What is true about the product of a number and its reciprocal?

The product of a number and its reciprocal is always equal to one. This is because the reciprocal of a number ( x ) is defined as ( \frac{1}{x} ). When you multiply a number by its reciprocal, the operation can be expressed mathematically as:

[

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

]

provided that ( x ) is not zero, since the reciprocal is undefined for zero. This fundamental property holds true for all non-zero real numbers, which establishes a consistent result in mathematics.

Because the product results in one, this is a crucial concept in various areas of mathematics, including algebra and fractions, demonstrating the relationship between a number and its reciprocal.