Go Halves Meaning

(idiomatic) To divide equally between two parties.

Example:   Would you like to go halves in the grocery bill?
  Let's go halves in this big watermelon.
1906, Edith Nesbit, The Railway Children, Chapter 4: The engine-burglar,
  Bobbie couldn't help her face changing a little--not so much because she was disappointed at not getting the engine, as because she had thought it so very noble of Peter, and now she felt she had been silly to think it. Also she felt she must have seemed greedy to expect the engine as well as the sweets. So her face changed. Peter saw it. He hesitated a minute; then his face changed, too, and he said: "I mean not all the engine. I'll let you go halves if you like."