Rational Number equations help

  • Context: MHB 
  • Thread starter Thread starter Paige1
  • Start date Start date
  • Tags Tags
    Rational
Click For Summary

Discussion Overview

The discussion revolves around the properties of rational numbers, specifically focusing on the product of a rational number and its inverse. Participants are exploring the concept of multiplicative inverses and identifying exceptions to the general rule, particularly concerning zero.

Discussion Character

  • Homework-related, Mathematical reasoning

Main Points Raised

  • One participant asks for help in showing that the product of a rational number and its inverse equals 1, seeking to identify an exception.
  • Another participant identifies zero as the exception, noting that it does not have an inverse.
  • A later post reiterates that zero is the exception and questions what the product of a rational number and its inverse would be.
  • Another participant proposes a representation of a rational number as $$\frac{m}{n}$$, where $$m$$ and $$n$$ are integers and $$m$$ is not equal to zero, and asks about the multiplicative inverse of $$m$$.

Areas of Agreement / Disagreement

Participants generally agree that zero is the exception to the rule regarding the product of a rational number and its inverse, but the discussion remains unresolved regarding the specific product of a rational number and its inverse.

Contextual Notes

The discussion includes assumptions about the definitions of rational numbers and their inverses, and it does not resolve the mathematical steps involved in determining the product of a rational number and its inverse.

Paige1
Messages
2
Reaction score
0
I have a question in math I need help with please:
Show that the product of a rational number and it's inverse is equal to 1, with one exception. what is the exception? can anyone help please?
 
Mathematics news on Phys.org
Paige said:
I have a question in math I need help with please:
Show that the product of a rational number and it's inverse is equal to 1, with one exception. what is the exception? can anyone help please?

zero is the exception as it does not have inverse
 
kaliprasad said:
zero is the exception as it does not have inverse

Thank you!

- - - Updated - - -

kaliprasad said:
zero is the exception as it does not have inverse

however, what is the product of the rational number and it's inverse?
 
We could choose to let the rational number be:

$$\frac{m}{n}$$ where $$m,n\in\mathbb{Z}\land m\ne0$$ (This just means $m$ and $n$ are integers, with $m$ not equal to zero.)

So, what would the multiplicative inverse, or reciprocal, of $m$ be?
 

Similar threads

Undergrad The Fundamental Theorem of Arithmetic and Rational Numbers
  • · Replies 6 ·
Replies
6
Views
2K
High School Proving the area formula for a rectangle for all positive real numbers
  • · Replies 10 ·
Replies
10
Views
3K
High School Extending the Fundamental Theorem of Arithmetic to the rationals
  • · Replies 35 ·
2
Replies
35
Views
5K
Undergrad Five points in space with rational distances that are not co-linear
  • · Replies 13 ·
Replies
13
Views
3K
MHB How Can Rational and Irrational Numbers Combine in Arithmetic Operations?
  • · Replies 16 ·
Replies
16
Views
3K
Undergrad Expressing any given point on plane with one unique number
  • · Replies 4 ·
Replies
4
Views
2K
MHB Rational function equation problem solving
  • · Replies 2 ·
Replies
2
Views
3K
MHB Practice problems of Rational Equations ?
  • · Replies 10 ·
Replies
10
Views
3K
MHB Is 7 an irrational number in the set of integers?
  • · Replies 5 ·
Replies
5
Views
3K
High School Uncomputable Numbers and Rational Approximations
  • · Replies 4 ·
Replies
4
Views
2K