write the fraction representing the shaded amount, and...
TRANSCRIPT
Review of Basic Concepts
R - 1
1.1 Fractions
For 1-5) Write the fraction representing the shaded amount, and the fraction representing the un-shaded amount: 1.
2.
3.
4.
5.
For 6-10) Simplify each fraction completely (reduce to lowest terms):
6. 68
7. 1535
8. 1449
9. 4872
10. 3451
For 11-13) Write the requested fraction/s: 11. A professional basketball player made 7 free-throws out of 11 attempts. What
fraction of the free- throws did he make? 12. A professional basketball player made 8 free-throws in 11 attempts.
a) What fraction of the free-throws did he make? b) What fraction of the free-throws did he miss?
13. A professional basketball player made 9 free-throws in 13 attempts. What fraction of
the free-throws did he miss?
Review of Basic Concepts
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For 14-16) Write each shaded amount as both mixed number and as an improper fraction: 14. 15. 16. For 17-22) Change each improper fraction to a mixed number or whole number:
17. 53
18. 234
19. 76
20. 155
21. 152
22. 1346
For 23-27) Change each mixed number to an improper fraction:
23. 415
24. 123
25. 374
26. 192
27. 3178
For 28-47) Add, subtract, multiply, or divide. Simplify (reduce) answers if possible:
28. 7 112 12
+ 29. 7 38 8−
30. 2 25 15+ 31. 7 1
12 3−
32. 7 58 12− 33. 3 2
5 9⋅
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34. 6 48 5⋅ 35. 1 2
3 3⋅
36. 3 58 12÷ 37. 7 2
9 3÷
38. 1 212 3+ 39. 3 52
4 11⋅
40. 1 523 6÷ 41. 1 73 1
4 8−
42. 14 105⋅ 43. 5 7
6 10+
44. 35 45÷ 45. 110 2
2÷
46. 5 19 6− 47. 36 2
4⋅
For 48-58) Solve the word problem:
48. In order to run electric power to his house, Jason must dig a trench 58
of a mile
long. If he has already dug 310
of a mile of trench, how much does he have left
to dig?
49. Jennifer mixes 318
pounds of cashews, 122
pounds of peanuts, and 124
pounds
of almonds, how many ponds of mixed nuts will it make?
50. If 34
pound of fudge candy is cut into 12 equal pieces, how much will each piece
weigh?
51. Maria ran 318
miles every day for 12 days. How many total miles did she run
during the 12 day period?
52. Nai bought some Generous Electric stock for 5$358
per share. The first week
the stock lost 1$4
per share, but the next week it gained 3$18
per share. What
was the price per share at the end of the second week?
Review of Basic Concepts
R - 4
53. The gas tank of a small car holds 2123
gallons when it is full. After a fill-up, 910
gallon of gas is used. How much gas is left?
54. The gas tank of a small car holds 2123
gallons when it is full. How many gallons
of gas are in the tank when it is 910
full?
55. If a developer buys 175
acres of land, how many 35
acre lots will he be able to
sell?
56. A road crew has to pave 528
miles of road. If the crew has 7 days to finish the
job, how much must it pave each day?
57. A rectangular parcel of land measures 314
mile by 23
mile. Find the perimeter of
the parcel of land and the area of the parcel of land.
58. A rancher owns the 518
square mile Lazy-H ranch. In order to pay for a new
barn, he plans to sell a piece of his land which measures 38
mile by 23
mile.
After he sells the land, how much will he have left?
Review of Basic Concepts
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1.2 Order of Operations and Variable Expressions For 1-8) Write using exponential notation. 1. 2 2 2⋅ ⋅ 2. 7 7⋅ 3. 9 9 9 9⋅ ⋅ ⋅ 4. 2 2 2 2 2 2⋅ ⋅ ⋅ ⋅ ⋅ 5. 3 3 5 5 5⋅ ⋅ ⋅ ⋅ 6. 7 7. (1.2)(1.2)(1.2) 8. 2 2 2 2
3 3 3 3⋅ ⋅ ⋅
For 9-15) Calculate the value of the exponential expressions. Round to 4 decimal places if necessary. 9. 35 10. 73 11. 122 12. 3(1.2) 13. 5(3.61) 14.
