The additive identity property states that the sum of any number and zero is the original number. Zero is called the additive identity. Examples show that adding 0 to any number a yields a, such as 9 + 0 = 9. The document also provides an example of changing a subtraction problem, 3 - 15, into an equivalent addition problem by treating the subtrahend as a negative number: -15 + 3. This relates to the additive identity property by rewriting the subtraction as an addition with 0: 15 - 3 + 0 is the same as 15 - 3.