# Reciprocals

The reciprocal or multiplicative inverse of a number $x$ is the number which, when multiplied by $x$ , gives $1$ .

So, the product of a number and its reciprocal is $1$ . (This is sometimes called the property of reciprocals .)

Example 1:

$3×\frac{1}{3}=1$

so the reciprocal of $3$ is $\frac{1}{3}$ (and the reciprocal of $\frac{1}{3}$ is $3$ .)

Example 2:

$\frac{-4}{779}×\frac{779}{-4}=1$

so $\frac{-4}{779}$ and $-\frac{779}{4}$ are reciprocals.

Note that zero has no reciprocal .

Reciprocals are used to solve simple linear equations, for instance:

$-\frac{2}{11}x=3$

To solve, multiply both sides by the reciprocal of $-\frac{2}{11}$ .

$\left(-\frac{11}{2}\right)\left(-\frac{2}{11}\right)x=\left(-\frac{11}{2}\right)\left(3\right)$

$x=-\frac{33}{2}$