423
⎛ ⎞⎜ ⎟⎝ ⎠
(give answer as a fraction)
15. 33
4⎛ ⎞⎜ ⎟⎝ ⎠
(give answer as a fraction)
For 16-26) Calculate each square root. Round to four decimal places if necessary. 16. 25 17. 49
18. 16 19. 1
20. 0 21. 2
22. 17 23. 361
24. 116
(give answer as fraction) 25. 2564
(give answer as fraction)
26. 43
For 27-34) Tell which operation is to be done first according to Order of Operations. 27. 350 5 2− ⋅ 28. 27 (20 2 8)+ − ⋅ 29. 15 2(2.5)÷ 30. 15 64 5 7− ⋅ 31. 13 7 4− + 32. 325 2(1.5)−
33. 2 33 (5 3)+ − 34. 44 3 (2.1)(3.5)+ −
Review of Basic Concepts
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For 35-58) Use Order of Operations to simplify each expression. 35. 15 2 3− ⋅ 36. 7 9 14 2⋅ + ÷ 37. 45 10 2 13− ⋅ + 38. 23 5⋅ 39. 4 25 28 7− ÷ 40. 2(20 81)− 41. 70 35 5− +
42. 28 3(5)−
43. 217 3
5 1−−
44. 42 2 3⋅ ÷
45. 42 2 3÷ ⋅ 46. 76 (10 12)− + 47. 5(28 3 6)− ⋅ 48. (72 51)(15 8)− −
49. 2
5(7) 2(4)18 3
−−
50. 84 [50 (22 3)]− − +
51. 2 34(3) (7 5)− − 52. 11 1 512 2 6
− ⋅
53. 23 1 230 3 5
⎛ ⎞− +⎜ ⎟⎝ ⎠ 54. 7 1 1
8 4 2− +
55. 3 2 58 3 9÷ ⋅
56. 4[10.3 3(1.5 0.9)]+ −
57. 2(4.1)(3.6) (0.3)− 58. 11.7 2.25(0.6)(2.5)
−
For 59-62) Use the formula to calculate the requested value. Round decimal answers to two decimal places if necessary. When π is required, use the π -key on your calculator.
59. Fahrenheit to Celsius temperature conversion
5 ( 32)9
C F= − a) 68F =
b) 212F = c) 100F =
60. Area of a triangle
12
A bh= a) 35b in= 11h in=
b) 23b ft= 7h ft=
c) 172
b yd= 123
h yd= (Give the answer as a mixed number)
Review of Basic Concepts
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61. Surface area of a cylinder
22 2A r rhπ π= + a) 6r ft= 11h ft=
b) 7.2r cm= 23.1h cm=
c) 45
r m= 263
h m=
62. Simple Interest
PrI t= a) 10,000P = 0.04r = 15t =
b) 25,000P = 0.025r = 10t =
For 63-68) Evaluate the expression for the given values of the variable/s. Give exact answers. 63. 5 2x − a) 7x = b) 1.8x =
64. 2 2x x+ a) 3x = b) 1.8x =
65. 23 7x y− a) 3x = 2y = b) 2.3x = 0.25y =
66. 2 2 5x xy x− + a) 7x = 3y = b) 5.5x = 1.2y =
67. 2x yy−
a) 17x = 5y = b) 7.8x = 1.5y =
68. 23 2
5( )y xx y−−
a) 6x = 5y =
b) 2.05x = 1.8y =
For 69-98) Translate to an algebraic expression, using x to stand for any unknown number.
69. The sum of a number and 34
.
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70. The product of a number and 7.
71. The difference of a number and 12.
72. The difference of 12 and a number.
73. A number decreased by 9.
74. 9 decreased by a number.
75. A number increased by 23
.
76. 23
of a number.
77. 2 is more than a number.
78. 2 more than a number.
79. Twice a number.
80. 4 less than a number.
81. 4 is less than a number.
82. A number multiplied by 5.
83. A number increased by 5.
84. A number divided by 6.
85. The quotient of a number and 6.
86. The quotient of 6 and a number.
87. 23
subtracted from 172
.
88. 23
subtracted from a number.
89. A number subtracted from 23
.
90. The square root of a number.
91. The square of a number.
92. The cube of a number.
93. Seven minus 3 times a number.
94. 3 times the total of a number and 5.2.
95. 4 times the difference of a number and 9.
96. The difference of 4 times a number and 9.
97. 7 times a number is increased by 11.
98. The product of a number and 9 is decreased by 12.
Review of Basic Concepts
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1.3 Signed Numbers For 1-9) Write each number as a signed number.
