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HOW TO ORDER FRACTIONS FROM GREATEST TO LEAST?

How to order fractions from greatest to least: In SAT Math you sometimes may encounter a question that asks you to arrange or order fractions from greatest to least. To put fractions in order from greatest to least or vice versa compare them by multiplying numerator of one fraction with denominators of other fractions. Then fraction with greatest product shall be greatest, and the fraction with least product shall be least.

HOW TO ORDER FRACTIONS FROM GREATEST TO LEAST?
Example

Which one of following arrangements of three fractions is in order from greatest to least?

(A)  1/3, 2/7, 4/5
(B)  2/7, 4/5, 1/3
(C)  4/5, 1/3, 2/7

Solution

For ordering these three fractions from greatest to least, multiply numerator of one fraction with denominators of other two fractions as follows:

HOW TO ORDER FRACTIONS FROM GREATEST TO LEAST?

After cross-multiplication we see that 84 is the greatest and 30 is the least. So 4/5 is the greatest and 2/7 is the least fraction. In order from greatest to least we can arrange these 3 fractions this way.

4/5, 1/3, 2/7

So (C) is the correct choice.

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