HP vs Death Recap

I've never fully understood how the numbers in League of legends work, in fact I don't believe they are always reliable. A recent game as Galio is only one of few that my mind has been blown. I tank a lot, with voli mainly but now with galio. I sat with 3,112 HP with gargoyle stone plate, spirit visage, mercury treads, and warmog's armor. I went in to a full ap team fight and died in 8 seconds. The death recap showed all damage was magic based and that the total damage i received in 7 seconds was 812. My HP going into that fight was 3,112. By my math: (3,112 - 812 = 2,300). Can someone explain to me what I'm missing here? I feel like no matter how much armor, magic resist, or health I have I just get shredded.

I'd really like to understand more about league of legends because I just always feel afraid to engage, even if I'm 2 items ahead because I never know if I'll win or not. I just never seem to absorb, or deal the amount of damage I expect to based on my items vs theirs.