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# Comparing fractions

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06 Jan 2010, 21:32
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Just want to point out something that I discovered today while studying PS. In questions that ask you to compare fractions, the trick is often not to compare them directly via converting all the fractions to have a common denominator. For example, when you are asked to find the biggest and smallest # in

$$\frac{5}{9}$$, $$\frac{5}{12}$$, $$\frac{23}{48}$$, $$\frac{11}{24}$$, $$\frac{3}{7}$$

the trick is to recognize that these numbers are all close to $$\frac{1}{2}$$, so you just have to find the difference between the numbers and $$\frac{1}{2}$$.

$$\frac{5}{9}$$ is > than 0.5, biggest #

$$\frac{5}{12}$$: distance is $$\frac{1}{12}$$

$$\frac{23}{48}$$: distance is $$\frac{1}{48}$$

$$\frac{11}{24}$$: distance is $$\frac{1}{24}$$

$$\frac{3}{7}$$: distance is $$\frac{1}{14}$$

since $$\frac{1}{12}$$ is the largest number, $$\frac{5}{12}$$ is the smallest #.

Hope this is helpful for others to recognize this pattern.
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01 Feb 2010, 10:42
Great logic!! But not sure if this is useful in all problems. I'll definitely start using it and will let you know my experience in few days.

Thanks for sharing!!
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16 Nov 2015, 18:48
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Re: Comparing fractions   [#permalink] 16 Nov 2015, 18:48
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