Developmental Mathematics Basic

Mathematics and Algebra 4th Edition

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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Find the value of the exponential expression.

1) 5 4
A) 625 B) 5 C) 20 D) 9
Answer: A

2) 212
A) 42 B) 882 C) 23 D) 441
Answer: D

3) 4 6
A) 5 B) 4096 C) 24 D) 46
Answer: B

5 3
4)
7
125 5 125 343
A) B) 3 C) D)
343 7 7 125
Answer: A

5) (0.04)2
A) 0.08 B) 0.02 C) 0.16 D) 0.0016
Answer: D

Simplify.
6) 14 ∙ 5 + 13 ∙ 10
A) 200 B) 830 C) 2520 D) 1890
Answer: A

7) 5.2 ∙ 15.1 + 10.5 ∙ 6.3

A) 144.67 B) 838.7 C) 560.8 D) 422.5
Answer: A

8) 240 ÷ 8 - 4
A) 228 B) 236 C) 26 D) 60
Answer: C

9) 6 2 + 52
A) 22 B) 121 C) 44 D) 61
Answer: D

10) 27 + 29 ∙ 21
A) 804 B) 1176 C) 77 D) 636
Answer: D

11) 9 ∙ 8 - 5
A) 67 B) 27 C) 360 D) 77
Answer: A

1
 12) 10 ∙ 7 - 3 ∙ 4
A) 58 B) 268 C) 840 D) 160
Answer: A

13) 73 - 6 ∙ 2 ∙ 4
A) 536 B) 244 C) 61 D) 25
Answer: D

14) 63 ÷ 8 - 6
A) 214 B) 21 C) 27 D) 108
Answer: B

6 1 5 1
15) ∙ + ∙
5 7 6 5
71 71 13 71
A) B) C) D)
210 160 42 110
Answer: A

Find the value of the expression.

16) 2[5 + 6(6 2 )]
A) 442 B) 3362 C) 6724 D) 2602
Answer: A

17) (7 + 7)[7 + (5 + 6)]

A) 91 B) 1813 C) 882 D) 252
Answer: D

3(8 + 8) + 3 ∙ 8
18)
3(8 - 1)
21 24 131 131
A) B) C) D)
23 7 21 23
Answer: B

8(5 - 2) + 8 ∙ 4
19)
8(8 - 2)
7 10 24 5
A) B) C) D)
6 31 31 12
Answer: A

20) 7[32 + 6(5 + 6)]

A) 525 B) 1155 C) 315 D) 87
Answer: A

2
 3(12 - 22 )
21)
2 ∙ 6 ∙ 13
2 17 13
A) 2 B) C) D)
13 6 2
Answer: B

1 1 9
22) + ∙
2 2 14
18 1 9 4
A) B) C) D)
7 7 14 11
Answer: C

5(2 + 1) - 7(1 + 1)
23)
5(4 - 2) - 23
1 1 1
A) B) C) D) 4
6 8 2
Answer: C

24) 0.69 + 3.5(0.35)

A) 1.6165 B) 1.915 C) 1.3065 D) 1.4665
Answer: B

25) 16.5 ÷ 0.4(0.3) + (1.8)2

A) 20.215 B) 13.015 C) 17.115 D) 15.615
Answer: D

Determine whether the statement is true or false.

26) 9 < 15
A) True B) False
Answer: A

27) 18 > 9
A) True B) False
Answer: A

28) 3 ≤ 20 - 11
A) False B) True
Answer: B

7 ∙ (4 + 7) + 7 ∙ 7
29) < 15
7 ∙ (8 - 1)
A) True B) False
Answer: A

30) 4 2 < 7 2 - 42
A) False B) True
Answer: B

3
 31) (7 + 8)[5 + (4 + 3)] < 119
A) False B) True
Answer: A

32) 8[4 + (8 - 4)] < 50

A) False B) True
Answer: A

9(7 + 5) + 2 ∙ 7
33) ≤ 17
8(3 + 3)
A) False B) True
Answer: B

6(8 - 3) + 4(8 - 3)
34) ≥ 3
7(9 - 2) - 8(9 - 3)
A) False B) True
Answer: B

Write the word statement in symbols.

35) Thirteen is greater than three plus nine.
A) 13 + 3 > 9 B) 13 > 3 + 9 C) 3 + 9 > 13 D) 13 < 3 + 9
Answer: B

36) Five is less than or equal to nine.

A) 5 ≤ 9 B) 5 > 9 C) 5 ≥ 9 D) 5 < 9
Answer: A

37) Seven is not equal to eight.

A) 7 < 8 B) 7 ≠ 8 C) 7 ≥ 8 D) 7 > 8
Answer: B

38) Twelve is less than or equal to eight plus five.

A) 12 ≤ 8 + 5 B) 12 + 8 ≥ 5 C) 8 + 5 ≤ 12 D) 12 < 8 + 5
Answer: A

39) Six is equal to thirteen minus seven.

A) 13 = 6 - 7 B) 13 < 6 + 7 C) 6 = 13 - 7 D) 6 - 13 < 7
Answer: C

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Write the statement in words and decide whether it is true or false.

40) 5 ≤ 7
Answer: Five is less than or equal to seven. True

41) 5 ≠ 8
Answer: Five is not equal to eight. True

42) 5 ≥ 3
Answer: Five is greater than or equal to Three. True

4
 43) 11 > 8 + 2
Answer: Eleven is greater than eight plus two. True

44) 8 ≤ 4 + 5
Answer: Eight is less than or equal to four plus five. True

13 5
45) ≠
8 4
Answer: Thirteen-eighths is not equal to five-fourths. True.

2 3
46) ≠
5 10
Answer: Two-fifths is not equal to three-tenths. True.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Rewrite the statement so the inequality symbol points in the opposite direction.
47) 4 < 38
A) 38 ≥ 4 B) 4 > 38 C) 38 < 4 D) 38 > 4
Answer: D

48) 36 > 4
A) 36 ≥ 4 B) 4 > 36 C) 4 < 36 D) 36 < 4
Answer: C

49) 45 ≥ 32
A) 45 > 32 B) 32 ≥ 45 C) 32 ≤ 45 D) 45 ≤ 32
Answer: C

50) 4 ≤ 43
A) 4 ≥ 43 B) 43 > 4 C) 43 ≤ 4 D) 43 ≥ 4
Answer: D

51) 0.679 ≥ 0.598

A) 0.598 ≥ 0.679 B) 0.679 ≤ 0.598 C) 0.598 ≤ 0.679 D) 0.679 < 0.598
Answer: C

52) 0.009 < 0.087

A) 0.009 ≥ 0.087 B) 0.087 ≤ 0.009 C) 0.087 > 0.009 D) 0.009 > 0.087
Answer: C

5
Answer the question.
53) The table shows the number of pupils per teacher in selected states.
State Pupils per Teacher
Alaska 16.7
Texas 14.7
California 20.5
Wyoming 12.5
Maine 12.3
Idaho 17.8
Missouri 13.9

Which states have a figure greater than 14.7?

A) Alaska, California, Idaho B) Alaska, California, Wyoming, Idaho
C) Alaska, Texas, California D) Alaska, Texas, California, Idaho
Answer: A

54) The table shows the number of pupils per teacher in selected states.

State Pupils per Teacher

Alaska 16.7
Texas 14.7
California 20.5
Wyoming 12.5
Maine 12.3
Idaho 17.8
Missouri 13.9

Which states have a figure greater than 12.5?

A) Maine
B) Alaska, Texas, California, Idaho, Missouri
C) Alaska, Texas, California, Wyoming, Idaho, Missouri
D) Wyoming, Maine
Answer: B

55) The table shows the number of pupils per teacher in selected states.

State Pupils per Teacher

Alaska 16.7
Texas 14.7
California 20.5
Wyoming 12.5
Maine 12.3
Idaho 17.8
Missouri 13.9

Which states have a figure greater than 16.7?

A) Idaho B) Alaska, California, Idaho
C) California, Idaho D) Alaska, Texas, Wyoming, Maine, Missouri
Answer: C

6
56) The table shows the number of pupils per teacher in selected states.

State Pupils per Teacher

Alaska 16.7
Texas 14.7
California 20.5
Wyoming 12.5
Maine 12.3
Idaho 17.8
Missouri 13.9

Which states have a figure that is at most 14.7?

A) Alaska, Texas, California, Idaho B) Texas, Wyoming, Maine, Missouri
C) Wyoming, Maine, Missouri D) Alaska, California, Idaho
Answer: B

57) The table shows the number of pupils per teacher in selected states.

