1-2 Properties of Real Numbers. Name the sets of numbers to which each number belongs. SOLUTION:

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2. Name the sets of numbers to which each number belongs. 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.

12 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.

1 2. Name the sets of numbers to which each number belongs. 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 -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 Name the property illustrated by each equation. 6. 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 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. Find the additive inverse and multiplicative inverse for each number. Since, the additive inverse of is. Since, the multiplicative inverse of is. 12. Since, the additive inverse of is. Since, the multiplicative inverse of is. esolutions Manual - Powered by Cognero Page 1

2 Simplify each expression Name the sets of numbers to which each number belongs. 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 20. Since = 5, this is a real number. Since 5 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 part of the set { 0, 1, 2, 3, } so it is a whole number and since it is not 0 it is also a natural number. N, W, Z, Q, R esolutions Manual - Powered by Cognero Page 2

3 22. The number = 3 and is a real number. Since 3 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 part of the set { 0, 1, 2, 3, } so it is a whole number and since it is not 0 it is also a natural number. N, W, Z, Q, R 24. The number = 3 and is a real number. Since 3 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 part of the set { 0, 1, 2, 3, } so it is a whole number and since it is not 0 it is also a natural number. N, W, Z, Q, R Name the property illustrated by each equation. 26. Additive Inverse Property; the Additive Inverse Property states that a number added to its opposite is zero. 28. Associative Property of Addition; the Associative Property of Addition states that the way the factors are grouped does not affect the sum. Find the additive inverse and multiplicative inverse for each number Since = 0, the additive inverse of 8 is 8. Since, the multiplicative inverse of 8 is Since = 0, the additive inverse of 0.25 is Since, the multiplicative inverse of 0.25 is 4. esolutions Manual - Powered by Cognero Page 3

4 34. Since, the additive inverse of is. Since, the multiplicative inverse of is. esolutions Manual - Powered by Cognero Page 4

5 36. CONSTRUCTION Jorge needs two different kinds of concrete: quick drying and slow drying. The quick-drying concrete mix calls for pounds of dry cement, and the slow-drying concrete mix calls for pounds of dry cement. He needs 5 times more quick-drying concrete and 3 times more slow-drying concrete than the mixes make. a. How many pounds of dry cement mix will he need? b. Use the properties of real numbers to show how Jorge could compute this amount mentally. Justify each step. a. Write an expression. Jorge needs 5 times the amount of dry cement,, for the quick-drying mix plus 3 times the amount of dry cement,, for the slow-drying mix. He will need b. pounds of dry cement. esolutions Manual - Powered by Cognero Page 5

6 Simplify each expression esolutions Manual - Powered by Cognero Page 6

7 44. PETS The chart shows the percent of dogs registered with the American Kennel Club that are of the eight most popular breeds. a. Illustrate the Distributive Property by writing two expressions to represent the number of registered dogs of the top four breeds. b. Evaluate the expressions you wrote to find the number of registered dogs of the top four breeds. a. Expression representing the number of registered dogs of the top four breeds is 870,192( ). Use the Distributive Property to rewrite the expression. 870,192( ) = 870,192(0.142) + 870,192(0.056) + 870,192(0.05) + 870,192(0.049) b. So, the number of registered dogs of the top four breeds is about 258,447. esolutions Manual - Powered by Cognero Page 7

8 46. Simplify each expression. 48. esolutions Manual - Powered by Cognero Page 8

9 50. MODELING Mary is making curtains out of the same fabric for 5 windows. The two larger windows are the same size, and the three smaller windows are the same size. One larger window requires yards of fabric, and one smaller window needs yards of fabric. a. How many yards of material will Mary need? b. Use the properties of real numbers to show how Mary could compute this amount mentally. a. Since one larger window requires yards of fabric and a smaller window requires yards of fabric, the expression that represents the requirement of total yards of fabric is. So, Mary requires b. yards of fabric. esolutions Manual - Powered by Cognero Page 9

10 52. CLOTHING A department store sells shirts for $12.50 each. Dalila buys 2, Latisha buys 3, and Pilar buys 1. a. Illustrate the Distributive Property by writing two expressions to represent the cost of these shirts. b. Use the Distributive Property to find how much money the store received from selling these shirts. a ( ) Use the Distributive Property to rewrite the expression ( ) = b. So, the store received $ CHALLENGE If 12(5r + 6t) = w, then in terms of w, what is 48(30r + 36t)? 56. REASONING Determine whether the following statement is sometimes, always, or never true. Explain your reasoning. An irrational number is a real number underneath a radical sign. Sometimes; π and e are two examples of irrational numbers that do not involve the radical symbol but 117 is a real number while is 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 and 2.5 Sample answer: a b and Sample answer: a b esolutions Manual - Powered by Cognero Page 10

11 62. EXTENDED RESPONSE Lenora bought several pounds of cashews and several pounds of almonds for a party. The cashews cost $8 per pound, and the almonds cost $6 per pound. Lenora bought a total of 7 pounds and paid a total of $48. Write and solve equations to determine the pounds of cashews and the pounds of almonds that Lenora purchased. Let c be the number of pounds of cashews and a be the number of pounds of almonds. Eight pounds of cashews and 6 pounds of almonds costs $48. So, 8c + 6a = 48. Lenora bought 7 pounds of cashews and almonds. So, c + a = 7. Substitute c = 7 a in the equation 8c + 6a = 48. Substitute a = 4 in the equation c = 7 a. Therefore, Lenora bought 3 pounds of cashews and 4 pounds of almonds. 64. GEOMETRY What are the coordinates of point A in the parallelogram? F (b a, c) H (b, c) G (a b, c) J (c, c) Since the points A and B are in the horizontal line segment, the y-coordinate of the point A is equal to the y- coordinate of B. From the figure, the x-coordinate of A is negative. Since OABC is a parallelogram, the distance between O and C is same as the distance between A and B. Since b > a, the x-coordinate of A is a b. So, the coordinate of A is A(a b, c). So, the correct choice is G. esolutions Manual - Powered by Cognero Page 11

12 66. Evaluate 8(4 2) GEOMETRY The formula for the area A of a circle with diameter d is. Write an expression to represent the area of the circle. Substitute d = (x + 3) in the formula. The area of the circle is. 70. Factor each polynomial. The GCF of the terms 14x 2, 10x and 8 is 2. esolutions Manual - Powered by Cognero Page 12

13 72. The GCF of the terms 8x 2, 16x and 12 is 2 2 or The GCF of the terms 7x 2, 14x and 21 is 7. Find each product. 76. Use the FOIL method to find the product. 78. Use the FOIL method to find the product. esolutions Manual - Powered by Cognero Page 13

14 80. Use the FOIL method to find the product. Evaluate each expression if a = 3,, and c = b c a + b + c 88. esolutions Manual - Powered by Cognero Page 14

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AB EXAM. 2. When the first 2003 positive odd primes are multiplied together, what is the units digit of the product?

AB EXAM. 2. When the first 2003 positive odd primes are multiplied together, what is the units digit of the product? AB EXAM 1. During the first four days of Arthur s new job, he had to wake up at 5:30, 5:30, 7:10 and 7:30. On average, at what time did he have to wake up each morning? 2. When the first 2003 positive