point a is 8/15 and point b is 9/15. what 2 points fall between them

Question

This is math question given to a middle schooler.

Answer 1

There is an infinitude of points between any two points, because the domain of real numbers is continuous.
I would pick two points that are equidistant from each other and from the two given points.
To do this I would first divide the space between them into 3: 1/3 of 9/15-8/15=1/45.
Then I would add 1/45 to 8/15: 24/45+1/45=25/45=5/9 and subtract 1/45 from 9/15: 27/45-1/45=26/45.
So what do we have? 24/45, 25/45, 26/45 and 27/45 or 8/15, 5/9, 26/45 and 3/5 (9/15).
Another way I could have done this is to work out 8 1/3 (25/3) and 8 2/3 (26/3) divided by 15: 25/(3*15)=25/45=5/9; 26/(3*15)=26/45.