What is the outcome when a number is multiplied by its inverse?

When a number is multiplied by its inverse, the outcome is always one. The inverse of a number is defined as the number that, when multiplied by the original number, results in the identity element for multiplication, which is one. For instance, if you take a number ( x ), its multiplicative inverse (or reciprocal) is ( \frac{1}{x} ). Therefore, when you multiply ( x ) by ( \frac{1}{x} ):

[

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

]

This relationship holds true for any non-zero number. Since the identity property of multiplication states that multiplying any number by one does not change its value, the product of a number and its inverse is indeed one.

Understanding this principle is fundamental in algebra, especially in solving equations and understanding the properties of numbers.