Chapter 6 Section 3

Objectives 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Least Common Denominators Find the least common denominator for a group of fractions. Write equivalent rational expressions

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objective 1 Find the least common denominator for a group of fractions. Slide 6.3-3

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Find the least common denominator for a group of fractions 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 number divisible by both 9 and 12. We can often find least common denominator by inspection. For example, the LCD for and is 6m. What about these denominators makes it easy to see the LCD? Slide 6.3-4

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Finding the Least Common Denominator (LCD) Step 1: Factor each denominator into prime factors. Step 2: List each different denominator factor the greatest number of times it appears in any of the denominators. MAKE LCD SOUP Step 3: Multiply the selected denominator factors to obtain the LCD When each denominator is factored into prime factors, every prime factor must be a factor in the least common denominator soup. Do not put too many factors in the soup! Slide 6.3-5

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Find the LCD for each pair of fractions. Solution: Factor Make Soup Slide Finding the LCD CLASSROOM EXAMPLE 1

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Find the LCD for 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. Slide Finding the LCD CLASSROOM EXAMPLE 2

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Solution: Find the LCD for the fractions in each list. Either x − 1 or 1 − x, since they are opposite expressions. Slide Finding LCDs CLASSROOM EXAMPLE 3

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objective 2 Write equivalent rational expressions. Slide 6.3-9

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Writing A Rational Expression with a Specified Denominator 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 same amount, numerator and denominator. (That is, multiply by 1.)

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Rewrite each rational expression with the indicated denominator. Solution: Slide Writing Equivalent Rational Expressions CLASSROOM EXAMPLE 4

Copyright © 2012, 2008, 2004 Pearson Education, Inc. Rewrite each rational expression with the indicated denominator. Solution: Slide Writing Equivalent Rational Expressions CLASSROOM EXAMPLE 5