5.3 The Rational Numbers 245 Example 16 Rice Preparation Following are the instructions given on a box of instant rice. Determine the amount of (a) rice and water, (b) salt, and (c) butter or margarine needed to make 3 servings of rice. Now try Exercise 91 Directions 1. Bring water, salt, and butter (or margarine) to a boil. 2. Stir in rice. Cover; remove from heat. Let stand 5 minutes. Fluff with fork. To Make Rice and Water (Equal Measures) Salt Butter or Margarine 2 servings 2 3 cup 1 4 tsp 1 tsp 4 servings 11 3 cups 1 2 tsp 2 tsp Solution Since 3 is halfway between 2 and 4, we can determine the amount of each ingredient by determining the average of the amount for 2 and 4 servings. To do so, we add the amounts for 2 servings and 4 servings and divide the sum by 2. a) Rice and water: + = + = = = 1 2 2 2 2 2 1 cup 2 3 1 3 2 3 4 3 6 3 b) Salt: + = + = = ⋅ = 2 2 2 3 4 1 2 3 8 tsp 1 4 1 2 1 4 2 4 3 4 c) Butter or margarine: + = 1 2 2 3 2 , or 1 tsp 1 2 7 Exercises Warm Up Exercises In Exercises 1–10, fill in the blanks with an appropriate word, phrase, or symbol(s). 1. The set of rational numbers is the set of numbers of the form p q , where p and q are _________ and ≠ q 0. Integers 2. For the rational number p q , p is called the _________. Numerator 3. For the rational number p q , q is called the _________. Denominator 4. Rational numbers such as 2 3 4 and −1 1 2 are examples of _________ numbers. Mixed 5. Rational numbers such as 11 4 and − 3 2 are examples of _________ fractions. Improper 6. The number 1 2 can be represented as a(n) __________ decimal number. Terminating 7. The number 1 3 can be represented as a(n) _________ decimal number. Repeating 8. In the decimal number 0.285714, the 2 is in the _________ position. Tenths 9. In the decimal number 0.285714, the 7 is in the _________ position. Ten-thousandths 10. The rational numbers 1 2 and 5 10 are examples of _________ fractions. Equivalent Practice the Skills In Exercises 11–16, reduce each fraction to lowest terms. 11. 4 10 2 5 12. 20 25 4 5 13. 28 63 4 9 14. 36 56 9 14 SECTION 5.3 Instructor Resources for Section 5.3 in MyLab Math • Objective-Level Videos 5.3 • PowerPoint Lecture Slides 5.3 • MyLab Exercises and Assignments 5.3 Ecuadorpostales/ Shutterstock
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