Definition/Procedure Example Find the LCM Using Prime Factorization Step 1: Write the prime factorization of each number. Step 2: Identify the factors that will be in the least common multiple. The LCM will contain each different factor the greatest number of times it appears in any single factorization. Step 3: The LCM is the product of the factors identifi ed in Step 2. (p. 232) Find the LCM of 9 and 15 using prime factorization. Step 1: Write the prime factorization of each number. 1 factor of 3 T 9 3 3 and 15 3 5 T u 2 factors of 3 1 factor of 5 Step 2: The LCM will contain each different factor the greatest number of times it appears in any single factorization. The LCM will contain 3 3 and 5. 2 factors of 3 Step 3: The LCM is the product of the factors identifi ed u Writing a Fraction with a Different Denominator in Step 2. The LCM of 9 and 15 is 3 3 5 45. 4.3 Finding the Least Common Denominator Step 1: Ask yourself, “By what number do I multiply the original denominator to get the new denominator?” Step 2: Multiply the numerator and denominator of the original fraction by that number to get the equivalent fraction. When we multiply the numerator and denominator by the same number, we do not change the value of the fraction. We get an equivalent fraction. (p. 236) Write 2 7 as an equivalent fraction with a denominator of 21. Step 1: Ask yourself, “By what number do I multiply 7 to get 21?” That number is 3. Step 2: Multiply the numerator and denominator of 2 7 by 3: 2 7 3 3 6 21 Therefore, 2 7 6 21 . Least Common Denominator The least common denominator, or LCD, of a group of fractions is the least common multiple of the denominators. (p. 237) The least common denominator of 1 4 and 5 12 is 12 because 12 is the least common multiple of 4 and 12. Writing a Group of Fractions with an LCD To write a group of fractions with their least common denominator, identify the LCM of the denominators, then rewrite each fraction with the LCM as the least common denominator. (p. 237) Write 9 8 and 4 7 as equivalent fractions with the LCD as their denominators. The LCM of 8 and 7 is 56. So, the LCD is 56. Write each fraction with a denominator of 56. We want to fi nd 9 8 ? 56 and 4 7 ? 56 9 8 7 7 63 56 4 7 8 8 32 56 The LCD of 9 8 and 4 7 is 56, and 9 8 63 56 and 4 7 32 56 . www.mhhe.com/messersmith CHAPTER 4 Summary 281
messersmith_power_basic_college_1e_ch4_7_10
To see the actual publication please follow the link above