How do you rationalize fractions

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Discussion Overview

The discussion revolves around the concept of rationalizing fractions, with participants exploring the definitions and implications of the term "rationalize" in relation to fractions, particularly in mathematical contexts. The conversation includes clarifications on whether fractions can be rationalized and the specific processes involved.

Discussion Character

  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • Some participants assert that fractions are inherently rational numbers, questioning the need for rationalization.
  • One participant defines rationalizing a fraction as rewriting the denominator as a natural number, providing an example involving the square root of 2.
  • Others express confusion over the term "realizing" a fraction, suggesting it may stem from a misunderstanding or translation issue.
  • There is mention of rationalizing both the numerator and denominator, with some participants indicating that it is generally not possible to rationalize both simultaneously.
  • Several participants acknowledge corrections regarding the terminology and express regret for any confusion caused by their earlier statements.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the terminology and the concept of rationalizing fractions, with multiple competing views on what rationalization entails and whether it applies to fractions in general.

Contextual Notes

Some participants reference specific examples and personal experiences that may influence their understanding of rationalization, indicating a potential dependence on educational background and terminology used in different regions.

afcwestwarrior
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how do you do that
 
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Fractions are already rational. Here's what "rational" means: http://en.wikipedia.org/wiki/Rational_number"
 
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eccefeles said:
Fractions are already rational. Here's what "rational" means: http://en.wikipedia.org/wiki/Rational_number"

Incorrect!
A "fraction" is a real number that is written as the product of one real number a (called the "numerator"), and the multiplicative inverse of a real (non-zero) number b (called the denominator).

To "rationalize" a fraction means to rewrite the denominator as a natural number, if possible.

Example:
[tex]\frac{1}{\sqrt{2}}=\frac{1}{\sqrt{2}}*1=\frac{1}{\sqrt{2}}*\frac{\sqrt{2}}{\sqrt{2}}=\frac{\sqrt{2}}{2}[/tex]
 
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What does this have to do with calculus? I am moving it to "General Math".
 
I've never heard of "realizing" a fraction! What language is that translated from? However, I will agree that one does not rationalize fractions!
The example arildno gave was rationalizing the denominator of a fraction. There are also times when one would want to rationalize the numerator of a fraction. In general, it is not possible to rationalize both numerator and denominator at the same time.
 
I've never heard of "realizing" a fraction! What language is that translated from?

My apologies! I've made a big fool of myself once again. I was thinking about "realising" as in making the denominator of a fraction (containing complex numbers) real! (I was taught this term back in high school, here in Australia.) arildno and Hallsofivy are absolutely correct.

I'm really sorry for wasting everyone's time. I think I should go back to lurking. :blushing:
 
HallsofIvy said:
I've never heard of "realizing" a fraction! What language is that translated from? However, I will agree that one does not rationalize fractions!
The example arildno gave was rationalizing the denominator of a fraction. There are also times when one would want to rationalize the numerator of a fraction. In general, it is not possible to rationalize both numerator and denominator at the same time.

I stand corrected.
 
eccefeles said:
My apologies! I've made a big fool of myself once again. I was thinking about "realising" as in making the denominator of a fraction (containing complex numbers) real! (I was taught this term back in high school, here in Australia.) arildno and Hallsofivy are absolutely correct.

I'm really sorry for wasting everyone's time. I think I should go back to lurking. :blushing:

"realizing"! I like that. Reminds me of when, in an algebra class, we were learning about 'adding' an identity to a semigroup (to make it a monoid) and we had quite an argument about what the process should be called.

Suggestions were "unification", "one-ification" and "identification"!
 

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