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 × (1/3) = 1,

so the reciprocal of 3 is 1/3 (and the reciprocal of 1/3 is 3.)

Example 2:

(–4/779) × (–779/4) = 1,

so –4/779 and –779/4 are reciprocals.

Note that zero has no reciprocal.

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

(–2/11)x = 3

To solve, multiply both sides by the reciprocal of –2/11.

(–11/2)(–2/11)x = (–11/2)(3)

x = –33/2