- A
- B
- C
- D
Step-by-Step Solution
A number times its reciprocal is 1, so the multiplier is . ✓ Traps: loses the sign and yields −1, while is what you would ADD to to reach 1 — the additive question, not the multiplicative one.
Answer: D)
By what number must be multiplied to get 1?
Class 8Rational NumbersRational Numbers
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).
**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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