Child key derivation - size of child private keys - don't get it

I got this book about bitcoin, I'm trying to understand what's going on, but things don't quite add up for me...I've included the portion of the book below, so you can see what I'm talking about.It says the parent private key is 256bits. I hash the parent public key + parent chain code + i to get a 512bit hash. I take the left half (256bits) and add it to the parent private key (256bits)... so? that would be 512 bits then? But apparently no - it's just 256bits -- which kind of makes sense, because the parent private key was 256bits, so we would expect the child private key to be the same... but it doesn't add up for me. Can anyone explain pls?​http://bit.ly/2DQkF70 via /r/Bitcoin http://bit.ly/2OsHCkM