When the product of two numbers is one, they are called reciprocals or multiplicative inverses of each other. For example, 
and 
are reciprocals because 
. This is the motivation for the following property of fractions.
where a and b are nonzero. The fraction 
is called the multiplicative inverse of 
(or reciprocal) and vice versa.
Notice that a reciprocal (multiplicative inverse) can be formed from any common fraction by exchanging the positions of the numerator and denominator. The reciprocal of 
is 
, of 
is 
, and 
is 
. The reciprocal (multiplicative inverse) for a mixed number is found by first changing the mixed number to an improper fraction. For example, 
so the reciprocal of 
is 
.
Find the reciprocal (multiplicative inverse) for each of the following.
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7 |
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0 |
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Important Note. The reciprocal of zero is undefined.
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Date last modified: June 10, 2010.
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By Kris Montis and Timothy Peil
