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Best Strategy To Solve Fractions Questions

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by farukhawais » Sat Jun 12, 2010 1:57 am
If we are given a few fractions like:

Q1) 6/7 , 7/8 , 9/10 , 12/13 , 34/35

Q2) 3/8 , 5/7 , 7/8 , 9/12

And we are asked to find the smallest or the largest of the given fractions then what is the best, fool proof and above all the quickest strategy to solve such questions?
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by asamaverick » Sat Jun 12, 2010 3:05 am
The best trick is to get the denominator of all to the same number, I am sure you were aware of this.

But this is not always the easiest thing to do. Take for instance Q1 above. Here the denominators are 7, 8, 10, 13, 35....13 & 7 being prime, each of these fractions will have to be multiplied by 13*7*2*5*2*2. This is not the easiest thing to do.
Another quick approach I always use is this.

Note that for every positive p & q, p/q is < (p+1)/(q+1).
This will easily help you solve Q1 above.

For Q2, you can reduce the terms to 3/8, 5/7, 7/8, 6/8.
It's clear that 3/8 is the lowest and if you apply my trick here, you will know that out of 5/7 , 7/8 and 6/8 - 7/8 is largest.

Hope this helps.
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