State Pupils per Teacher

Alaska 16.7
Texas 14.7
California 20.5
Wyoming 12.5
Maine 12.3
Idaho 17.8
Missouri 13.9

Which states have a figure that is at most 12.5?

A) Alaska, Texas, California, Wyoming, Idaho, Missouri
B) Alaska, Texas, California, Idaho, Missouri
C) Maine
D) Wyoming, Maine
Answer: D

58) The table shows the number of pupils per teacher in selected states.

State Pupils per Teacher

Alaska 16.7
Texas 14.7
California 20.5
Wyoming 12.5
Maine 12.3
Idaho 17.8
Missouri 13.9

Which states have a figure that is at most 16.7?

A) Alaska, California, Idaho B) Alaska, Texas, Wyoming, Maine, Missouri
C) Texas, Wyoming, Maine, Missouri D) California, Idaho
Answer: B

7
59) The table shows the number of pupils per teacher in selected states.

State Pupils per Teacher

Alaska 16.7
Texas 14.7
California 20.5
Wyoming 12.5
Maine 12.3
Idaho 17.8
Missouri 13.9

For which states are the values not less than 14.7?
A) Texas, Wyoming, Maine, Missouri B) Alaska, California, Idaho
C) Alaska, Texas, California, Idaho D) Wyoming, Maine, Missouri
Answer: C

60) The table shows the number of pupils per teacher in selected states.

State Pupils per Teacher

Alaska 16.7
Texas 14.7
California 20.5
Wyoming 12.5
Maine 12.3
Idaho 17.8
Missouri 13.9

For which states are the values not less than 12.5?
A) Alaska, Texas, California, Wyoming, Idaho, Missouri
B) Maine
C) Alaska, Texas, California, Idaho, Missouri
D) Wyoming, Maine
Answer: A

61) The table shows the number of pupils per teacher in selected states.

State Pupils per Teacher

Alaska 16.7
Texas 14.7
California 20.5
Wyoming 12.5
Maine 12.3
Idaho 17.8
Missouri 13.9

For which states are the values not less than 16.7?
A) Texas, Wyoming, Maine, Missouri B) Alaska, California, Idaho
C) California, Idaho D) Alaska, Texas, Wyoming, Maine, Missouri
Answer: B

8
Find the numerical value of the expression for a) x = 4 and b) x = 18.
62) x + 7
A) a) 3 b) 11 B) a) 28 b) 126 C) a) 11 b) 25 D) a) 25 b) 11
Answer: C

63) x - 1
A) a) 3 b) 17 B) a) 4 b) 18 C) a) 17 b) 3 D) a) 5 b) 19
Answer: A

64) 9x
A) a) 27 b) 13 B) a) 36 b) 162 C) a) 162 b) 36 D) a) 13 b) 27
Answer: B

x+9
65)
5
27 13 36 162 5 5 13 27
A) a) b) B) a) b) C) a) b) D) a) b)
5 5 5 5 13 27 5 5
Answer: D

3x - 4
66)
3x
2 25 8 29 4 25 25 2
A) a) b) B) a) b) C) a) b) D) a) b)
3 27 27 27 27 27 27 3
Answer: A

x+6
67)
x-1
24 10 2 12 10 24 12 2
A) a) b) B) a) b) C) a) b) D) a) b)
17 3 5 19 3 17 19 5
Answer: C

68) 8x2 + 9x
A) a) 164 b) 2754 B) a) 100 b) 450 C) a) 68 b) 306 D) a) 92 b) 2430
Answer: A

7.854x
69) (Round to the nearest thousandth.)
5.6
A) a) 0.091 b) 0.409 B) a) 19.635 b) 11.220
C) a) 175.930 b) 791.683 D) a) 5.610 b) 25.245
Answer: D

0.41x
70) (Round to the nearest thousandth.)
0.91
A) a) 42.884 b) 868.400 B) a) 7.209 b) 145.978
C) a) 1.802 b) 8.110 D) a) 0.612 b) 2.753
Answer: C

9
Evaluate the expression for the given values. Expression your answer as a fraction unless otherwise indicated.
71) 2x + 8y + 7; x = 2, y = 6
A) 59 B) 57 C) 35 D) 19
Answer: A

5x
72) + y2 x = 5, y = 9
y
106 43 754
A) B) C) 34 D)
9 9 9
Answer: D

11x - 10y
73) x = 9, y = 6
6
89 13 53
A) B) C) 4 D)
6 2 2
Answer: B

x+y
74) x = 7, y = 10
10x - 13
17 7 17 17
A) B) C) D)
70 57 57 123
Answer: C

3x + 12y
75) x = 2, y = 3
3
A) 42 B) 14 C) 10 D) 11
Answer: B

13x - 2y
76) x = 8, y = 6
x + 10
23 31 46 31
A) B) C) D)
4 9 9 8
Answer: C

77) (x + 4y) 2 x = 2, y = 3
A) 36 B) 14 C) 196 D) 28
Answer: C

x(y + 11)
78) x = 9, y = 5
2(x - y)
A) 4 B) 18 C) 10 D) 2
Answer: B

79) 9x2 + 3y x = 7, y = 8
A) 465 B) 3744 C) 3993 D) 597
Answer: A

10
 80) 0.7x2 + 0.398y2 x = 4, y = 2 Round to the nearest tenth.
A) 12.8 B) 9.2 C) 45.9 D) 8.5
Answer: A

State the phrase as a mathematical expression. Use x to represent the variable.

81) Two times a number
2
A) 2x B) C) 2 - x D) 2 + x
x
Answer: A

82) A number increased by nine

A) x - 9 B) 9x C) 9 D) x + 9
Answer: D

83) A number multiplied by seven hundred fifty-six

756
A) B) 756 - x C) 756x D) 756 + x
x
Answer: C

84) A number minus six hundred five

A) 605 B) 605x C) x + 605 D) x - 605
Answer: D

85) The difference between five times a number and twelve

A) 12 - 5x B) 5x - 12 C) 12 + 5x D) 5 - x + 12
Answer: B

86) The quotient of a number and four

x
A) 4x B) C) 4 - x D) 4 + x
4
Answer: B

87) Seven divided by a number

7
A) B) 7 + x C) 7x D) 7 - x
x
Answer: A

88) The product of nine and five more than a number

A) 9 + 5 ∙ x B) 9(x + 5) C) (9 + 5)x D) 9 ∙ 5 + x
Answer: B

89) 206 divided by a number

206
A) 206 - x B) C) 206 + x D) 206x
x
Answer: B

90) Five times a number, added to 30

A) 5(x + 30) B) 5x + 30 C) 5x D) 5 ∙ 30 + x
Answer: B

11
Decide if the given number is a solution to the given equation.
91) p + 2 = 17; 15
A) No B) Yes
Answer: B

92) p - 6 = 7; 13
A) Yes B) No
Answer: A

93) 4m + 6 = 24; 4
A) Yes B) No
Answer: B

94) 9y + 9(y - 3) = 81; 6

A) Yes B) No
Answer: A

95) 3p + 4p - 3 = 11; 2
A) Yes B) No
Answer: A

96) 7x2 + 11 = 81; 5

A) Yes B) No
Answer: B

x+4 1
97) = ;- 2
2-x 2
A) No B) Yes
Answer: B

x + 7 9 59
98) = ;
x-5 2 7
A) Yes B) No
Answer: A

99) 6r2 + 3 = 20.34; 1.7

A) No B) Yes
Answer: B

100) 8z2 - 8 = 470.08; 7.6

A) No B) Yes
Answer: A

Change the word statement to an equation. Use x as the variable.

101) A number minus 4 equals 4.
A) 4 - x = 4 B) x - 4 = 4 C) x = 4 - 4
Answer: B

12
 102) 5 times a number equals 4 less than 6 times the number.
A) 5x = 6x - 4 B) 5x = 4 - 6 C) 5x = 4 - 6x
Answer: A

103) Twice a number less 9 equals 3.

A) 9 - 2x = 3 B) 2x - 9 = 3 C) 2(x - 9) = 3
Answer: B

104) The sum of twice a number and 3 is 54.

