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Rational number word problem: ice

Word problems force us to put concepts to work using real-world applications. In this example, determine the volume of frozen water and express the answer as a fraction. Created by Sal Khan.

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• I'm confused. Why don't you just multiply 9 percent by 1/3? Why do you have to add 1/3 to the product of 1/3 times 9? That is what confuses me. Is it because when you times 9 by 1/3 that only tells you how much the water expands? Then you have to add that amount to 1/3 to get the total amount of volume of water?
• Yes, that's exactly it. Multiplying 1/3 by 9% will give you the amount of additioal volume that will be added when the water freezes, but to get the total volume of the ice, you'll have to add that addtional amount to the amount before freezing. The other way to do this is multiplying 1/3 by 109% (that's the same as multiplying it by 1.09).
• Hi In this example sal took 9% of 1/3 and then added with original 1/3 = 109/300 = 0.3633
What would have happened if we evaluated 1/3 = 0.33 and then taken 9% of 0.33 = 0.0297
Hence final answer would have been 0.33 + 0.0297 = 0.3597.
So can we say that taking % of fraction is more precise than converting it into decimal ?

Thanks
• Yes, usually working with fractions is more accurate than working with decimals, because when we use decimals we quite often create errors by rounding the numbers. You've given a good example, by saying that 1/3 = 0.33. It's not: 1/3 = 0.33333333... and so on forever. Try taking 9% of that instead -- you'll see that you get 0.03 and not 0.0297, so the final answer becomes 0.36333333..., and again so on forever. By contrast, the fraction 109/300 is totally accurate!
• is it important that denominator should be positive, while comparing rational numbers
• Good question. It makes it simpler to do the comparison if we don't have to worry about negative signs in the numerator and denominator. We can still compare them, but it's harder to do and we're more likely to make mistakes.

Making sure that the denominator is positive is one of those maths rules that doesn't actually change the value of anything, it just makes it easier for us to use. It's like using capital letters at the beginning of sentences - that doesn't change the meaning of a sentence, it just helps us when we're reading by making the beginning of the sentence more obvious.
• Why do you have to multiply 1/3 into 1/3+9%
• I'm confused.... how did he went from 1/3+3/100 to 100/300+9/300?
• It is easier to find the LCM of the denominators and then add the numerators while keeping the denominator the same. The LCM of 3 and 100 is 300, so the denominator becomes 300, and you multiply both numerators by the number it takes to get the denominator to 300.
• i wonder, does water actually enlarge by 1/3 when frozen or is this bogus?
• I believe so. My brother once put a can in the freezer and it exploded, because liquid expands when frozen.
• Im confused why did he add? I thought he was going to multiply
(1 vote)
• you have to add the original amount you started with, plus what it expanded to get the total amount. To do this you take the total volume you started with plus 9% of that volume. Which gives you your total volume.
• what is the definition of ratio
(1 vote)
• the quantitative relation between two amounts showing the number of times one value contains or is contained within the other.