is a real number. Since it is a nonterminating decimal it is irrational.

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1 Name the sets of numbers to which each number belongs. 19. The number is a real number. Since can be expressed as a ratio where a and b are integers and b is not 0 it is also a rational number. It is not a part of the set { -2, -1, 0, 1, 2, } so it is not an integer. Since it is not a part of the set { 0, 1, 2, 3, } it is not a whole number or a natural number. Q, R The number is a real number. Since is a repeating decimal it can be expressed as a ratio where a and b are integers and b is not 0 it is also a rational number. It is not a part of the set { -2, -1, 0, 1, 2, } so it is not an integer. Since it is not a part of the set { 0, 1, 2, 3, } it is not a whole number or a natural number. Q, R The number = 12 is a real number. Since 12 can be expressed as a ratio where a and b are integers and b is not 0 it is also a rational number. It is part of the set { 2, 1, 0, 1, 2, } so it is an integer. It is not part of the set { 0, 1, 2, 3, } so it is not a whole number and since it is not a whole number it is not a natural number either. Z, Q, R I, R is a real number. Since it is a nonterminating decimal it is irrational. Name the property illustrated by each equation. 27. Distributive Property; the Distributive Property states that there is no difference between a term multiplied by each term in a group and the term multiplied by the group. 29. Multiplicative Inverse Property; the Multiplicative Inverse Property states that a number multiplied by its reciprocal is 1. esolutions Manual - Powered by Cognero Page 1

2 Find the additive inverse and multiplicative inverse for each number Since ( 12.1) = 0, the additive inverse of 12.1 is Since, the multiplicative inverse of 12.1 is. 33. Since, the additive inverse of is. Since, the multiplicative inverse of is. 35. Since, the additive inverse of is. Since, the multiplicative inverse of is. Simplify each expression esolutions Manual - Powered by Cognero Page 2

3 FOOTBALL Illustrate the Distributive Property by writing two expressions for the area of a college football field. Then find the area of the football field. The width of the football field is 35 yards and the length is ( ) yards. The expression for the area of the field is 35( ) square yards. Use the Distributive Property to rewrite the expression. So, the area of the field is 6360 square yards. esolutions Manual - Powered by Cognero Page 3

4 55. ERROR ANALYSIS Luna and Sophia are simplifying 4(14a 10b) 6(b + 4a). Is either of them correct? Explain your reasoning. No; Luna did not distribute the negative sign to the second term and Sophia switched the a and b terms because usually a comes first. The correct answer is 32a 46b. 57. OPEN ENDED Determine whether the Closure Property of Multiplication applies to irrational numbers. If not, provide a counterexample. Sample answer: So,, which is not irrational. OPEN ENDED The set of all real numbers is dense, meaning between any two distinct members of the set there lies infinitely many other members of the set. Find an example of (a) a rational number, and (b) an irrational number between the given numbers. 59. and Sample answer: a. 3.2; and b. esolutions Manual - Powered by Cognero Page 4

5 61. WRITING IN MATH Explain and provide examples to show why the Commutative Property does not hold true for subtraction or division. Sample answer: The Commutative Property does not hold for subtraction or division because order matters with these two operations. In addition or multiplication, the order does not matter. For example, = results in 6 = 6 and 2 4 = 4 2 results in 8 = 8. However, with subtraction: and division: 63. SAT/ACT Find the 10th term in the series 2, 4, 7, 11, 16, A 41 B 46 C 56 D 67 E 72 The difference between the next term and the previous term is 1 more than the difference between the previous set of two terms = = = = = = = = = 56 So, the 10th term in the series is 56. The correct choice is C. 65. What is the domain of the function that contains the points ( 3, 0), (0, 4), ( 2, 5), and (6, 4)? A { 3, 6} C {0, 4, 5, 6} B { 3, 2, 0, 6} D { 3, 2, 0, 4, 5, 6} The domain is the set of x-coordinates. So, the correct choice is B. esolutions Manual - Powered by Cognero Page 5

6 67. Evaluate a + 3(b + c) d, if a = 5, b = 4, c = 3, and d = 2. Substitute a = 5, b = 4, c = 3, and d = 2 in the expression a + 3(b + c) d. 69. CONSTRUCTION A 10-meter ladder leans against a building so that the top is 9.64 meters above the ground. How far from the base of the wall is the bottom of the ladder? Use the Pythagorean Theorem. Substitute a =9.64 and c = 10 in the formula c 2 = a 2 + b 2. The distance from the wall to the base of the ladder is about 2.66 meters. Factor each polynomial. 71. The GCF of the terms 9x 2, 3x and 18 is 3. esolutions Manual - Powered by Cognero Page 6

7 73. The GCF of the terms 10x 2 and 20x is 2 5 x or 10x. 75. The GCF of the terms 12x 2, 18x and 24 is 2 3 or 6. Find each product. 77. Use the FOIL method to find the product. 79. Use the FOIL method to find the product. esolutions Manual - Powered by Cognero Page 7

8 81. Use the FOIL method to find the product. Evaluate each expression if a = 3,, and c = esolutions Manual - Powered by Cognero Page 8

9 89. esolutions Manual - Powered by Cognero Page 9

1-2 Properties of Real Numbers. Name the sets of numbers to which each number belongs ANSWER: N, W, Z, Q, R ANSWER: Q, R ANSWER: I, R

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