Section 3.2 Least Common Multiple 175 Answer 11. 4 5 7 5 3 5 4 7 b. 20 35 4 7 35 What number must we Multiply numerator and multiply 7 by to get 35? denominator by 5. From Example 5, we know that and Furthermore, because , then we know that 3 5 7 4 7 . 21 35 7 20 35 20 35 . 4 7 21 35 3 5 So, is equivalent to 4 7 . 20 35 TIP: Writing a fraction as an equivalent fraction is simply an application of the fundamental principle of fractions (see Section 2.3). In Example 5(a), we multiplied numerator and denominator of the fraction by 7. This is the same as multiplying the fraction by a convenient form of 1. This is the same as multiplying numerator and denominator by 7. 3 5 3 5 1 3 5 7 7 3 7 5 7 21 35 Comparing Two Fractions Fill in the blank with , , or . Solution: The fractions have different denominators and cannot be compared by inspection. The LCD is 24. We need to convert each fraction to an equivalent fraction with a denominator of 24. Multiply numerator and denominator by 3, because 8 3 24. Multiply numerator and denominator by 4, because 6 4 24. Because ,then The relationship between and is shown on the number line in Figure 3-2. 0 1 28 Figure 3-2 24 27 24 76 9 8 7 6 . 9 8 27 24 6 28 24 7 6 7 4 6 4 28 24 9 8 9 3 8 3 27 24 7 6 9 8 Example 6 Skill Practice Fill in the blank with , , or . 11. 5 9 4 7
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