Section 1.1 Fractions 9 In Example 2, we showed numerous steps to reduce fractions to lowest terms. However, the process is often simplified. Notice that the same result can be obtained by dividing out the greatest common factor from the numerator and denominator. (The greatest common factor is the largest factor that is common to both numerator and denominator.) The greatest common factor of 45 and 30 is 15. 3 2 1 3 15 2 15 1 45 30 3 15 2 15 The symbol is often used to show that a common factor has been divided out. Notice that “dividing out” the common factor of 15 has the same effect as dividing the numerator and denominator by 15.This is often done mentally. 3 45 30 2 3 2 45 divided by 15 equals 3. 30 divided by 15 equals 2. Avoiding Mistakes In Example 3, the common factor 14 in the numerator and denominator simplifies to 1. It is important to remember to write the factor of 1 in the numerator. The simplified form of the fraction is . 13 Example 3 14 42 32 12 14 42 1 14 3 14 1 1 14 3 14 1 3 1 1 14 42 3 1 3 Multiplying Fractions If b is not zero and d is not zero, then a b c d a c b d To multiply fractions, multiply the numerators and multiply the denominators. Answer 4. 8 3 Simplifying a Fraction to Lowest Terms Simplify to lowest terms. Solution: The greatest common factor of 14 and 42 is 14. Skill Practice Simplify to lowest terms. 4. 4. Multiplying Fractions 14 divided by 14 equals 1. 42 divided by 14 equals 3.
miller_beginning_intermediate_algebra_4e_ch1_3
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