1. The top of a coral reef is 32 ft below sea level.
2. The elevation of Mount Shasta’s peak is 14,162 ft above sea level.
3. The lowest point in Death Valley is 282 ft below sea level.
4. The temperature in Redding in July is often as high as 105 degrees Fahrenheit.
5. The temperature near the top of Mount Shasta can be as cold as 20 degrees
below zero Fahrenheit.
6. Alicia has a balance of $1,327.42 in her checking account.
7. Justin has overdrawn his checking account by $83.27.
8. On Sat. a professional golfer’s score was over par. Sunday was a better day, and
his score was 5 under par.
9. A football running back carried the ball only twice in one game. On his first run he
gained 2 yards, but on his second run he lost 10 yards. What was his total
yardage for the game?
For 10-14) Plot the number on a number line.
10. 4 and -4
11. 122
and 122
−
12. 314
and 314
−
13. 75
and 94
−
14. -1.2 and -2.87
For 15-20) Evaluate (determine the value of). 15. 7 16. 7−
17. 122
− 18. 1.85
19. 4− 20. 4− −
Review of Basic Concepts
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For 21-36) Insert the correct symbol >, <, or =. 21. 3 1.8 22. -3 1.8
23. 4.9 0 24. -5.19 0
25. -3 -10 26. -4.51 -4.32
27. 325
− -2.6 28. 716
37
−
29. 538
− -3.6 30. -5 5
31. 5− 5 32. -9 4
33. 9− 4 34. 6− 5.2
35. -4.3 1.6− 36. 6.2− 269
−
For 37-44) Write the opposite. 37. 4 38. -7 39. -2.65 40. 4
9
41. x 42. -x 43. 0 44. 3− For 45-53) Write an inequality that represents the set of numbers. For example, the set of all numbers greater than 7 would be represented by the inequality 7x > .
45. The set of all numbers that are less than 3.
46. The set of all numbers that are less than -3.
47. The set of all numbers greater than 2.5.
48. The set of all numbers greater than 233
− .
49. The set of all numbers that are greater than or equal to 5.
50. The set of all numbers that are not less than 5.
51. The set of all numbers that are less than or equal to 2.75.
52. The set of all numbers that are not greater than 2.75.
53. The set of all numbers that are less than or equal to 375
− .
Review of Basic Concepts
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For 54-60) Write an equivalent inequality using the opposite inequality symbol. For example, 5 2− < could be written equivalently as 2 5> − . 54. 8 10− > −
55. 3 1.5− <
56. 2 x< 57. 13
2x− <
58. 4.2 x≤ 59. 3 x≥
60. 728
x− ≥
For 61-64) Determine if each statement is true or false.
61. a) Zero is a whole number. b) Zero is a natural number. c) Zero is an integer.
62. a) 316
is a rational number.
b) 316
− is a rational number.
c) 316
− is an irrational number.
d) 316
− is a real number.
e) 316
− is an integer.
63. a) The Integers are made up of Natural Numbers, opposites (negatives) of natural numbers and zero.
b) The Rational Numbers and Irrational Numbers combined make up the Real Numbers. c) There is only one number that is both Rational and Irrational.
64. a) 712
is a rational number.
b) 213
− is a rational number.
c) 2.9 is a rational number. d) 0.6− is a rational number. e) 3 is a rational number. f) π is a rational number.
Review of Basic Concepts
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For 65-72) Answer each question using one or more of these:
a) The Natural Numbers. b) The Whole Numbers. c) The Integers. d) The Rational Numbers. e) The Irrational Numbers. f) The Real Numbers.
65. This set of numbers contains all the other sets.
66. These two sets combined make up the Real Numbers.
67. This set contains only fractions or numbers that can be written as fractions.
68. These sets contain no negative numbers.
69. These sets contain negative numbers.
70. These two sets do not contain zero.
71. Each of these two sets is contained in the Integers.
72. Each of these three sets is contained in the Rational Numbers.
For 73-80) List all the sets to which each number belongs. Use the same sets of numbers as for problems 57-64.
