comparing fractions

[wiltsman]

In NFER 11c q14 you are asked to find the largest out of 7/8 3/4 6/9 10/12 3/5. I can not see a common denominatorfor for all these numbers, and converting all of them to decimal could be time consuming in an exam. Has anyone has a really quick way to compare these fractions?

1) Reduce to lowest terms => 7/8 3/4 2/3 5/6 3/5

2) Eliminate quickly those that can't possibly be the largest.

a) 3/4 = 6/8 which is smaller than 7/8 so we drop 3/4
b) 2/3 = 0.666 and 3/5 = 6/10 = 0.6 so we drop 3/5
c) 2/3 = 4/6 which is smaller than 5/6 so we drop 2/3

We now have: 7/8 and 5/6

3) Use an easy test for the relative size of two fractions

Now for any fraction, if a/b > c/d then by cross-multiplying, ad > bc

So we can test:

Is 7/8 > 5/6 ?

Crossmultiply: Is 7*6 > 5*8 ? => Is 42 > 40 ?

42 is greater than 40 so 7/8 is greater than 5/6

=> 7/8 is the largest