Rational Numbers in an Interval

How many rational numbers in the interval \((0,1)\), when expressed in lowest terms, have denominators less than or equal to 10 ?

Details and assumptions

Clarification: The numbers \(0\) and \(1\) are not included in the open interval \( (0,1) \). On the other hand, the numbers \(0\) and \(1\) are included in the closed interval \([0,1] \).

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