conjugation (mnemonic)

In pre-college mathematics, students typically learn how to rationalize the denominator (or, in some cases, numerator) of expressions such as 311+2 and x+h-x-h2h. In to do this, they multiply the numerator and denominator of the fraction by an algebraic conjugate (or, in some cases, its negative) to eliminate the square root(s) ( in the appropriate part of the fraction. Typically, the only algebraic conjugates that pre-college students encounter are those in some quadratic extension.

Most students who have advanced far enough in mathematics to encounter rationalizing denominators or numerators have also encountered some (usually Indo-European) foreign . Such students are familiar with the concept of of verbs, in which the ending of the verb changes to make agreement with the person and number of the subject. A helpful mnemonic for students to the algebraic conjugates that they need to use is pointing out to them that the procedure in mathematics is (and actually easier) than in foreign . The algebraic conjugates (or their negatives) that they need are nothing more than changing the ending of the number. For example, the way that a pre-college student is taught to rationalize the denominator of an expression such as 311+2 is:


Title conjugationMathworldPlanetmath (mnemonic)
Canonical name Conjugationmnemonic
Date of creation 2013-03-22 16:00:59
Last modified on 2013-03-22 16:00:59
Owner Wkbj79 (1863)
Last modified by Wkbj79 (1863)
Numerical id 6
Author Wkbj79 (1863)
Entry type Definition
Classification msc 97D40
Classification msc 11R04
Related topic AlgebraicConjugates
Related topic Division
Related topic DifferenceOfSquares
Defines rationalize the denominator
Defines rationalize the numerator