What is the product of two reciprocal?

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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