Question

How many rational numbers are there strictly between $0$ and $1$ with the property that the sum of the numerator and denominator is $70$?

Answer 1

The rational numbers between $0$ and $1$ whose the sum of the numerator and denominator is $70$ are as follows:

$\frac{1}{69}=0.014$

$\frac{2}{68}=0.029$

$\frac{3}{67}=0.044$

$\frac{4}{66}=\mathrm{0.0.06}$

$⋮$

$⋮$

$⋮$

$⋮$

$\frac{33}{37}=0.89$

$\frac{34}{36}=0.94$

Hence, there are a total of $34$ positive rational numbers between $0$ and $1$ such that the sum of the numerator and denominator is $70$.