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• Elena, Joe, Owen, Samantha, and Tuck have weighed their backpacks. • Elena's backpack weighs the most. • Owen’s backpack weighs 0.45 lb less than Joe's backpack. • Samantha's lunch weighs 1.5 lb. With that lunch out of the backpack, the backpack weighs 16.55 lb. • Tuck's backpack weighs more than Owen's. • How much does each person's backpack weigh? Answer • Elena: 19.8 lb Joe: 19.35 lb Owen: 18.9 lb Samantha: 18.05 lb Tuck: 19.5 lb Lesson 5-8 LCM and Comparing and Ordering Rational Numbers LCM • A multiple is a product of natural numbers. Ex: 3 x 4 = 12, 12 is a multiple of 3 and 4. • The least common multiple is the common multiple that is less than any other common multiple of two or more numbers. • Three ways to find LCM: Listing multiples, prime factorization, cake method. Listing Multiples • List multiples of each number from least to greatest. • Ex. 12 and 8 12: 12 24 36 48 8: 8 16 24 32 40 48 Listing Multiples • List multiples of each number from least to greatest. • Ex. 12 and 8 12: 12 24 36 48 8: 8 16 24 32 The LCM is 24. 40 48 Prime Factorization 16 4 2 24 4 2 2 •2x2x2x2 •2x2x2x3 6 4 2 2 2 2 3 Prime Factorization 16 4 2 24 4 2 2 6 4 2 2 2 2 3 •2x2x2x2 •2x2x2x3 •Common: 2 x 2 x 2 x 2 x 3 = 48 LCM = 48 Cake Method 2 2 3 18 32 9 16 12 18 6 9 2 3 LCM = 288 2 x 2 x 3 x 3 = 36 LCM = 36 Your Turn • Find the LCM of 10 and 15 by listing multiples. LCM = 30 • Find the LCM of 45 and 75 by using prime factorization. LCM = 225 • Find the LCM of 32 and 48 by using the cake method. LCM = 96 LCD • A common denominator is a common multiple of 2 denominators. The least common denominator (LCD) is the LCM of the denominators. • Find the LCD of: 7 12 8 18 The LCD is 36 Compare the Fractions Using < or > 5 6 1 5 9 16 > 7 9 > 7 50 < 7 10 Order From Least to Greatest 0.6 48% 22% 1 5 0.3 2% 1 2 2 10 0.18 = 48% 1 2 = 2 10 22% = 2% 0.18 0.6 0.3 1 5 Homework • Complete Lesson 5-8 # 2-20 evens • Don’t forget that you have a Chapter 5 Test on Friday!! Start Studying