Difficulty: Easy
Correct Answer: 1
Explanation:
Introduction:
This question checks your understanding of the concept of multiplicative inverse, also called the reciprocal of a number. It is a fundamental concept in algebra and arithmetic, often used while solving equations and simplifying expressions.
Given Data / Assumptions:
Concept / Approach:
For any non-zero real number a, its multiplicative inverse (reciprocal) is the number 1 / a such that: a * (1 / a) = 1. The very definition of multiplicative inverse guarantees that their product is always 1.
Step-by-Step Solution:
Step 1: Let the number be a (a is non-zero). Step 2: Its multiplicative inverse is 1 / a. Step 3: Multiply the number and its inverse. Product = a * (1 / a) = 1. No matter what non-zero value a takes (for example 2, -3, 0.5, 10, etc.), the product will always be exactly 1.
Verification / Alternative Check:
Take specific values: If a = 2, then inverse = 1 / 2 and product = 2 * 1 / 2 = 1. If a = -4, then inverse = -1 / 4 and product = -4 * (-1 / 4) = 1. Each example confirms that the product is always 1.
Why Other Options Are Wrong:
0: A product of 0 would require one of the factors to be 0, but by definition the number is non-zero.
-1: This would correspond to special cases where one factor is negative reciprocal of the other, not the multiplicative inverse defined as 1 / a.
Infinity: This is not a finite real number and does not represent the product of a and 1 / a.
Common Pitfalls:
A common mistake is confusing additive inverse (which gives sum zero) with multiplicative inverse (which gives product 1). Also, students sometimes forget that 0 has no multiplicative inverse, which is why the question specifies a non-zero number.
Final Answer:
The product of a non-zero number and its multiplicative inverse is always 1.
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