14 Chapter 1 The Set of Real Numbers To add or subtract fractions with different denominators, we must first write each fraction as an equivalent fraction with a common denominator. A common denominator may be any common multiple of the denominators. However, we will use the least common denominator.The least common denominator (LCD) of two or more fractions is the LCM of the denominators of the fractions. The following example uses the fundamental principle of fractions (page 8) to rewrite fractions with the desired denominator. Note: Multiplying the numerator and denominator by the same nonzero quantity will not change the value of the fraction. Writing Equivalent Fractions and Subtracting Fractions a. Write each of the fractions and as an equivalent fraction with the LCD as its denominator. b. Subtract Solution: From Example 8, we know that the LCM for 9 and 15 is 45.Therefore, the LCD of and is 45. a. So, is equivalent to So, is equivalent to b. 1 9 Subtract. 1 15 Skill Practice 14. Write each of the fractions and as an equivalent fraction with the LCD as its denominator. 15. Subtract. 5 8 5 12 5 12 5 8 2 45 5 45 3 45 1 9 1 15 3 45 . 1 15 1 3 15 3 3 45 1 15 45 5 45 . 1 9 1 5 9 5 5 45 1 9 45 1 15 1 9 1 9 1 15 . 1 15 1 9 Example 9 What number must we multiply 9 by to get 45? Multiply numerator and denominator by 5. What number must we multiply 15 by to get 45? Multiply numerator and denominator by 3. Write and as equivalent fractions with the same denominator. Answers 14. 15. 5 24 5 8 15 24 and 5 12 10 24
miller_beginning_intermediate_algebra_4e_ch1_3
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