﻿ Multiplicative Inverse or Reciprocal Motivation Problems

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Model for Fraction Division

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Find Standard Algorithm

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Multiplicative Inverse or Reciprocal

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Standard Division Algorithm

# Multiplicative Inverse or Reciprocal

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.

Inverse Property for Fraction Multiplication  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  .

## Self-Check Problems

Find the reciprocal (multiplicative inverse) for each of the following.  reciprocal 7 reciprocal 0 reciprocal   reciprocal Important Note. The reciprocal of zero is undefined.