Bitcoin is not summed automatically. If 1 BTC is paid twice to a particular address (A), you can think of it as having two coins labeled 1 BTC, rather than having 2 BTC.
In such situations, if A uses these two coins to pay 1.5 BTC to another address (B), a new transaction is created where two new coins labeled 1.5 BTC and 0.5 BTC are created and the 1.5 BTC are paid to B and 0.5 BTC is sent back to A as change. (Strictly speaking, a fee is paid, so A will be given 0.4999, not 0.5.)
In cases like this where the amount cannot be paid exactly, some amount of "change" must be returned to the sender.