73. 37
74. -8
75. 5 76. 0 77. 2
78. -2.7 79. 3− 80. 0.27−
Review of Basic Concepts
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1.4 Operations with Signed Numbers For 1-10) Perform the indicated addition or subtraction. 1. 5 9+ 2. 5 ( 9)+ − 3. 5 9− + 4. 5 ( 9)− + − 5. 10 3− 6. 3 10− 7. 3 10− − 8. 10 ( 3)− − − 9. 10 ( 3)− − 10. 3 ( 10)− − For 11-20) Perform the indicated multiplication or division. 11. 4(7) 12. 4( 7)− − 13. 4(7)− 14. 4( 7)− 15. 42 6÷ 16. 42 ( 6)÷ − 17. 42 6− ÷ 18. 42 ( 6)− ÷ −
19. 364
− 20. 36
4−
For 21-60) Perform the indicated operation. For fraction or mixed number problems, give fraction or mixed number answer. For decimal problems, give exact decimal answer. 21. 7 ( 3)+ − 22. 5 8− ⋅ 23. 4 11− 24. 4 ( 8)− + − 25. 63 7− ÷ 26. 5(9) 27. 7 ( 12)− − 28. 7 13− +
29. 728
− 30. 168−
31. 6( 9)− − 32. 4 10− −
33. 3 64 7
− ⋅ 34. 1 74 8
⎛ ⎞+ −⎜ ⎟⎝ ⎠
35. 5 96 13÷ 36. 1 3
4 8− −
37. 4 155 22
⎛ ⎞⎛ ⎞− −⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠ 38. 1 3
6 4⎛ ⎞− − −⎜ ⎟⎝ ⎠
39. 2 43 5
⎛ ⎞− + −⎜ ⎟⎝ ⎠ 40. 3 5
10 6−
41. 5 316 8
⎛ ⎞− ÷ −⎜ ⎟⎝ ⎠ 42. 3 11
5 12⋅
Review of Basic Concepts
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43. 1 312 5
− ÷ 44. 5 19 6
− +
45. (0.25)( 1.3)− 46. 1.45 ( 0.35)− + − 47. 16.4 ( 4.8)− − − 48. ( 6)( 2.7)− −
49. 01.2
50. 1.20
51. 6.5 130− ÷ 52. (2.8)(0.9) 53. 1.27 1.43− + 54. ( 1000)(0.0048)− 55. 1.9 ( 0.25)− ÷ − 56. 10.65 ( 2.9)+ − 57. 4.1 6.5− 58. 4.56
1.5−
59. 5.40
− 60. 0
5.4−
For 61-70) Evaluate (calculate the value of) each exponential expression. 61. 25 62. 2( 5)− 63. 25− 64. 3( 4)−
65. 4( 3)− 66. 43−
67. 33
4⎛ ⎞⎜ ⎟⎝ ⎠
68. 334
69. 42
3⎛ ⎞−⎜ ⎟⎝ ⎠
70. 42
3⎛ ⎞−⎜ ⎟⎝ ⎠
For 71-78) Answer a) is positive, b) is negative or c) depends on the sizes (absolute values) of the numbers.
71. When two negative numbers are added, the result ___.
72. When two negative numbers are multiplied or divided, the result ___.
73. When two negative numbers are subtracted, the result ___.
74. When two numbers having opposite signs are multiplied, the result ___.
75. When two numbers having opposite signs are added, the result ___.
76. When a negative number is raised to the fourth power, the result ___.
77. When a negative number is raised to the third power, the result ___.
78. When a positive number is subtracted from a negative number, the result ___.
Review of Basic Concepts
R - 15
For 79-90) Calculate the value of each expression, being careful to follow Order of Operations. 79. 35 ( 3 8)− ÷ − + 80. 4(3 5) 5 16− − −
81. 9 5 5 9− + − 82. 30 6( 5)− ÷ −
83. 3 36 (2 5 4)− + − ⋅ 84. 2 2( 5) (7 3)− + −
85.
3 24 31 33 5
−
+
86. 21.79 (2.3)
0.2 0.9−−
87. 23 2 3
4 3 2⎛ ⎞− ÷ + ⎜ ⎟⎝ ⎠
88. 22.5 ( 2) 7(3)
2( 4)− − +
−
89. 3 9 17 22 4 10
− − −− −
90. 8 3(4)5 3( 5)− −− −
For 91-100) Evaluate each expression for 2x = , 3y = − , 5z = − .
