1) In mathematical theory (which I believe is what were are dealing with), simplest terms are always important. You don't say 2A=2(pi)r^2. You don't say .77e=.77mc^2. You don't say a^2 + b^2 + 10=c^2 +10. You can, but you don't. Simplest terms are always used in mathematical theory.
2) You are askewing definition. 2 and 2/1 are interchangable. 2 is an integer, is that to say 2/1 is not also an integer, even though 2/1=2? 1/1 is a fraction, but since 1/1=1 it is also an integer. I'm fairly certain that the definition is specifying a ratio of two integers that is not also an integer itself, or the definition could also go: any real number that cannot be expressed as an integer (making fractions irrational number). Example, integer is defined as any real number with no fractional component. Is that to say 2u0/5 (two and zero fifths) is a compound fraction and not an integer? Even though you can see a fractional component, 0/5=0, thus there is no fractional component.
P.S.: I love math too. This thread is awesome. I had to think about my rebuttle for a rather long time because you guys did give some good evidence to support this notion.
