b) Step 1: Ask yourself, “By what number do I multiply 12 to get 72?” That number is 6. Step 2: Multiply the numerator and denominator of 1 12 by 6: 1 12 6 6 6 72 Therefore, 1 12 6 72 . Follow the procedure! YOU TRY 2 Write each fraction with the indicated denominator. a) 6 11 ? 77 b) 1 15 ? 45 2 Rewrite Fractions with the Least Common Denominator In the next section, we will learn how to add and subtract fractions with different denominators. First, we must learn how to identify the least common denominator of a group of fractions and then write them as equivalent fractions with the least common denominator. Definition The least common denominator, or LCD, of a group of fractions is the least common multiple of the denominators. Example: The least common denominator of 2 3 and 1 6 is 6 because 6 is the least common multiple of 3 and 6. How is this different from or similar to finding the LCM? Identify the least common denominator of 1 4 and 5 6 , then write each fraction as an equivalent fraction with the LCD as its denominator. Solution The least common denominator of 1 4 and 5 6 is the least common multiple of 4 and 6. What is the least common multiple of 4 and 6? It is 12. Therefore, LCD 12 Write each fraction with a denominator of 12. We want to fi nd 1 4 ? 12 and 5 6 ? 12 1 4 3 3 3 12 5 6 2 2 10 12 The LCD of 1 4 and 5 6 is 12. Then, 1 4 3 12 and 5 6 10 12 . EXAMPLE 3 Always write down the LCD so that you can look at it. www.mhhe.com/messersmith SECTION 4.3 Finding the Least Common Denominator 237
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