Which rational number is its own additive inverse?

Class 8Rational NumbersRational Numbers

A1
B−1
C0
DThere is no such rational number

Step-by-Step Solution

We need

a = - a

, which forces

2 a = 0

and so

a = 0

; indeed 0 + 0 = 0. The trap is choosing 1 or −1 — those are the numbers that are their own MULTIPLICATIVE inverse, which is a different property entirely.

Answer: C) 0

Key idea: Identities and inverses

**Additive identity**: 0. For any rational a: a + 0 = a.

**Multiplicative identity**: 1. For any rational a: a × 1 = a.

**Additive inverse** (negation): For a, the additive inverse is −a. Their sum is 0. So a + (−a) = 0.

**Multiplicative inverse** (reciprocal): For non-zero a = p/q, the multiplicative inverse is q/p. Their product is 1. **0 has no multiplicative inverse** (1/0 is undefined).

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