additive inverse

Every number has a partner that perfectly cancels it out. Take 8 steps forward, then 8 steps back, and you are exactly where you started. That backward number — the one that brings the total to zero — is the additive inverse, also called the opposite.

Formally, the additive inverse of a number a is the number −a, because a + (−a) = 0. Zero, the additive identity, is its own inverse since 0 + 0 = 0. To find an opposite you simply flip the sign: the opposite of 5 is −5, and the opposite of −7 is 7 (a double negative becomes positive).

On the number line, a number and its additive inverse sit at equal distances from 0 on opposite sides, so they share the same absolute value. The existence of an additive inverse for every number is exactly why subtraction works: subtracting a number is the same as adding its opposite, that is, x − a = x + (−a).