A) 6x = 54x B) 6x = 54 C) 2x + 3 = 54
Answer: C

4
105) of a number plus 4 equals 8.
9
4 4 4
A) x+4=8 B) x=4+8 C) (x + 4) = 8
9 9 9
Answer: A

1
106) 1 divided by a number equals times that number."
4
1 1 1 x x
A) = 4x B) = x C) =
x x 4 1 4
Answer: B

107) When 3 times a number is subtracted from 7 times the number, the result is 32.
A) 3x + 8x = 32 B) 3x(7 - x) = 32 C) 7x - 3x = 32 D) 3(x - 7) = 32x
Answer: C

108) The sum of two-thirds a number and 74 is 58.

2 2 2 2
A) x + 74 = 58 B) x ∙ 74 = 58 C) x - 74 = 58 D) x + 58 = 74
3 3 3 3
Answer: A

Decide whether the problem is an equation or an expression.

109) 2(4x + 4) = 8(8x - 9)
A) Equation B) Expression
Answer: A

110) 7(2x + 6) - 2(4x - 7)

A) Expression B) Equation
Answer: A

8x + 6 8x
111) = -3
9 9
A) Expression B) Equation
Answer: B

13
 4x - 6 x
112) - +8
x+6 6
A) Expression B) Equation
Answer: A

2x + 2
113) 4x + 7 =
3
A) Expression B) Equation
Answer: B

9x + 4
114) 8(8 - x) +
3
A) Equation B) Expression
Answer: B

115) x + y = 6
A) Expression B) Equation
Answer: B

116) x + y - 4
A) Equation B) Expression
Answer: B

Answer the question.

117) Which phrase correctly translates the expression 16 - x?
A) x less than 16 B) x minus 16
C) x take away 16 D) 16 subtracted from x
Answer: A

118) Which one of the following is the correct method for evaluating the expression 3x2 - 5 for x = 6?
A) 3 ∙ 62 - 5 = 182 - 5 = 324 - 5 = 319 B) 3 ∙ 62 - 5 = 3 ∙ 36 - 5 = 108 - 5 = 103
C) 3 ∙ 62 - 5 = 3 ∙ 12 = 3 ∙ 1 = 3 D) 3 ∙ 62 - 5 = (18 - 5)2 = 13 = 169
Answer: B

119) According to the rules for order of operations, the first steps in evaluating the expression 57 - 5x3 for x = 2 are
to substitute 2 for x and then .
A) multiply 5 by 2 B) subtract 57 from 5 C) subtract 5 from 57 D) find the cube of 2
Answer: D

120) What value for x makes the expression 8 + 2x equal to 16?

A) 3 B) 4 C) 5 D) 7
Answer: B

121) What value for x makes the expression 22 - x equal to 15?

A) 8 B) 37 C) 7 D) 17
Answer: C

14
 122) Which pair of values of x and y makes 3x + y equal 7?
A) x = 1 and y = 2 B) x = 2 and y = 1 C) x = 2 and y = 3 D) x = 3 and y = 2
Answer: B

123) Which pair of values of x and y makes x - 3y equal 5?

A) x = 3 and y = 4 B) x = 11 and y = 2 C) x = 4 and y = 3 D) x = 2 and y = 11
Answer: B

124) In the equation 5x + y = 15, the value of x is 3. What is the corresponding value of y?
A) y = 0 B) y = 3 C) y = 10 D) y = 5
Answer: A

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Give a number that satisfies the given condition.

125) An integer greater than -6.3 and less than -5.3
Answer: -6

126) A whole number greater than 3.5

Answer: One example is 4. There are others.

127) A whole number less than 3.5

Answer: One example is 3. There are others.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

List all numbers from the set that are of the type indicated.

2 1
128) 0, 6, -12, , - 1 , 2.7, 5
3 2
Integers
A) 0, -12, 5 B) 19, -12 C) 19 D) 19, 6
Answer: A

6 1
129) 5, 8, -23, 0, , - 1 , 6.8
7 6
Whole numbers
A) 5 B) 5, 0 C) 5, -23 D) 5, -23, 0
Answer: B

8 1
130) 7, -15, 0, , - 1 , 7.5, 3
9 8
Natural numbers
A) 0 B) 0, 3 C) -15, 0 D) 3
Answer: D

131) {2, 5, -14, 0}

Real numbers
A) 2, 0 B) 2 C) 2, -14, 0 D) 2, 5, -14, 0
Answer: D

15
 132) {5, 5, -17, 0, 0.89}
Rational numbers
A) 5, -17, 0, 0.89 B) 5 C) 5, 0.89 D) 5, 0
Answer: A

133) {6, 5, -22, 0, 0.13}

Irrational numbers
A) 5, -22 B) 5 C) 5, 0.13 D) 5, 0, 0.13
Answer: B

Use an integer to express the number.

134) The stock market gained 18 points on Monday.
A) -18 B) 18
Answer: B

135) During one year, 26 employees quit their jobs at Newline Manufacturing Company.
A) 26 B) -26
Answer: B

136) A football team gained 2 yards on one play.

A) 2 B) -2
Answer: A

137) In one state, the highest point is 3977 feet above sea level.
A) 3977 B) -3977
Answer: A

138) One country exported $85,600,000 more than it imported, giving it a positive trade balance.
A) -85,600,000 B) 85,600,000
Answer: B

139) Sales at Andrea's Formal Wear Shop were $2394 less this week than the sales last week.
A) -2394 B) 2394
Answer: A

140) Mr. Voss increased his speed by 6 miles per hour.

A) -6 B) 6
Answer: B

141) On a sunny day, the water temperature in the swimming pool rises 9 degrees.
A) -9 B) 9
Answer: B

142) This year corn production increased 6,000 pounds from last year on Steve's farm.
A) -6,000 B) 6,000
Answer: B

16
Graph the numbers on a number line.
143) 1, 3, 5, 7

A) 0 1 2 3 4 5 6 7 8 9 B) 0 1 2 3 4 5 6 7 8 9

C) 8 9 10 11 12 13 14 15 16 17 D) 8 9 10 11 12 13 14 15 16 17

Answer: B

144) -8, -6, -4, -2

A) -9 -8 -7 -6 -5 -4 -3 -2 -1 0 B) -1 0 1 2 3 4 5 6 7 8

C) -9 -8 -7 -6 -5 -4 -3 -2 -1 0 D) -1 0 1 2 3 4 5 6 7 8

Answer: C

2 2
145) - 3 , -1, 1, 3
3 3

A) -3 -2 -1 0 1 2 3 4 5 B) 5 6 7 8 9 10 11 12 13

C) 6 7 8 9 10 11 12 13 14 D) -4 -3 -2 -1 0 1 2 3 4

Answer: D

3 1
146) - 1 , 1, 3, 5
4 4

A) 6 7 8 9 10 11 12 13 14 15 B) -3 -2 -1 0 1 2 3 4 5 6

C) -2 -1 0 1 2 3 4 5 6 7 D) 7 8 9 10 11 12 13 14 15 16

Answer: B

17
 7 5 5
147) - 2 , - , 1,
8 4 3

A) -4 -3 -2 -1 0 1 2 3 4 B) -4 -3 -2 -1 0 1 2 3 4

C) -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 D) -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12

Answer: A

Select the lesser of the two given numbers.

148) -19, -9
A) -9 B) -19
Answer: B

11 6
149) - ,-
16 11
11 6
A) - B) -
16 11
Answer: A

150) -167, 20
A) -167 B) 20
Answer: A

151) 9, ∣-23∣
A) ∣-23∣ B) 9
Answer: B

152) ∣-4 ∣, ∣-23∣

A) ∣-23∣ B) ∣-4 ∣
Answer: B

153) - ∣-5 ∣, - ∣-9 ∣

A) - ∣-9 ∣ B) - ∣-5∣
Answer: A

154) ∣10 - 1∣, ∣5 - 2∣

A) ∣5 - 2∣ B) ∣10 - 1∣
Answer: A

Decide if the statement is true or false.

155) -(-16) < -12
A) False B) True
Answer: A

18
 156) -(-4) > -9
A) True B) False
Answer: A

157) -11 > -3

A) False B) True
Answer: A

158) -20 ≤ -1
A) True B) False
Answer: A

159) -16 ≤ -(-23)

A) True B) False
Answer: A

160) -21 ≥ -(-7)

A) True B) False
Answer: B

161) -12 < -13

A) False B) True
Answer: B

162) - -12 ≤ - -14

A) False B) True
Answer: A

Find the opposite (additive inverse) of the number.

