Q. 5

Suppose and are two positive rational numbers. Where does lie, with respect to and ?

Answer :

I didn’t remember the concept used in this question.

There will be three cases for the question given above.


Case 1: when m/n >1 and p/q >1, this situation means that p > q and m > n


And this means that m + p > n + q and And this will mean > 1 and it will lie between m/p and n/q


Case 2: when m/n <1 and p/q <1, this situation means m < n and p < q


And thus m + p < n + q and this will mean < 1


And thus will lie less than m/p and n/q


Case 3: when any one is less than 1, then the case gets ambiguous.


Let m/n <1 and p/q >1


Now, m < n and p > q


Now we don’t know the nature of


And so this depends on the numbers taken.


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