## Intermediate Algebra (6th Edition)

The reciprocal of a number is a number or expression that you can multiply by it to get 1. Since $b=\frac{b}{1}$, and you need to get the numerator and the denominator to equal the same thing so that the expression equals one, the reciprocal of $\frac{b}{1}$ is $\frac{1}{b}$ for any nonzero number $b$. $\frac{b}{1}\times\frac{1}{b}=\frac{b}{b}$, or $1$.