163) 17
1
A) 17 B) -17 C) 0 D)
17
Answer: B

164) -25
1
A) -25 B) - C) 0 D) 25
25
Answer: D

1
165) -
22
1
A) -22 B) 0 C) D) 22
22
Answer: C

19
 1
166)
28
1
A) 28 B) - C) 0 D) -28
28
Answer: B

4
167) -
13
13 13 4 4
A) B) - C) - D)
4 4 13 13
Answer: D

Simplify.
168) ∣10∣
A) 20 B) 0 C) 10 D) -10
Answer: C

169) ∣20∣
A) 0 B) 20 C) 40 D) -20
Answer: B

170) ∣-19∣
A) 38 B) 19 C) 0 D) -19
Answer: B

171) - ∣-21∣
A) -21 B) 42 C) 0 D) 21
Answer: A

172) 7 - 8
A) 1 B) -1 C) 2 D) 0
Answer: A

6
173) - -
7
6 7 6 7
A) B) - C) - D)
7 6 7 6
Answer: C

1
174) -
2
1 2 2 1
A) B) C) - D) -
2 1 1 2
Answer: D

20
Refer to the table to answer the question.

Production Change Change

Category 2008-2009 2009-2010
Public Relations 3.5 4.2
Training 1.7 2.8
Sales -4.3 1.6
Catalog 2.3 -1.1

175) Which category and year shows the largest increase?

A) Sales, 2008-2009 B) Catalog, 2008-2009
C) Public Relations, 2008-2009 D) Public Relations, 2009-2010
Answer: D

176) Which category and year represents the least change?

A) Training 2008-2009 B) Catalog, 2008-2009
C) Catalog 2009-2010 D) Sales, 2009-2010
Answer: C

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Provide an appropriate response.

177) Is the integer 0 positive or negative? Explain.
Answer: The integer is neither. It is not a signed integer.
It is the starting point on a number line.

178) How is the order of operations applied to integers?

Answer: The same way as for whole numbers.

179) What is the additive inverse of 0?

Answer: 0 itself

180) How can you rewrite a subtraction of integers problem to make it easier to solve? Give an example.
Answer: Change subtraction to addition, and change the sign of the subtrahend to its opposite.
-6 - (-3) = -6 + (+3) = -3

181) Explain what happens when an integer is multiplied by 1, -1, and 0.

Answer: An integer multiplied by 1 gives the same integer, multiplied by -1 gives the opposite of the integer, and
multiplied by 0 gives 0.

182) A whole number less than 7.5.

Answer: One example is 7. There are others.

183) Fill in the blanks with the correct numbers.

The opposite of -8 is _____.
The absolute value of -8 is _____.
The opposite of the absolute value of -8 is _____.
The absolute value of the opposite of -8 is _____.
Answer: 8, 8, -8, 8

21
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

184) Give one number between -8 and 8 that is a negative real number but not an integer.
A) 7.009 B) Not possible C) 3 D) -7.009
Answer: D

185) Give one number between -8 and 8 that is a negative real number but not an integer.
A) Not possible B) -2 C) -2.6457513 D) 2.64575131
Answer: C

186) Give one number between -10 and 10 that is a real number but not not an integer.
A) -2 B) Not possible C) 3.74165739 D) - 9
Answer: C

Find the sum.

187) 6 + (-4)
A) -10 B) -2 C) 2 D) 10
Answer: C

188) -4 + 13
A) -9 B) -17 C) 17 D) 9
Answer: D

189) -10 + (-12)

A) -22 B) 2 C) 22 D) -2
Answer: A

190) -14.0 + (-11.2)

A) 2.8 B) 25.2 C) -25.2 D) -2.8
Answer: C

191) -461 + 664

A) 1125 B) 203 C) -203 D) -1125
Answer: B

192) 20 + [(-2) + (-19)]

A) 3 B) 37 C) -1 D) 41
Answer: C

193) 7 + [7 + (-20)]
A) -6 B) 20 C) 34 D) -20
Answer: A

194) -20 + [12 + (-13)]

A) 5 B) -21 C) 45 D) 19
Answer: B

195) 5.6 + [(-4.0) + (-5.4)]

A) 7 B) 15 C) 4.2 D) -3.8
Answer: D

22
 196) -7.2 + [(-5.0) + (-4.0)]
A) 8.2 B) 6.2 C) -16.2 D) -1.8
Answer: C

197) [-16 + (-1)] + [(-13) + (-23)]

A) -53 B) -21 C) -19 D) 5
Answer: A

198) [7 + (-1)] + [7 + (-20)]

A) -21 B) 35 C) -7 D) 19
Answer: C

199) -21.0 + [15.4 + (-9.7)]

A) 46.1 B) 4.1 C) 26.7 D) -15.3
Answer: D

3 9
200) + -
4 16
3 1 3 3
A) B) C) D)
64 2 16 4
Answer: C

11 3
201) - +
20 4
1 1 1
A) B) C) D) 1
2 5 20
Answer: B

1 4
202) 15 + -7
5 5
2 2 2 1
A) 22 B) 21 C) 7 D) 7
5 5 5 5
Answer: C

4 1
203) - 6 + 13
9 9
2 2 2 1
A) 6 B) 19 C) 18 D) 6
3 3 3 3
Answer: A

Perform the indicated operations to decide whether the statement is true or false.
204) -11 + 13 = 13 + (-11)
A) True B) False
Answer: A

23
 15 15
205) 3 + - =- +3
11 11
A) False B) True
Answer: B

206) -7 + 1 = -7 + (-1)
A) True B) False
Answer: B

207) -2 + [-9 + 5] = [(-2) + (-9)] + 5

A) False B) True
Answer: B

Write a numerical expression for the phrase and simplify it.

208) The sum of -9 and 13 and 4
A) -9 - 13 - 4; -26 B) -9 + 13 + 4; 8 C) 13 + 4 - 9; 18 D) 9 + 13 + 4; 26
Answer: B

209) The sum of -5 and -12, increased by -10

A) [(-5) + (-12)] + (-10); -27 B) [(-5) + (-12)] + 10; -7
C) [(-5) + (-12)] + (-10); -17 D) [5 + 12] + 10; 27
Answer: A

210) 14 added to the sum of -10 and 12

A) 14 + 12 - 10; 8 B) 14 + 10 + 12; 36
C) -14 - 10 - 12; -36 D) 14 + [(-10) + 12]; 16
Answer: D

211) 4 more than the sum of -8 and 13

A) [-8 + 13] + 4; 9 B) -8 - [13 - 4]; -25 C) [8 + 13] + 4; 25 D) 13 + [4 - 8]; 17
Answer: A

212) -8 added to the sum of -8 and 5

A) 8 - 8 - 5; -5 B) -8 + 8 + 5; 5 C) -8 + 5 - 8; 21 D) -8 + [(-8) + 5]; -11
Answer: D

1 5 1
213) more than the sum of - and
8 8 8
5 1 1 7 5 1 1 5 5 1 1 3 1 1 5 5
A) + + ; B) + - + ; C) - + + ; - D) - + + ;
8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8
Answer: C

214) 0.27 added to the sum of 5.19 and -7.18

A) [5.19 + 0.27] + (7.18); -12.64 B) [5.19 + 7.18] + 0.27; 12.64
C) [5.19 + (-7.18)] + 0.27; -1.72 D) 5.19 + [(-7.18)+ 0.27]; 1.72
Answer: C

24
Solve the problem.
215) The stock market gained 17 points on Tuesday and lost 54 points on Wednesday. It had closed on Monday at
2563 points. Where did the market close on Wednesday?
A) 2600 points B) 2634 points C) 2492 points D) 2526 points
Answer: D

216) During one year 16 new employees began work at Daniel's Manufacturing Company and 34 employees left. At
the beginning of the year there were 331 employees. What was the number of employees at the end of the year?
A) 347 employees B) 381 employees C) 281 employees D) 313 employees
Answer: D

217) A football team gained 36 yards on one play, lost 12 yards on another, and gained 26 yards on the last play of
the first half. They had already gained 391 yards during the half. What was the total yardage gain for the first
half?
A) 441 yards B) 465 yards C) 453 yards D) 341 yards
Answer: A

218) Annica owes $476.98 on her charge card. She returns for credit items costing $24.09 and $41.27. She makes a
purchase for $23.42 and additional purchases of $33.80, $172.62, and $177.98. She then makes a payment of
$540.35. Find the amount she now owes.
A) $674.87 B) $279.09 C) $409.81 D) $544.15
Answer: B

