What is the result of multiplying a number by its inverse according to the inverse property of multiplication?

Multiplying a number by its inverse results in 1, according to the inverse property of multiplication. The inverse of a number is defined as the value that, when multiplied with the original number, yields the multiplicative identity, which is 1. For example, if the original number is ( x ), its inverse is ( \frac{1}{x} ). Therefore, when you multiply ( x ) by ( \frac{1}{x} ), you get:

[

x \times \frac{1}{x} = 1

]

This principle is fundamental in mathematics and helps establish the concept of inverses across various operations. Understanding this property allows students to solve equations more efficiently by recognizing how to manipulate terms effectively. The other options do not align with the definition of the inverse property of multiplication; for instance, multiplying by zero does not yield one, and the sum of a number and its inverse is not relevant in this context. Thus, identifying that the product of a number and its inverse is always 1 underlines the importance of understanding multiplicative relationships in mathematics.