8 Chapter 1 The Set of Real Numbers 3. Simplifying Fractions to Lowest Terms The process of factoring numbers can be used to reduce or simplify fractions to lowest terms. A fractional portion of a whole can be represented by infinitely many fractions. For example, Figure 1-2 shows that is equivalent to , and so on. 24 , 36 , 48 1 2 The fraction is said to be in lowest terms because the numerator and denominator share no common factor other than 1. To simplify a fraction to lowest terms, we use the following important principle. Fundamental Principle of Fractions Suppose that a number, c, is a common factor in the numerator and denominator of a fraction.Then 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 45 30 Simplify to lowest terms. Solution: Factor the numerator and denominator. Apply the fundamental principle of fractions. Any nonzero number divided by itself is 1. Any number multiplied by 1 is itself. Skill Practice Simplify to lowest terms. 3. 20 50 3 2 3 2 1 1 3 2 3 3 5 5 45 30 3 3 5 2 3 5 a c b c a b c c a b 1 a b 12 Answer 3. 2 5 12 24 36 48 Figure 1-2
miller_beginning_intermediate_algebra_4e_ch1_3
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