Two numbers are reciprocals, or multiplicative inverses, of each other when their product is the multiplicative identity. For example, the reciprocal of 9 is 19 because their product is 1. 9*1/9=1 The reciprocal of a number a can be found by dividing 1 by a.

Shortcuts exist to find the reciprocals of specific types of numbers such as natural numbers, integer numbers, fractions, and decimals.

Type	Reciprocal	Example
Natural number a	1/a	The reciprocal of 2 is 12.
Integer numbers a, a≠0	1/a	The reciprocal of -6 is - 16.
Fraction a/b, b≠0	b/a	The reciprocal of 32 is 23.
Decimal a	1/a	The reciprocal of 0.2 is 10.2.

Finding the reciprocal of a mixed number is like finding the reciprocal of a fraction. However, the mixed number must first be written as an improper fraction.