Section 2.3 Simplifying Fractions to Lowest Terms 115 Answers 3. 4. 5. 10 7 2 15 3 7 Fundamental Principle of Fractions Suppose that a number, c, is a common factor in the numerator and denominator of a fraction. Then a b a b 1 a b c c a c b c To simplify a fraction, we begin by factoring the numerator and denominator into prime factors. This will help identify the common factors. Simplifying a Fraction to Lowest Terms Example 2 Simplify to lowest terms. a. b. c. Solution: a. Factor the numerator and denominator. Notice that 2 is a common factor. Apply the fundamental principle of fractions. Any nonzero number divided by itself is 1. b. Factor the numerator and denominator. Apply the fundamental principle of fractions. Any nonzero number divided by itself is 1. 5 3 5 3 5 3 2 2 17 17 1 1 c. Factor the numerator and denominator. Apply the fundamental principle of fractions. 5 6 5 6 1 1 5 3 2 2 2 2 2 20 24 5 2 2 3 2 2 2 170 102 5 2 17 3 2 17 3 5 3 5 1 3 5 2 2 6 10 3 2 5 2 20 24 170 102 6 10 Skill Practice Simplify to lowest terms. 3. 4. 5. 150 105 26 195 15 35
miller_basic_college_math_3e_ch1_3
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