219) A machinist has flat metal plate that is 8.108 cm thick. He laminates the metal plate with four more layers that
are 3.980 cm, 1.513 cm, 3.107 cm, and 4.489 cm thick. He then grinds off 1.508 cm from the top of the plate, then
4.511 cm more, and finally another 1.726 cm. Find the new thickness of the plate.
A) 2.764 cm B) 25.490 cm C) 14.960 cm D) 13.452 cm
Answer: D

220) In four rounds of a card game, you get scores of -3, -4, -8, and 9. What is your final score?
A) 6 B) -6 C) -18 D) 18
Answer: B

221) Your bank account has $90 in it when you write checks for $52, $33, and $47. You then deposit $42 and $34.
How much is in the account? Are you overdrawn?
A) $81, no B) $146, no C) -$146, yes D) $34, no
Answer: D

222) A bike road race starts at an elevation of 530 feet and passes through 5 stages where the elevation changes by
583 feet, -313 feet, 504 feet, 387 feet, and 174 feet. At what elevation does the race end?
A) 821 feet B) -2491 feet C) 1865 feet D) 2491 feet
Answer: C

223) The ocean surface is at 0 feet elevation. A diver is underwater at an elevation of -193 feet near a rock formation.
In this area, the ocean floor has an elevation of -195 feet. The rock formation rises to a peak 102 feet above the
ocean floor. How many feet below the top of the rock formation is the diver?
A) 93 feet B) 100 feet C) 2 feet D) 91 feet
Answer: B

25
Answer the question or complete the sentence to make a true statement.
224) In order to add -9 and 7, I should begin by finding the of the of -9 and 7.
A) Difference, absolute values B) Sum, absolute values
C) Difference, additive inverses D) Sum, opposites
Answer: A

225) In order to add -5 and -1, I should begin by finding the of the of -5 and -1.
A) Opposite, additive inverses B) Difference, absolute values
C) Additive inverses, opposites D) Sum, absolute values
Answer: D

226) When the absolute value of a positive number equals the absolute value of a negative number, the sum of the
positive and the negative number is .
A) Zero B) Not known C) Negative D) Positive
Answer: A

227) According to the rules for the order of operations, what should be the first step when simplifying the expression
[9 + (-5 + 4)] + (-6)?
A) Find the sum of -5 and 4 B) Find the sum of 9 and -5
C) Find the sum of 4 and -6 D) Find the sum of 9 and -6
Answer: A

228) According to the rules for the order of operations, what should be the first step when simplifying the expression
[-4 + (-7 + 4)] + (-8 + 6)?
A) Find the sum of 4 and -8 B) Find the sum of -4 and -8
C) Find the sum of -4 and -7 D) Find the sum of -7 and 4
Answer: D

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

229) Under what condition will the sum of a positive number and a negative number be negative?
Answer: The absolute value of the negative number must be greater than the absolute value of the positive
number.

230) Under what condition will the sum of a positive number and a negative number be positive?
Answer: The absolute value of the positive number must be greater than the absolute value of the negative
number.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

231) The sum of two positive numbers will always be a number.

A) Positive B) Negative
Answer: A

232) The sum of a negative number and 0 will always be a number.

A) Negative B) Positive
Answer: A

233) The sum of three negative numbers will always be a number.

A) Negative B) Positive
Answer: A

26
Find the difference.
234) 6 - 9
A) 15 B) -15 C) 3 D) -3
Answer: D

235) -1 - 11
A) 10 B) -10 C) 12 D) -12
Answer: D

236) -10 - (-9)

A) 1 B) -19 C) 19 D) -1
Answer: D

237) 4 - (-1)
A) -5 B) -3 C) 3 D) 5
Answer: D

238) -36 - 36
A) 0 B) 72 C) -72 D) -108
Answer: C

239) 1 - (15 - 5)
A) -9 B) 11 C) 21 D) -19
Answer: A

240) (-6 + 7) - (-5 + 17)

A) -21 B) -25 C) -11 D) -13
Answer: C

241) (9 + 13) - (20 - 19)

A) 17 B) -35 C) 35 D) 21
Answer: D

242) -3 - [(11 - 1) - (-7 + 2)]

A) -18 B) -20 C) -12 D) -8
Answer: A

243) -5 - (-3) - 9 + 5
A) 22 B) -12 C) 6 D) -6
Answer: D

1 3
244) - -
10 10
2 1 1 2
A) B) C) - D) -
5 5 5 5
Answer: A

27
 4 7
245) - -
5 10
3 11 3 3
A) B) - C) - D) -
2 10 2 10
Answer: C

4 7
246) - - -
5 10
1 11 1 3
A) - B) - C) D) -
10 10 10 10
Answer: A

9 3 1
247) - -
10 11 10
8 7 1 8
A) - B) C) - D)
11 10 2 11
Answer: D

4 1
248) - -
5 2
13 13 9 3
A) - B) C) - D)
10 10 50 10
Answer: B

3 5
249) - - -
4 8
1 1 1
A) B) - C) - 1 D) -
8 8 4
Answer: B

1 1
250) - -
7 3
10 4 1 10
A) B) - C) - D) -
21 21 14 21
Answer: A

1 2 1
251) - - -
2 3 3
3 7 3
A) B) 6 C) - D)
4 12 2
Answer: D

1 1 11
252) - - - - -5
4 2 8
35 45 23 57
A) - B) C) D) -
8 8 8 8
Answer: B

28
 253) -13.8 - 13.9
A) 27.7 B) -27.7 C) -0.1 D) 0.1
Answer: B

254) -14.9 - (-13.5)

A) 1.4 B) 28.4 C) -28.4 D) -1.4
Answer: D

255) [-21.3 + (16.3 - 3.2)] - 2.8

A) -5.4 B) -38 C) 31.6 D) -11
Answer: D

256) [-3.45 - (5.35 - 10.75)] - 12.24

A) -10.29 B) 10.29 C) -0.41 D) 0.41
Answer: A

Write a numerical expression for the phrase and simplify it.

257) The difference between 19 and -7
A) 19 - (-7); 26 B) 7 - 19; -12 C) -7 - 19; -26 D) 19 - (-7); 12
Answer: A

258) 12 less than -9

A) 12 - 9; 3 B) -9 - 12; 21 C) 12 - (-9); 21 D) -9 - 12; -21
Answer: D

259) The sum of 7 and -7, decreased by 3

A) [7 + (-3)] + 7; 11 B) [7 + (-7)] + 3; 3 C) [7 - (-7)] - 3; 11 D) [7 + (-7)] - 3; -3
Answer: D

260) 20 less than the difference between 6 and -2

A) (6 - 2) - 20; -16 B) 20 - [6 - (-2)]; 12 C) [6 - (-2)] - 20; -12 D) [6 - (-2)] - 20; -16
Answer: C

261) 8 less than the difference between 20 and -3

A) -3 - 20 - 8; -31 B) [20 - (-3)] - 8; 15 C) 8 - 20 - (-3); -9 D) 3 - 20 - 8; -31
Answer: B

Solve the problem.

262) The stock market gained 57 points on Tuesday and lost 40 points on Wednesday. Find the difference between
these changes.
A) -97 points B) -17 points C) 17 points D) 97 points
Answer: D

263) Nikki is fishing from a bank 32 feet above water level. In this location, the fish tend to feed at 44 feet below the
surface. How long must Nikki's fish line be to reach the fish?
A) -12 feet B) 76 feet C) 12 feet D) -32 feet
Answer: B

29
 264) Wayne has $11.80 in his wallet. Janice has a debt note for $25.28 in her wallet. Find the difference between these
amounts.
A) -$37.08 B) $37.08 C) -$13.48 D) $13.48
Answer: B

265) Company A showed a profit of $80,180 last year, while Company B had a loss of $61,720. Find the difference
between these amounts.
A) -$141,900 B) $18,460 C) $141,900 D) -$18,460
Answer: C

266) The temperature at the South pole was 37° at 8 am. At 3 pm, it was -26°. By how many degrees did the
temperature drop?
A) -63° B) -11° C) 63° D) 11°
Answer: C

267) The ocean surface is at 0 ft elevation. A diver is underwater at an elevation of -184 ft near a rock formation. In
this area, the ocean floor has an elevation of -327 ft. The rock formation rises to a peak 132 ft above the ocean
floor. How many feet above the top of the rock formation is the diver?
A) 143 ft B) 11 ft C) 52 ft D) 195 ft
Answer: B

268) After one round in a card game, your score was -30 points. After the second round, your score was 3 points.
How many points did you gain in the second game?
A) 33 points B) 3 points C) -27 points D) 27 points
Answer: A

269) In a certain location, the highest temperature recorded was 101°F. The lowest temperature recorded was 138
degrees less than the highest. What was the lowest temperature?
A) -37°F B) 0°F C) -138°F D) 37°F
Answer: A

270) The two charts show the weight gain of some people and the weight loss of other people. Use the information
given to answer the question below.

