Am I half Native American?

I already know my mom is half native american, my gran is full blood embera. now I'm finding out that both of my dad's grandmothers were indigenous as well, we have pictures and I went on ancestry.com to confirm this. But anyway, everyone is telling me that makes me genetically half indian. Ummm how so? just because they were my great grandmothers doesn't make me half native, that blood is too far back to make me a half blood right? I just see myself as black hispanic and that's it.