As ChristopherSchlegel indicates, do not think of it as math...(im an engineer so I can relate to your quandry...) but relate to it as a construct or a division of TIME....

a clock... 4/4 time... 1 hour... 3/4 time... 45 minutes... 1/2 time...30 mins...

put another way...using math...

4/4 time... 1 second per note... 3/4 time = .75 seconds per note...1/2 time = .5 seconds per note... given there are 4 NOTES per measure....

all of this is per measure though.... now the "Math" part gets confusing when you get to 3/2 time lol... im still a beginner on guitar, and Piano, but I come from a Clarinet background and learned time signitures early on...

ChristopherSchlegel did I state this correctly?