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# Comparing fractions

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Manager
Joined: 27 Apr 2008
Posts: 190
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Kudos [?]: 46 [1] , given: 1

Comparing fractions [#permalink]  06 Jan 2010, 20:32
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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.
Senior Manager
Joined: 28 Jun 2009
Posts: 454
Location: United States (MA)
Followers: 16

Kudos [?]: 130 [0], given: 46

Re: Comparing fractions [#permalink]  01 Feb 2010, 09:42
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!!
Re: Comparing fractions   [#permalink] 01 Feb 2010, 09:42
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