Luckily for me, the butter stick is divided into eight tablespoons (eighths!), so I went to go cut 3 tablespoons off. I looked again and thought that 3 tablespoons looked a little small. I looked at my math again. Sure enough, 3/8ths is the answer, so 3 tablespoons.
I could not figure out where I had gone wrong. I puzzled about it for a while, then decided to come at the problem from a different angle: 3/4 cup butter is 12 tablespoons, so to halve it, I wanted 6.
I called my mom to see what had failed in my calculations. We decided that my math was sound but that I had forgotten that a stick of butter (the eight tablespoons in question) is only a half a cup.
And now, I feel dumb.