How do you rationalize fractions

Main Question or Discussion Point

how do you do that

Answers and Replies

Fractions are already rational. Here's what "rational" means: http://en.wikipedia.org/wiki/Rational_number" [Broken]

Last edited by a moderator:
arildno
Science Advisor
Homework Helper
Gold Member
Dearly Missed
Fractions are already rational. Here's what "rational" means: http://en.wikipedia.org/wiki/Rational_number" [Broken]
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:
$$\frac{1}{\sqrt{2}}=\frac{1}{\sqrt{2}}*1=\frac{1}{\sqrt{2}}*\frac{\sqrt{2}}{\sqrt{2}}=\frac{\sqrt{2}}{2}$$

Last edited by a moderator:
HallsofIvy
Science Advisor
Homework Helper
What does this have to do with calculus? I am moving it to "General Math".

HallsofIvy
Science Advisor
Homework Helper
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.

arildno
Science Advisor
Homework Helper
Gold Member
Dearly Missed
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.

HallsofIvy
Science Advisor
Homework Helper
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.
"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"!