A reciprocal of a number is \(1\) over that number (\(1\) divided by that number.

Every number has a reciprocal, except for \(0\) as division by \(0\) is undefined.

Some examples of reciprocals are

• The reciprocal of \(3\) is \(\dfrac{1}{3}\)
• The reciprocal of \(-23\) is \(\dfrac{1}{-23}\)
• The reciprocal of \(x\), for \(x \neq 0\) is \(\dfrac{1}{x}\). This can also be written as \(x^{-1}\).

The result of multiplying a number (except zero) by its reciprocal is \(1\).

As \(1\) is the multiplicative identity (when you multiply any number by \(1\), you get the original number back), another term for reciprocal is multiplicative inverse.