1 / 13

Understanding Rationalizing Denominators and Conjugates in Algebra

This educational guide provides a comprehensive overview of rationalizing denominators, focusing on the use of conjugates. You'll learn how to express fractions with irrational denominators as equivalent fractions with rational denominators through the multiplication of both numerator and denominator by a conjugate. Key concepts like rational and irrational numbers, perfect squares, and the importance of the identity element are explored. Several model problems demonstrate step-by-step processes for simplification and rationalization, enhancing your understanding of these essential algebraic techniques.

nitsa
Télécharger la présentation

Understanding Rationalizing Denominators and Conjugates in Algebra

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Aim: How do we rationalize a denominator? Factor completely: 2x2 – 50 Do Now:

  2. What is the conjugate of (x – 6) Conjugates 2x2 - 50 = 2(x – 5)(x + 5) conjugates of each other a2 – b2 = (a – b)(a + b) General Terms When conjugates are multiplied, the result is the difference between perfect squares. = x2 – 36 (x+ 6) = x2 – 5 = 9 – 7 = 2

  3. Ex. 2, 1.765, 1/2, 0.33 Rational & Irrational Numbers Rational Numbers - Any number, integer, fraction, decimal; positive or negative, mixed or improper, that can be expressed as a fraction. Every rational number can be expressed as either a repeating or terminating decimal. Irrational Numbers - Any and all numbers that can not be expressed as a fraction. Ex. .439439543957. . . p = 3.1415926535897932 . . . = 1.4141213562 . . .

  4. Real Number Family Rational Numbers Integers Irrational Numbers Whole Numbers Counting Numbers Irrational Numbers a/b Counting Numbers 1, 2, 3, 4, 5, . . . Whole Numbers 0, 1, 2, 3, 4, 5, . . Integers . . . -3, -2, -1, 0, 1, 2, 3, . . Rational Numbers a/b

  5. rational number irrational number Rationalizing a Monomial Denominator means to remove the irrational number from the denominator Multiply fraction by a form of the identity element 1. Simplify the radical, if possible

  6. a2 – b2 = (a – b)(a + b) How can we use the conjugate to rationalize Rationalizing a Denominator binomial denominator (of a fractionwhere the denominator is not a rational number) means to find a denominator in which the denominator is a rational number.   Multiply fraction by a form of the identity element 1.

  7. 3 Model Problems Rationalize the denominator: Express as an equivalent fraction with a rational denominator. Write an equivalent expression for

  8. Model Problems Simplify/Rationalize:

  9. Model Problems Simplify/Rationalize:

  10. Model Problems Simplify/Rationalize:

  11. Model Problems Simplify/Rationalize:

  12. Model Problems Simplify/Rationalize:

  13. Model Problems Simplify/Rationalize:

More Related