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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 .)

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 $-\frac{2}{11}$ .

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

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