Beginner Mathematics-2

Relevant wiki: Euler's Totient Function

Fraction $\dfrac mn$ , where $m$ and $n$ are positive integers and $m < n$ , is proper when $m$ and $n$ are coprime integers.

Therefore the number of positive proper fractions with $n$ as denominator is the number of coprime integers of $n$ smaller than $n$ or the Euler's totient function $\phi (n)$ . For $n=75$ , we have $\phi (75) = 75 \times \dfrac 23 \times \dfrac 45 = \boxed{40}$ .