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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