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Chapter 6

Chapter 6. Section 3. Least Common Denominators. Find the least common denominator for a group of fractions. Write equivalent rational expressions. 6.3. 2. Objective 1. Find the least common denominator for a group of fractions. Slide 6.3-3.

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Chapter 6

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  1. Chapter 6 Section 3

  2. Least Common Denominators Find the least common denominator for a group of fractions. Write equivalent rational expressions. 6.3 2

  3. Objective 1 Find the least common denominator for a group of fractions. Slide 6.3-3

  4. 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. Find the least common denominator for a group of fractions We can often find least common denominator by inspection. For example, the LCD for and is 6m. Whatabout these denominators makes it easy to see the LCD? Slide 6.3-4

  5. Finding the Least Common Denominator (LCD) Step 1: Factoreach denominator into prime factors. Step 2:List each different denominator factorthe greatest number of times it appears in any of the denominators. MAKE LCD SOUP Step 3:Multiplythe 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

  6. Find the LCD for each pair of fractions. CLASSROOM EXAMPLE 1 Finding the LCD Solution: Factor Make Soup Slide 6.3-6

  7. Find the LCD for CLASSROOM EXAMPLE 2 Finding the LCD Solution: When finding the LCD, use each factor the greatestnumber of times it appears in any single denominator, not the totalnumber of times it appears. Slide 6.3-7

  8. Find the LCD for the fractions in each list. CLASSROOM EXAMPLE 3 Finding LCDs Solution: Either x− 1or 1 − x, since they are opposite expressions. Slide 6.3-8

  9. Objective 2 Write equivalent rational expressions. Slide 6.3-9

  10. Writing A Rational Expression with a Specified Denominator Step 1:Factorboth denominators. Step 2:Decide what factor (s) the denominator must be multiplied byin order to equal the specified denominator. Step 3:Multiplythe rational expression by the same amount, numerator and denominator. (That is, multiply by 1.) Slide 6.3-10

  11. Rewrite each rational expression with the indicated denominator. CLASSROOM EXAMPLE 4 Writing Equivalent Rational Expressions Solution: Slide 6.3-11

  12. Rewrite each rational expression with the indicated denominator. CLASSROOM EXAMPLE 5 Writing Equivalent Rational Expressions Solution: Slide 6.3-12

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