Question

Question #929af

Answer 1

Actually, there are infinite. Just to show you some, remember that given two fraction, if the numerators are equal, the greatest fraction is the one with the smaller denominators.

So, if we fix the numerator to be `5`, we have that every fraction with denominator `>7` will be smaller than `5/7`, and of course will still be positive. So, you have infinite fractions of the form
`5/8, 5/9, 5/10, 5/11, 5/12, ...` which are between 0 and `5/7`

Otherwise, if the denominator if fixed, the greatest fraction is the one with the greatest numerator.

So, if we fix the denominator to be `7`, we have that every fraction with numerator `<5` will be smaller than `5/7`, and of course will still be positive. Examples are
`1/7, 2/7, 3.5/7, 4/7,...`