What is the difference between the weight gain of Carl and the weight loss of Don?
A) -4653 grams B) 4653 grams C) -1263 grams D) 1263 grams
Answer: B

Provide an appropriate response.

271) If a, b, and c are real numbers, is this statement true or false? 0 - a = -a
A) True B) False
Answer: A

272) If a, b, and c are real numbers, is this statement true or false? If a = b, then a - b = b - c.
A) True B) False
Answer: B

30
 273) If a, b, and c are real numbers, is this statement true or false? -(-a) = -a
A) True B) False
Answer: B

274) If a, b, and c are real numbers, is this statement true or false? -(a + b) = -a - b
A) True B) False
Answer: A

275) If a, b, and c are real numbers, is this statement true or false? a - 0 = -a

A) True B) False
Answer: B

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

276) Is this statement true or false? Why? (8 - 8) - 8 = 8 - (8 - 8)

Answer: False. Answers will vary.

277) Is this statement true or false? Why? (4 + 4) - 4 = 4 + (4 - 4)

Answer: True. Answers will vary.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

278) Given the problem 8 - [1 - (-2 - 12)], is the first step in solving to subtract -2 from -12?
A) Yes B) No
Answer: B

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

279) Make up a subtraction problem in which the difference between two negative numbers results in a positive
number.
Answer: Answers may vary. One possible answer is -5 - (-12) = 7.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Find the product.

280) -7(18)
A) -56 B) 70 C) 15 D) -126
Answer: D

281) -9(-9)
A) 81 B) -81 C) -91 D) 91
Answer: A

282) -3(19)
A) 42 B) -57 C) -37 D) 157
Answer: B

283) -17(0)
A) 17 B) 1 C) 0 D) -17
Answer: C

31
 5 24
284) - -
16 5
3 1
A) B) C) 3 D) - 1
2 3
Answer: A

5
285) -6 -
4
15 5 5 15
A) - B) - C) D)
2 2 2 2
Answer: D

286) 7.4(3.69)
A) 27.306 B) 2.7306 C) 0.27306 D) 273.06
Answer: A

287) -0.05(0.9)
A) 0.45 B) 4.5 C) -0.045 D) -0.0045
Answer: C

288) 2.5(-4.79)
A) -2.29 B) 7.29 C) -11.975 D) 7.39
Answer: C

Find the quotient.

-104
289)
4
1
A) 26 B) -26 C) - D) -36
26
Answer: B

115
290)
-5
1
A) -23 B) 23 C) -33 D) -
23
Answer: A

-518
291)
74
1
A) 7 B) - C) -17 D) -7
7
Answer: D

-306
292)
-51
1
A) -4 B) C) -6 D) 6
6
Answer: D

32
 0
293)
-15
A) 1 B) 0 C) Undefined D) 15
Answer: B

7 3
294) - ÷ -
15 11
7 77 77 45
A) - B) - C) D)
55 45 45 77
Answer: C

1 3
295) ÷ -
2 5
5 5 6 3
A) B) - C) D) -
6 6 5 10
Answer: B

-8
296)
0
A) 8 B) 0 C) Undefined D) -8
Answer: C

4.844
297)
4
A) 0.3 B) 1.211 C) -1.211 D) -0.3
Answer: B

Perform the indicated operation.

-2(-5)
298)
2 - (-3)
A) -2 B) -10 C) 2 D) 10
Answer: C

-8(2) + 6(6)
299)
-3 - (-7)
A) -13 B) 13 C) 5 D) -5
Answer: C

-19(-4) - (-12)(-5)
300)
-6(2) - 4(-1)
A) 17 B) -1 C) -2 D) 2
Answer: C

32 - 112
301)
2(-2 + 6)
A) 14 B) 7 C) -7 D) -14
Answer: D

33
Evaluate the expression, given x = -2, y = 3, and a = -4.
302) -7x - 4y - 5a
A) 7 B) 26 C) 15 D) 22
Answer: D

303) (-6x - 5y)(8a)

A) -96 B) -744 C) 256 D) 96
Answer: D

304) -9a + 2y + 9x
A) -60 B) 37 C) 59 D) 24
Answer: D

305) (4 + x)(-5 + y)(-9 - a)

A) -20 B) 20 C) 52 D) 156
Answer: B

306) (-3a)(-2x - 6y)

A) 72 B) 168 C) -168 D) -264
Answer: C

1 3 1
307) x- y - a
4 5 5
46 26 46 39
A) - B) - C) - D)
5 25 25 25
Answer: C

6ax - 12y
308)
a+y
A) 36 B) -12 C) -1 D) -36
Answer: B

309) 6y - 9a 2
A) -54 B) 162 C) -18 D) -126
Answer: D

5a 2 - y
310)
x+2
77 83
A) B) 0 C) Undefined D) -
4 4
Answer: C

Write a numerical expression for the phrase and simplify it.

311) The product of -9 and 8, added to 9
A) (9)(-9 + 8); -9 B) 9 + (-9)(8); -63 C) (-9)(8)(9); -648 D) (-9 + 9)(8); 0
Answer: B

34
312) The product of 8 and -5, added to -1
A) (-1)(-5)(8); 40 B) (-1)(-5) + 8; 13 C) (-1 + 8)(-5); -35 D) (-1) + (8)(-5); -41
Answer: D

313) The product of -5 and 9, subtracted from -1

A) (-1)(-5)(9); 45 B) -1 - (-5)(9); 44 C) -1 + (-5)(9); -46 D) [-1 - (-5)](9); 36
Answer: B

314) Twice the product of -6 and -7, subtracted from 2

A) (2 - 2)(-6 ∙ -7); 0 B) (2)(2)(-6)(-7); 168 C) (2)(2)(-6 + 7); 4 D) 2 - 2(-6 ∙ -7); -82
Answer: D

315) 9 subtracted from the product of -9.8 and 8.4

A) (9)(-9.8)(8.4); -740.88 B) 9 - (-9.8)(8.4); 91.32
C) (-9.8)(8.4) - 9; -91.32 D) [9 + (-9.8)](8.4); -6.72
Answer: C

316) The product of 6 and the difference between 7 and -3

A) (6)(7) - (-3); 45 B) 6[7 - (-3)]; 60 C) 6[-3 - 7]; -60 D) (6 - 7)(-3); 3
Answer: B

317) The product of -5 and the sum of 1 and -2

A) (-5)(-2) + 1; 11 B) -5 + (1)(-2); -7 C) -5[1 + (-2)]; 5 D) (-5)(1) + (-2); -7
Answer: C

318) Five-eighths of the sum of -5 and -11.

5
A) (5 + 8)(-5) + (-11); -76 B) + [(-5) + (-11)]; 3
8
5 5
C) [(-5) + (-11)]; -10 D) [(-5) + (-11)]; -20
8 8
Answer: C

319) Five-ninths of the difference between -7 and -25.

A) 5(9) [(-7) - (-25)]; 810 B) 5(9) [(-7) - (-25)]; 10

5 5
C) [(-7) - (-25)]; 10 D) + [(-7) - (-25)]; 30
9 9
Answer: C

320) The quotient of -18 and -9

-18 1 -9 1 -18
A) (-9)(-18); 162 B) ; C) ; D) ;2
-9 2 -18 2 -9
Answer: D

321) The quotient of 16 and the sum of 6 and -4

16 6 + (-4) 1 16
A) 16 + 6 + (-4); 18 B) ; -8 C) ; D) ; 8
6 + (-4) 16 8 6 + (-4)
Answer: D

35
 322) The quotient of -153 and the sum of 10 and 7
-153 10 + 7 1 -153
A) -153 + 10 + 7; -136 B) ; 9 C) ; - D) ; -9
10 - 9 -153 9 10 + 7
Answer: D

323) The sum of 36 and -6, divided by the product of 3 and -5

3(-5) 1 36 + 6 36 + (-6) -6
A) ; - B) ; - 15 C) ; -2 D) 36 + ; -2
36 + (-6) 2 3 - (-5) 3(-5) 3(-5)
Answer: C

324) The sum of 1 and -9, divided by the product of 1 and -4

-9 5 1 + (-9) 8 -9 1 + (-9)
A) 1 + ; - B) ; - C) 1 + ; 3 D) ; 2
1(-4) 8 1 - (-4) 5 1 + (-4) 1(-4)
Answer: D

2 5 1
325) The product of and , divided by - .
5 8 3
2 5 2 5 2 1
-
5 8 1 5 8 3 5 48 3 4
A) ;- B) ;- C) ;- D) ;-
1 12 1 4 5 1 25 2 5 3
- - -
3 3 8 3 5 8

Answer: B

Write the sentence with symbols, using x to represent the number.

