QR: Comparing Fractions

[theun4given]

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For the QR questions where they give you five fractions and ask either which is the smallest or which is the largest, what is the FASTEST possible way to do this question? Currently I am using the technique where you take two fractions at a time, multiply each by the denominator of the other, and compare the results. This method runs me about 3 to 3 and a half minutes, and no question is worth doing on QR if it takes longer than a minute I suppose. It just hurts to let these ones go when I know exactly how to get the right answer given more time. So any better methods anyone could recommend would be greatly appreciated.

Streetwolf, you out there?

 

[Streetwolf]

Right here.

If you have A/B and C/D you just need to compare AD to BC. If AD > BC then A/B > C/D. If not then C/D > A/B.

So then you either eliminate A/B or C/D as an answer. Let's say C/D > A/B. Then you know A/B isn't an answer.

Now check C/D with E/F. Do the same thing. Whichever is greater you would then compare with G/H. And whichever of those is greater you would compare with I/J. Whichever of those is greater is the answer.

That's assuming you want the greatest fraction. If you want the least greatest fraction you'd look for the lesser of the two values and continue on in that fashion.

If you want to do it all in one shot you would have to do it this way.

A/B C/D E/F G/H I/J

ADFHJ compared to CBFHJ compared to EBDHJ compared to GBDFJ compared to IBDFH. Whichever is the greatest value is the winner (or least).

In other words, the numerator of one fraction times the denominators of all the others (only the others...). The winning fraction is the value whose numerator is being multiplied. So if EBDHJ is the greatest value then E/F is the greatest fraction since E is in the numerator and in the value EBDHJ.

Of course that's a lot of junk to multiply so I'd stick with the first method.

Remember that some fractions are obvious to eliminate. If you have 4/7 and 5/7 in the same group of answers, you can eliminate one of them immediately and skip over it while testing. If you have 1/3 and 1/2 you know that 1/3 < 1/2 so you can eliminate one of those. Just be smart... Sometimes it's easy to draw the line at 1/2 and eliminate fractions that are obviously on the wrong side of that value. Of course that won't work if they are all less than or all greater than 1/2.