114 Chapter 2 Fractions and Mixed Numbers: Multiplication and Division Section 2.3 Simplifying Fractions to Lowest Terms 1. Equivalent Fractions The fractions all represent the same portion of a whole. See Figure 2-5. Therefore, we say that the fractions are equivalent. 36 , 24 , and 12 3 6 2 4 1 2 Figure 2-5 One method to show that two fractions are equivalent is to calculate their cross products. If their cross products are equal, then the fractions are equivalent. For example, to show that we have 3 6 3 4 ? 6 2 12 12 Yes. The fractions are equivalent. 2 4 36 24 , Determining Whether Two Fractions Are Equivalent Fill in the blank with or a. b. Solution: a. b. 7 7 18 13 ? 39 6 234 234 45 49 Therefore, Therefore, . 2. Simplifying Fractions to Lowest Terms In Figure 2-5, we see that all represent equal quantities. However, the fraction is said to be in lowest terms because the numerator and denominator share no common factors other than 1. 12 To simplify a fraction to lowest terms, we apply the following important principle. 36 , 24 , and 12 7 9 5 7 6 13 . 18 39 5 9 ? 7 9 5 7 6 13 18 39 7 9 5 7 6 13 18 39 . Example 1 Concepts 1. Equivalent Fractions 2. Simplifying Fractions to Lowest Terms 3. Applications of Simplifying Fractions Avoiding Mistakes The test to determine whether two fractions are equivalent is not the same process as multiplying fractions. Multiplying of fractions is covered in Section 2.4. Skill Practice Fill in the blank with or . 1. 2. Answers 1. 2. 54 24 9 4 6 11 13 24
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