326) 6 times a number is -48.
-48
A) 6x = -48 B) =x C) -6x = -48 D) -8x = -48
-8
Answer: A

327) The quotient of a number and 5 is -2.

-10 1 x x
A) =5 B) 5x = - C) = -2 D) =5
x 2 5 -2
Answer: C

328) 7 less than a number is -2.

A) 7 - x = 5 B) x - 7 = -2 C) x + 7 = -2 D) x - 2 = 7
Answer: B

329) When 2 is added to another number the result is -4.

A) x + 2 = -4 B) -6 - 4 = x C) x - 4 = 2 D) -4 - 2 = x
Answer: A

Find the average of the numbers.

330) 4, 3, 10, 15, 3
A) 8.75 B) 7 C) 8 D) 36
Answer: B

36
 331) 11, 9, 15, 19, 14, 1, 18, 1
A) 12.57 B) 10 C) 11 D) 12
Answer: C

332) 12, -6, -6, 12, -2

A) 2.5 B) 2 C) 1.7 D) 1
Answer: B

333) What is the average of all integers between 3 and 23, inclusive of both?
A) 56 B) 14 C) 273 D) 13
Answer: D

334) What is the average of all the even integers between -18 and 2, inclusive of both?
A) -7 B) -88 C) -6 D) -8
Answer: D

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Provide an appropriate response.

335) What values of a and b make the result negative? -(a - b)
Answer: a must be greater than b

336) If x and y are both replaced by negative numbers, is the value of 3x - 5y positive or negative?
Answer: Positive if ∣5y∣ is greater than ∣3x∣;
negative if the opposite is true.

337) The reciprocal of a positive number is a number.

Answer: Positive

9+9
338) Is the following expression undefined?
9-9
Answer: Yes

339) A positive number multiplied by two negative numbers and then divided by a positive number is .
Answer: Positive

340) The average of a group of positive numbers is a number.

Answer: positive

341) The only real number that does not have a reciprocal is .
Answer: zero

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

342) Assume a is positive, b is negative, and c is positive for the expression

a + ( b ∙ c)
Tell whether the value of the given expression is positive, negative or cannot be determined.
A) Negative B) Cannot be determined C) Positive
Answer: B

37
 343) Assume a is positive, b is negative, and c is positive for the expression (b + a) ∙ c
Tell whether the value of the given expression is positive, negative or cannot be determined.
A) Positive B) Cannot be determined C) Negative
Answer: B

344) Assume a is positive, b is negative, and c is positive for the expression

a ∙ b2 ∙ c
Tell whether the value of the given expression is positive, negative or cannot be determined.
A) Cannot be determined B) Negative C) Positive
Answer: C

Decide whether the statement is an example of the commutative, associative, identity, inverse, or distributive property.
345) 6 ∙ 1 = 6
A) Inverse B) Distributive C) Identity D) Commutative
Answer: C

346) (7 + 8) + 2 = (8 + 7) + 2
A) Associative B) Commutative C) Distributive D) Identity
Answer: B

347) 6(x + 7) = 6x + 6 ∙ 7
A) Commutative B) Distributive C) Associative D) Identity
Answer: B

348) 6 + (-6) = 0
A) Commutative B) Inverse C) Identity D) Associative
Answer: B

349) 8 + 8 = 8 + 8
A) Associative B) Commutative C) Distributive D) Identity
Answer: B

350) (6 ∙ 2) ∙ 1 = 6 ∙ (2 ∙ 1)
A) Associative B) Identity C) Distributive D) Commutative
Answer: A

351) 2 ∙ 5 = 5 ∙ 2
A) Distributive B) Identity C) Commutative D) Associative
Answer: C

7 9
352) =1
9 7
A) Identity B) Commutative C) Associative D) Inverse
Answer: D

353) 3(5f) - 3(5g) = 3(5f - 5g)

A) Identity B) Associative C) Distributive D) Commutative
Answer: C

38
Use the indicated property to provide a new expression equal to the given expression. Simplify, if possible.
354) 6 + x; commutative
A) x - 6 B) -x - 6 C) 6 - x D) x + 6
Answer: D

355) z + 0; identity
A) 0 B) 0 + z C) z D) 1
Answer: C

356) -7 + 0; identity
A) 7 B) -7 C) 0 D) 1
Answer: B

357) 8(r + k); distributive

A) 8r + 8k B) r(8 + k) C) 8r + k D) 8r - 8k
Answer: A

1
358) 5 ∙ ; inverse
5
A) 25 B) 1 C) -1 D) 5
Answer: B

359) 10 + (-10); inverse

A) -20 B) 0 C) 100 D) 20
Answer: B

360) -2(x + 4); distributive

A) -2x - 8 B) 2x - 8 C) -2x + 4 D) x - 8
Answer: A

361) 8(k - 2); distributive

A) k - 16 B) 8k + 16 C) 8k - 16 D) 8k - 2
Answer: C

362) -3 ∙ 1; identity
A) -3 B) 3 C) 1 D) -1
Answer: A

363) (4x + 3y) + 9z; associative

A) (4x + 3y + 9z) B) 4x + (3y + 9z) C) (3y + 4x) + 9z D) 4x + 3y + 9z
Answer: B

Use the properties of real numbers to simplify the expression.

1 5 11 1
364) - + + +
3 8 8 3
A) 2 B) 4 C) 0 D) 8
Answer: A

39
 7 9
365) (-0.46)
9 7
7
A) 1 B) -0.46 C) D) -1
9
Answer: B

Use the distributive property to rewrite the expression.

366) 7(x + 9)
A) 63x B) 7x + 63 C) 7x + 9 D) 7x + 7
Answer: B

367) 8(4x + 5y + 6)
A) 32x + 5y + 6 B) 32x + 40y + 48 C) 32x + 40y + 6 D) 32x + 5y + 48
Answer: B

368) 7(6r + 6 + 9s)

A) 42r + 6 + 9s B) 42r + 6 + 63s C) 42r + 42 + 63s D) 42r + 42 + 9s
Answer: C

369) -8(5x) - 8(5y)

A) -8x(5 + 5) = -80x B) -16(5x + 5y) C) -8(5x + 5y) D) -40x - 40y
Answer: C

9
370) - (8x + 8y)
8
A) -9x - 9y B) -18x C) 9x + 9y D) -9x + 9y
Answer: A

371) 9 ∙ x + 9 ∙ z
A) 9(xz) B) 81(x + z) C) 18(x + z) D) 9(x + z)
Answer: D

2
372) (78x + 15y)
3
A) 62xy B) 52x + 10y C) 62(x + y) D) 26x + 5y
Answer: B

Use the distributive property to write without parentheses.

373) - (7x + 7y)
A) -7x + 7y B) 7x - 7y C) -7x - 7y D) 7x + 7y
Answer: C

374) - (-4v - 2r)

A) -4v + 2r B) -4v - 2r C) 4v - 2r D) 4v + 2r
Answer: D

375) - (-5m + 4n - 9p)

A) 5m - 4n - 9p B) -5m + 4n + 9p C) -5m + 4n - 9p D) 5m - 4n + 9p
Answer: D

40
 376) - (6z - 2w + 6y)
A) -6z - 2w - 6y B) -6z + 2w - 6y C) -6z - 2w + 6y D) -6z + 2w + 6y
Answer: B

377) - (-5t - 4r - 6s)

A) -5t - 4r + 6s B) -5t - 4r - 6s C) 5t + 4r + 6s D) 5t + 4r - 6s
Answer: C

378) - (2n + 7w + 7g)

A) 2n + 7w + 7g B) 2n - 7w + 7g C) -2n - 7w + 7g D) -2n - 7w - 7g
Answer: D

Decide whether or not the events are commutative.

379) Recording a check or a deposit in your check book if both are made on the same day.
A) No B) Yes
Answer: B

380) Putting sugar or cream into your coffee first.

