What is a reciprocal?

A reciprocal is defined as the number that, when multiplied by the original number, results in 1. This property is fundamental in mathematics and is crucial for operations involving fractions, division, and solving equations.

For any non-zero number x, its reciprocal is expressed as 1/x. This means that if you take a number x and multiply it by its reciprocal (1/x), the product will equal 1, illustrated by the equation: x * (1/x) = 1. This definition applies because division by x is essentially multiplying by its reciprocal.

The context provided in the question helps solidify the understanding of reciprocals. Knowing that reciprocals are essential for division and fraction manipulation can also clarify why the other choices don't hold true. For instance, a number x does not equal itself when considering its reciprocal (not correct), the reciprocal is never 0 (as that would be undefined), and x squared does not represent the concept of a reciprocal; it relates instead to exponential operations. Thus, the accurate definition of a reciprocal aligns perfectly with the formulation of 1/x, making it the correct and appropriate answer.