Chapter 7 Section 3 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.

Slides:



Advertisements
Similar presentations
Chapter 7 Section 5 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
Advertisements

Slide 7- 1 Copyright © 2012 Pearson Education, Inc.
Copyright © 2010 Pearson Education, Inc. All rights reserved. R.1 – Slide 1.
The Fundamental Property of Rational Expressions
Chapter 6 Section 3. Objectives 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Least Common Denominators Find the least common denominator for.
Copyright © Cengage Learning. All rights reserved.
Chapter 7 Section 2 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 5.3 Adding and Subtracting Rational Expressions with the Same Denominator and Least.
Section 6.1 Rational Expressions.
Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Digital Lesson on Operations on Rational Expressions.
Chapter 7 Section 2. Objectives 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Multiplying and Dividing Rational Expressions Multiply rational.
CHAPTER 6 Polynomials: Factoring (continued) Slide 2Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. 6.1Multiplying and Simplifying Rational Expressions.
Addition and Subtraction with Like Denominators Let p, q, and r represent polynomials where q ≠ 0. To add or subtract when denominators are the same,
Chapter 7 Section 4. Objectives 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Adding and Subtracting Rational Expressions Add rational expressions.
6.4 Adding and Subtracting Rational Expressions. Objective 1 Add rational expressions having the same denominator. Slide
Chapter 2 Fractions.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 3 Adding and Subtracting Fractions.
Chapter 1 Basic Concepts.
§ 8.5 Adding and Subtracting Rational Expressions with the Same Denominator and Least Common Denominators.
6.3 Least Common Denominators
Chapter 7 Section 3. Objectives 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Least Common Denominators Find the least common denominator for.
Chapter 7 Section 1 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
Chapter 6 Section 1 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
Chapter 1 Section 1 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
6-1 Copyright © 2014, 2010, and 2006 Pearson Education, Inc. Addition, Subtraction, and Least Common Denominators Addition When Denominators Are the Same.
HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Section 7.2.
Chapter P Prerequisites: Fundamental Concepts of Algebra Copyright © 2014, 2010, 2007 Pearson Education, Inc. 1 P.6 Rational Expressions.
Copyright © 2007 Pearson Education, Inc. Slide R-1.
+ Adding and Subtracting. + How do you add or subtract fractions?
Chapter 7 Section 6 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
Copyright © 2011 Pearson Education, Inc. Rational Expressions Section P.6 Prerequisites.
Chapter 7 Section 4 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
Copyright © 2015, 2011, 2007 Pearson Education, Inc. 1 1 Chapter 7 Rational Expressions and Equations.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 14 Rational Expressions.
Chapter 6 Section 4 Objectives 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Adding and Subtracting Rational Expressions Add rational expressions.
CHAPTER 6 Rational Expressions and Equations Slide 2Copyright 2011, 2007, 2003, 1999 Pearson Education, Inc. 6.1Multiplying and Simplifying Rational Expressions.
Math /7.4 – Rational Expressions: LCD, Adding, and Subtracting 1.
Copyright © 2015, 2011, 2007 Pearson Education, Inc. 1 1 Chapter 7 Rational Expressions and Equations.
Copyright © 2012, 2009, 2005, 2002 Pearson Education, Inc. Chapter 2 Fractions.
Slide 7- 1 Copyright © 2012 Pearson Education, Inc.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 4.4 Adding and Subtracting Like Fractions, Least Common Denominator, and Equivalent.
Chapter 8 Section 5 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
Section 3Chapter 7. 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objectives Complex Fractions Simplify complex fractions by simplifying.
Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 14 Rational Expressions.
Chapter 1 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 1-1 Real Numbers.
Chapter P Prerequisites: Fundamental Concepts of Algebra Copyright © 2014, 2010, 2007 Pearson Education, Inc. 1 P.6 Rational Expressions.
Copyright 2013, 2009, 2005, 2001, Pearson, Education, Inc.
Dear Power point User, This power point will be best viewed as a slideshow. At the top of the page click on slideshow, then click from the beginning.
Chapter P Prerequisites: Fundamental Concepts of Algebra 1 Copyright © 2014, 2010, 2007 Pearson Education, Inc. 1 P.6 Rational Expressions.
Copyright © 2013, 2009, 2006 Pearson Education, Inc. 1 Section 6.3 Complex Rational Expressions Copyright © 2013, 2009, 2006 Pearson Education, Inc. 1.
Rational Expressions and Functions: Adding and Subtracting
Copyright © 2013, 2009, 2006 Pearson Education, Inc.
Copyright © 2008 Pearson Education, Inc
CHAPTER R: Basic Concepts of Algebra
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Adding and Subtracting Rational Expressions
Complex Fractions Method 1 Method 2
Operations Multiplying Dividing
Rational Expressions and Functions
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Rational Expressions and Functions: Adding and Subtracting
The Real Numbers And Their Representations
Rational Expressions and Functions
Operations Adding Subtracting
Adding and Subtracting Rational Expressions
Simplifying Complex Rational Expressions
Adding and Subtracting Rational Expressions
Chapter 7 Section 2.
Adding and Subtracting Rational Expressions
Presentation transcript:

Chapter 7 Section 3 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley

Least Common Denominators Find the least common denominator for a group of fractions. Rewrite rational expressions with given denominators

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 1 Objective 1 Find the least common denominator for a group of fractions. Slide

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Find the least common denominator for a group of fractions. Adding or subtracting rational expressions often requires a least common denominator (LCD), the simplest expression that is divisible by all of the denominators in all of the expressions. For example, the least common denominator for the fractions and is 36, because 36 is the smallest positive number divisible by both 9 and 12. Slide We can often find least common denominators by inspection. For example, the LCD for and is 6m. In other cases, we find the LCD by a procedure similar to that used in Section 6.1 for finding the greatest common factor.

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Find the least common denominator for a group of fractions. (cont’d) To find the least common denominator, use the following steps. Step 1: Factor each denominator into prime factors. Slide Step 2: List each different denominator factor the greatest number of times it appears in any of the denominators. Step 3: Multiply the denominator factors from Step 2 to get the LCD. When each denominator is factored into prime factors, every prime factor must be a factor of the least common denominator.

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 1 Find the LCD for each pair of fractions. Solution: Finding the LCD Slide

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Find the LCD for EXAMPLE 2 Finding the LCD Slide Solution: When finding the LCD, use each factor the greatest number of times it appears in any single denominator, not the total number of times it appears.

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 3 Solution: Finding the LCD Slide Find the LCD for the fractions in each list. Either x − 1 or 1 − x, since they are opposite expressions.

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley 2 Objective 2 Rewrite rational expressions with given denominators. Slide

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Rewrite rational expressions with given denominators. Once the LCD has been found, the next step in preparing to add or subtract two rational expressions is to use the fundamental property to write equivalent rational expressions. Step 1: Factor both denominators. Slide Step 2: Decide what factor(s) the denominator must be multiplied by in order to equal the specified denominator. Step 3: Multiply the rational expression by the factor divided by itself. (That is, multiply by 1.)

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Rewrite each rational expression with the indicated denominator. EXAMPLE 4 Solution: Writing Rational Expressions with Given Denominotors Slide

Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison-Wesley EXAMPLE 5 Rewrite each rational expression with the indicated denominator. Solution: Writing Rational Expressions with Given Denominators Slide