Hi, I'm a DIYer and have an old (1950's or so) bathtub faucet I need to change. The pipe leading to it is brass (looks like 1/2 inch I think). I would like to cut the brass pipe to remove the old faucet and then install a new single handle faucet. My thinking is connect a copper pipe to the brass pipe and then install the new faucet connected to the copper pipe.

My question is: Can I simply cut the brass pipe and solder a copper pipe to it using some type of connector? If yes, what is the connector called and can I use the same flux and solder I normally use when going copper-copper?