# Reciprocal

The reciprocal of a number is 1 divided by the number. So, the reciprocal of the number, 5, is . Another way to think of the reciprocal is that it is what you need to multiply a number by for the product of the two numbers to be 1. Since

we can confirm that is the reciprocal of 5.

You can also think of the reciprocal as "flipping" the number. Flipping refers to switching the position of the numerator and denominator of a fraction as if you were flipping the fraction upside down. When taking the reciprocal of whole numbers, we need to add the fraction bar and the number 1.

Example

Find the reciprocal of :

We can simply switch the position of the numbers in the numerator and denominator of the fraction to find that the reciprocal of the fraction is .

To understand why, we can use the definition of the reciprocal as 1 divided by the number, where the number in this case is .

If you are familiar with exponents, given a number, n, the reciprocal can also be written as n^{-1}.

See also dividing fractions.