Firstly, it depends on what she means by a "proper fraction." As others have said, there is a definition.
Secondly, it depends on how much math your parents have studied. I can make an argument that if they've had only a bit or have studied advanced mathematics at uni, in either case they might object to it as a fraction (though in the latter case, they'd probably not use the term "proper fraction").
After that, although arithmetically correct, it's usually not done. It can make equation manipulation a real headache (ok, more of a headache in some situations). It's more of a best practices thing. Were a student/offspring come to me with (7.5)/8, depending on their background I'd use different ways to dissuade them from using that notation.
So, yes, the arithmetic checks out. It's generally not represented in that way for reasons.
Edit to say: It may depend, too, on why you're reducing the fraction. If this is for a uni assignment, depending on the instructions/assignment professors may not accept it as a valid fraction.