SOLUTION: I am a proper fraction.The sum of my numerator and my denominator is a one-digit number.Their product is a cube.What am I? our topic is fractions

If the numerator is 1, then the product of it and the denominator will be that
denominator, so choose it as the only digit greater than 1 which is a cube,
which is 8. Then the sum of numerator and denominator will still be a one-digit
number, 9. 

So one solution is .

But there another solution because 8 is also the product of 2 and 4, and 2+4=6
is a one digit number 

The only other solution is .  I agree that's not reduced to lowest terms, but 
the instructions don't state anything about it having to be reduced.

There are no more solutions because the next cube after 8 is 27, but it has
factors 3 and 9, whose sum is 12, which is not a 1-digit number.

Answers:  and 

Edwin