﻿ Multiplicative Inverse or Reciprocal

Motivation Problems

------------------------

Model for Fraction Division

------------------------

Find Standard Algorithm

------------------------

Multiplicative Inverse or Reciprocal

------------------------

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.

 7 0

Important Note. The reciprocal of zero is undefined.