176 Chapter 3 Fractions and Mixed Numbers: Addition and Subtraction Answer 12. 8 15 , 5 9 , 3 5 Ranking Fractions in Order from Least to Greatest Rank the fractions from least to greatest. Solution: We want to convert each fraction to an equivalent fraction with a common denominator. The least common denominator is the LCM of 20, 15, and 9. ⎫⎪⎬⎪⎭ 20 2 2 5 15 3 5 The least common denominator is 2 2 3 3 5 180. 9 Now convert each fraction to an equivalent fraction with a denominator of 180. Multiply numerator and denominator by 9 because 20 9 180. Multiply numerator and denominator by 12 because 15 12 180. Multiply numerator and denominator by 20 because 9 20 180. 49 Ranking the fractions from least to greatest, we have This is equivalent to , 20,9 15. 7 80 180, 81 180, 84 180. 4 9 4 20 9 20 80 180 7 15 7 12 15 12 84 180 9 20 9 9 20 9 81 180 3 3 9 20 , 7 15 , 4 9 Example 7 Skill Practice 12. Rank the fractions from least to greatest. 5 8 3 , , and 9 15 5 Section 3.2 Practice Exercises Study Skills Exercise Where do you usually do your homework? Is this the best place for you to concentrate? Explain. Vocabulary and Key Concepts 1. a. A of a number is the product of the number and a nonzero whole number. b. The (LCM) of two numbers is the smallest whole number that is a multiple of each given number. c. The (LCD) of two fractions is the LCM of the denominators of the fractions. Review Exercises 2. Simplify. a. b. c. d. 2 5 1 5 2 5 1 5 2 5 1 5 2 5 1 5
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