- A
- B
- C
- D
Step-by-Step Solution
The orange bar covers 3 of the 7 equal parts, so its length is . We need , so is the reciprocal: would be ADDED to reach 1, not multiplied.)
Answer: D)
The unit bar (blue) is cut into equal parts, and the orange bar is as long as some of those parts. By which number must the orange bar's length be multiplied so that it becomes exactly 1 unit long?
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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