Which statement identifies the additive identity element?

Which statement identifies the additive identity element?

• A. Zero is the additive identity
• B. One is the additive identity
• C. Two is the additive identity
• D. Negative one is the additive identity

Answer: (A)

The additive identity is the element that doesn’t change a number when you add it. Zero has that role because for any number a, a + 0 = a. For example, 7 + 0 equals 7, and -4 + 0 equals -4. That’s why zero is the additive identity. The other numbers don’t fit this idea: adding one changes the value (a + 1 ≠ a), so one isn’t the additive identity; the same is true for two or negative one. Remember, the identity for addition is the neutral element that leaves numbers unchanged, which in standard arithmetic is zero.

The additive identity is the element that doesn’t change a number when you add it. Zero has that role because for any number a, a + 0 = a. For example, 7 + 0 equals 7, and -4 + 0 equals -4. That’s why zero is the additive identity. The other numbers don’t fit this idea: adding one changes the value (a + 1 ≠ a), so one isn’t the additive identity; the same is true for two or negative one. Remember, the identity for addition is the neutral element that leaves numbers unchanged, which in standard arithmetic is zero.