2 CHAPTER R Review of Basic Concepts The shaded region represents of the circle. 3 8 Figure 1 Writing a Fraction in LowestTerms Step 1 Write the numerator and denominator in factored form. Step 2 Replace each pair of factors common to the numerator and denominator with 1. Step 3 Multiply the remaining factors in the numerator and in the denominator. (This procedure is sometimes called “simplifying the fraction.”) EXAMPLE 1 Writing Fractions in LowestTerms Write each fraction in lowest terms. (a) 10 15 (b) 15 45 (c) 150 200 SOLUTION (a) 10 15 = 2 # 5 3 # 5 = 2 3 # 5 5 = 2 3 # 1 = 2 3 5 is the greatest common factor of 10 and 15. (b) 15 45 = 1 # 15 3 # 15 = 1 3 # 1 = 1 3 (c) 150 200 = 3 # 50 4 # 50 = 3 4 # 1 = 3 4 50 is the greatest common factor of 150 and 200. Another strategy is to choose any common factor and work in stages. 150 200 = 15 # 10 20 # 10 = 3 # 5 # 10 4 # 5 # 10 = 3 4 # 1 # 1 = 3 4 The same answer results. S Now Try Exercises 7 and 15. Remember to write 1 in the numerator. Recall that fractions are a way to represent parts of a whole. See Figure 1. In a fraction, the numerator gives the number of parts being represented. The denominator gives the total number of equal parts in the whole. The fraction bar represents division Qa b = a , bR. Fraction bar 3 8 Numerator Denominator A fraction is classified as either a proper fraction or an improper fraction. Proper fractions 1 5 , 2 7 , 9 10 , 23 25 Numerator is less than denominator. Value is less than 1. Improper fractions 3 2 , 5 5 , 11 7 , 28 4 Numerator is greater than or equal to denominator. Value is greater than or equal to 1. R.1 Fractions, Decimals, and Percents ■ LowestTerms of a Fraction ■ Improper Fractions and Mixed Numbers ■ Operations with Fractions ■ Decimals as Fractions ■ Operations with Decimals ■ Fractions as Decimals ■ Percents as Decimals and Decimals as Percents ■ Percents as Fractions and Fractions as Percents Lowest Terms of a Fraction A fraction is in lowest terms when the numerator and denominator have no factors in common (other than 1).
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