A) No B) Yes
Answer: B

381) Putting an Easter ham or a loaf of bread into a small grocery sack first.
A) Yes B) No
Answer: B

382) Turning on the printer and printing a computer report.

A) No B) Yes
Answer: A

383) Setting the table and eating dinner.

A) Yes B) No
Answer: B

384) Putting on your left glove and then your right glove.
A) Yes B) No
Answer: A

385) 17 - (3 - 5) and (17 - 3) - 5

A) No B) Yes
Answer: A

Answer the question.

386) There is a commutative property for both addition and multiplication. Is there a commutative property for
subtraction? If so, state the property.
A) Yes. x - y = y - x B) No.
Answer: B

41
 387) There is a distributive property for multiplication with respect to addition: a(b + c) = ab + ac. Is there a
distributive property for multiplication with respect to subtraction? If so, state the property.
A) Yes. a(b - c) = ab - ac B) No.
Answer: A

388) Choose the expression that is equivalent to the following: 0 + 9c

A) 9 + c B) -9c C) 9c D) 0
Answer: C

389) Choose the expression that is equivalent to the following: 1(4y2 )

A) 4y3 B) 4y2 C) 5y2 D) 1
Answer: B

390) Choose the expression that is equivalent to the following: 3(2a) + 3(3b)
A) 6(5ab) B) 3(5ab) C) 3(2a + 3b) D) 6(2a + 3b)
Answer: C

391) Choose the expression that is equivalent to the following: 12x + 3y

A) 3(4x + y) B) 3(9x + y) C) 3(4x + 3y) D) 15xy
Answer: A

392) Choose the expression that is equivalent to the following: (7x + 8y)(2y + 4x)
A) (7x + 8y)(4x + 2y) B) (7x + 4y)(8x + 2y) C) 11x + 10y D) (7x + 8y)(4y + 2x)
Answer: A

393) Choose the expression that is equivalent to the following: (9x + 5y)(2y3 )
A) (2y3 )(9x+ 5y) B) (9x) + (5y)(2y3 ) C) 9x + (5y + 2y3) D) (9x + 2y3 )(5y)
Answer: A

1
394) Choose the expression that is equivalent to the following: 5( )
5
5 1 1 1
A) B) 5 C) D) 5 +
5 5 25 5
Answer: A

395) Choose the expression that is equivalent to the following: 4 - 4

A) 4 + (-4) B) (-2)(4) C) 2(4) D) (4)(4)
Answer: A

Simplify the expression.

396) 9a - 3a + 6
A) 6a + 6 B) -6a + 6 C) 12a + 6 D) 12a
Answer: A

397) -6 + 7(11 - 7m)

A) 71 + 49m B) 77 - 49m C) 71 - 7m D) 71 - 49m
Answer: D

42
 398) -14 - (3 - 13s)
A) -17 + 13s B) 17 + 13s C) 11 - 13s D) -11 - 13s
Answer: A

399) 5g + 20 - 9
A) 5g + 29 B) 16g C) 5g - 11 D) 5g + 11
Answer: D

400) 4 + 6(x + 3y)

A) 4 + 6x + 18y B) 10x + 3y C) 4 + 6x + 3y D) 4 + 18xy
Answer: A

401) 4 - 5(s - 7t)

A) 4 + 5s + 35t B) 4 - 5s + 35t C) 4 - 5s - 35t D) 4 + 5s - 35t
Answer: B

Give the numerical coefficient of the term.

402) z
A) z B) -1 C) 0 D) 1
Answer: D

403) -4y8
A) y8 B) -4 C) 8 D) 4
Answer: B

404) -6y
A) -6 B) y C) 6 D) 6y
Answer: A

405) -10
A) 1 B) 10 C) -10 D) 0
Answer: C

406) 2
A) 0 B) 1 C) 2 D) -1
Answer: C

407) wy
A) w B) 0 C) wy D) 1
Answer: D

408) -w
A) 0 B) -w C) 1 D) -1
Answer: D

409) 5k2
A) 2 B) 5 C) 25 D) 10
Answer: B

43
Identify the group of terms as like or unlike.
410) 13z, -5z
A) Unlike B) Like
Answer: B

411) 14a 7 , 14a 6

A) Like B) Unlike
Answer: B

412) 14m, 5m, -6m

A) Like B) Unlike
Answer: A

413) 3, 5, -8
A) Like B) Unlike
Answer: A

414) 9b, 3, 14a

A) Unlike B) Like
Answer: A

415) -2m, -11m

A) Unlike B) Like
Answer: B

416) u, v
A) Like B) Unlike
Answer: B

417) 7v2 , -13v4

A) Like B) Unlike
Answer: B

418) 7v4 , -13v4

A) Like B) Unlike
Answer: A

Simplify the expression by combining like terms.

419) 9p2 + 6p3 - 4p2 - 9p3
A) 2p2 B) 5p2 - 3p3 C) 2p2 p3 D) 15p2 - 13p3
Answer: B

5 17 13
420) - + 18y + y - 11 + y
12 12 12
41 53 41 137
A) 20y B) +6 C) y- 6 D) y-
2 3 2 12
Answer: D

44
 421) -5(9r + 10) + 7(7r + 9)
A) 4r + 5 B) 4r + 10 C) -95r D) 4r + 13
Answer: D

422) 12t + 5(2 - 5t)

A) -13t + 10 B) 7t + 10 C) 37t - 10 D) 13t - 10
Answer: A

423) -3(7x + 1) - (3x + 7) - 2x + 8

A) 26x + 8 B) -26x + 4 C) -26x - 2 D) -20x + 12
Answer: C

424) -4.5p + 5.8 - (9p + .5) + 5.8p

A) 10.3p + 6.3 B) -7.7p + 5.3 C) 10.3p + 5.3 D) -7.7p + 6.3
Answer: B

3 1
425) - (z - 16) - z
4 8
7 7 5 7
A) z + 12 B) z - 12 C) z + 16 D) - z + 12
8 8 8 8
Answer: D

Write the phrase as a mathematical expression. Use x to represent the number. Combine like terms if possible.
426) Four times a number, added to the sum of the number and six.
A) 10x B) 5x C) (x + 6) + 4x; 5x + 6 D) 4x + 6
Answer: C

427) A number multiplied by -2, subtracted from the sum of 18 and four times the number.
A) (18 + 4x) - (-2)x; 18 + 6x B) 2x - (18 + 4x); -2x - 18
C) (18 + 4x) + (-2)x; 18 + 2x D) 2x - 22
Answer: A

428) A number multiplied by 4, added to -8, subtracted from 8 times the sum of 2 times the number and 9
A) 4(-8 + x) + 8(2 + 9x); 13x - 16 B) 4x - 8 + 8(2 + 9x); 76x + 20
C) 8(2x + 9) - [4x + (-8)]; 12x + 80 D) 4(-8 + x) + 8(2x + 9); 20x - 23
Answer: C

429) 8 times a number added to -6, added to 7 times the sum of 5 times the number and 6
A) 8x - 6 + 7(5 + 6x); 50x + 43 B) 8(-6 + x) + 7(5x + 6); 43x - 42
C) 8(-6 + x) + 7(5 + 6x); 14x - 13 D) 7(5x + 6) + [8x + (-6)]; 43x + 36
Answer: D

430) Five times a number added to -5, subtracted from twice the sum of nine times the number and -8.
A) (-5 + 5x) - 2(9x - 8); 11 - 13x B) (2 + 9)(x + -8) - 5(x - 5); -63 + 6x
C) 5(x - 5) - (2 + 9)(x - 8); 63 - 6x D) 2(9x - 8) - (-5 + 5x); -11 + 13x
Answer: D

45
Another random document with
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‘talpa maledicta,’ C. T. iii. 17.
‘Thetis,’ v. 812, vii. 1067, C. T. i. 80.
Titiuillus, iv. 864.
Tresilian, Robert, C. T. i. 162.
Tribulus (Nicholas Brembre), C. T. i. 154.
‘Troianus,’ vi. 1273.

vicecomes, vi. 433.

Vox Clamantis referred to, V. P. 52, 181, 246

Walsingham’s Chronicle referred to, i. 855, 941, 1173, iv. 723, 959,
C. T. i. 65, 80, 142, 150, 154, iii. 256, 394, 432.
Warwick, earl of, C. T. ii. 201 ff.
Wycliffe, vi. 1267, V. P. 32, 36.

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