Inverse and reciprocal numbers

This publication discusses what are reciprocal and reciprocal numbers. We also give a rule by which they can be found, and a practical example is analyzed for a better understanding of the theoretical material.

Content

Definition of reciprocals

Let’s say we have an ordinary fraction 
3/7

.

If we swap the numerator and denominator in places (i.e., “turn over” the fraction), we get 
7/3

.

Fraction 
7/3

 called inverse fractions 

3/7

.

Also, if we flip 
7/3

, then you get the original fraction 

3/7

.

Consequently, the 
3/7

 и 

7/3

 are reciprocal numbers.

 

Note: the product of mutually reciprocal numbers is equal to one.

a ·
1/a

 = 1

 

For example:

9/XNUMX/XNUMX
1/9

 = 1

2/11

 · 

11/2

 = 1

The rule for finding the reciprocal

  1. We represent the original number (whole or mixed) as an ordinary fraction.
  2. Reverse the resulting fraction.

 

Example

Find the reciprocal of the mixed fraction 3
4/5

.

 

Decision:

First, let’s convert the fraction to a common fraction:

3
4/5

 = 

3 5 + 4/5

 = 

19/5
Swapping the numerator and denominator, we get the reciprocal of the number equal to 
5/19

.

Leave a Reply