 is the same thing as 100 over 300 and to go from 100 to 300 we had to multiply by 3 in the denominator so we have to multiply by 3 in the numerator as well so 300 is the same thing as 9 9 3 hundredths and now we're ready to add this is going to be 100 plus 9 over 300 which is 109 over 300 so this is the volume of ice that I now have expressed as a fraction