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Find the number of distinct rational num...

Find the number of distinct rational numbers `x` such that `oltxlt1 and x=p//q` , where `p ,q in {1,2,3,4,5,6}` .

Text Solution

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As `0 lt x lt 1, " we have" p lt q`.

Thus, the number of rational number is 5+4+3+2+1=15.
When p and q have a common factor, we get some rational numbers, which are not different from those already counted. Here, there are four such numbers : `2//4, 2//6, 3//6, 4//6`. Therefore, the required number of rational numbers is 15-4=11.
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