Section 1.1 Fractions 13 Solution: 1 12 7 12 1 7 12 TIP: The sum can a. Add the numerators. Simplify to lowest terms. 13 5 3 5 8 12 2 3 13 3 b. Subtract the numerators. Simplify. Simplify to lowest terms. 10 5 2 5 Skill Practice Add or subtract as indicated. 2 3 5 3 11. 12. 5 8 1 8 In Example 7, we added and subtracted fractions with the same denominators.To add or subtract fractions with different denominators, we must first become familiar with the idea of a least common multiple between two or more numbers. The least common multiple (LCM) of two numbers is the smallest whole number that is a multiple of each number. For example, the LCM of 6 and 9 is 18. multiples of 6: 6, 12, 18, 24, 30, 36,… multiples of 9: 9, 18, 27, 36, 45, 54,… Listing the multiples of two or more given numbers can be a cumbersome way to find the LCM.Therefore, we offer the following method to find the LCM of two numbers. Finding the LCM of Two Numbers Step 1 Write each number as a product of prime factors. Step 2 The LCM is the product of unique prime factors from both numbers. Use repeated factors the maximum number of times they appear in either factorization. Finding the LCM of Two Numbers Example 8 Find the LCM of and Solution: 9 15. LCM 3 3 5 45 Skill Practice Find the LCM. 13. 10 and 25 1 12 7 12 be visualized as the sum of the pink and blue sections of the figure. Answers 11. or 12. 13. 50 1 2 2 1 3 7 3 For the factors of 3 and 5, we circle the greatest number of times each occurs.The LCM is the product. 3’s 5’s 9 3 3 15 3 5
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