91. 4 3x y− + 92. 23 5x x−
93. x yy x+−
94. 2z xy−
95. 6 3yx z−−
96. 22 3y z− +
97. 3 5x xy− 98. 2 3x z− + 99. 2 2y x− −
100. 2 43 2yx y−+
Review of Basic Concepts
R - 16
1.5 Properties of Real Numbers For 1-8) Use the commutative property of addition or the commutative property of multiplication to rewrite in an equivalent form. 1. 4 20+ 2. 9 7⋅ 3. 3 x+ 4. 5x ⋅ 5. yx 6. y x+ 7. 13 2x+ 8. 8 r− ⋅ For 9-14) Use the associative property of addition or the associative property of multiplication to rewrite in an equivalent form. Simplify if possible. 9. ( 5) 7x + + 10. ( )a b c+ + 11. 3(4 )a− 12. ( 9 )x y− 13. 8 (3 )r− + + 14. ( 7) 2r ⋅ ⋅ For 15-22) Use commutative and/or associative properties to simplify. 15. ( 4) 5x + + 16. ( 2 ) 7x− + + 17. 3(8 )a− 18. (6 )( 2)x −
19. 2 33 2
r⎛ ⎞⎜ ⎟⎝ ⎠
20. 1 (4 )4
x
21. 3124x⎛ ⎞
⎜ ⎟⎝ ⎠ 22. 315
5a⎛ ⎞−⎜ ⎟⎝ ⎠
For 23-50) Use the distributive property to write an equivalent expression with no parentheses. 23. 4(3 5 )x y+ 24. 4(3 5 )x y− 25. 4(3 5)x + 26. 4(3 5)x − 27. 4(3 )x y+ 28. 4(3 )x y− 29. 5(2 3 4)a b+ − 30. 5(2 7)x + 31. 5(2 7)x− + 32. 6( 3 4)x− + 33. 6( 3 4)x− − + 34. 4(3 7)x − 35. 4(3 7)x− − 36. 3( 5 1)x y− + 37. 3( 5 1)x y− − + 38. 2(1.7 4.35)x −
39. 1 (3 4)5x − 40. 2 3 1
3 4 4x⎛ ⎞+⎜ ⎟⎝ ⎠
41. 1(7 3)r− + 42. (7 3)r− +
Review of Basic Concepts
R - 17
43. 1(7 3)r− − 44. (7 3)r− − 45. ( 5) 3x + ⋅ 46. (2 4) 7x + ⋅ 47. ( 3 5)(2)a− + 48. ( 3 5)( 2)a− + − 49. (3 5)( 2)a − − 50. (7 6)x y+ For 51-59) Match the letter of the property to the appropriate problem number.
51. 3x ⋅ can be written as 3x . a) Commutative property of addition.
52. This property involves two operations, multiplication and addition (or subtraction).
b) Commutative property of multiplication.
53. ( 7) 4x + + can be rewritten as (7 4)x + +
c) Associative property of addition.
54. 1 x x⋅ = (or equivalently 1x x= ). d) Associative property of multiplication.
55. 2(5 )x− is the same as ( 2 5)x− ⋅ . e) Distributive property.
56. 3 ( 3) 0+ − = f) Additive identity (identity property for addition).
57. 7 x+ can be rewritten as 7x + . g) Multiplicative identity (identity property for multiplication).
58. 2 0 2x x+ = h) Additive inverse property (property of opposites).
59. 2 7 17 2⋅ =
i) Multiplicative inverse property (property of reciprocals).
For 60-68) Fill in the blank.
60. The ____________ properties of addition and multiplication say the order of numbers can be changed without affecting the results of the calculation. 61. The multiplicative inverse of a number is the same as its ____________. 62. Adding ____________ to a number does not change the number. 63. The ____________ properties of addition and multiplication involve changing parentheses or groupings. 64. Anything can be multiplied by ____________ without affecting its value.
Review of Basic Concepts
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65. Another name for the additive inverse of a number is the ____________ of the number. 66. When additive inverses (opposites) are added, the result is ____________. 67. Multiplication distributes over ____________ (two possible answers). 68. When multiplicative inverses (reciprocals) are multiplied, the result is
____________. For 69-76) First find the additive inverse (opposite), then find the multiplicative inverse (reciprocal).
69. 23
70. 34
−
71. 15
72. 15
−
73. 5 74. -5
75. x 76. x−
Review of Basic Concepts
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Answers to Problems on: p. R-1 to R-4 1.1 Fractions # answer # answer # answer 1 3
4 14
3 2
5 35
5 5
12
712
7 37
9 2
3
11 711
13 413
15 1 72
3 3
17 213
19 116
21 17
2
23 95
25 314
27 139
8
29 12
31 14
33 2
15
35 29
37 7 116 6or
39 5 114 4or
41 11 318 8or
43 23 8115 15
or 45 4 47 33 116
2 2or
49 49 1lb 6 lb8 8
or 51 116 mi
2
53 2311 gal30
55 12 lots 57 5Perimeter: 4 mi6
Area:7 1sq mi 1 sq mi6 6
or
Review of Basic Concepts
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Answers to Problems on: p. R-5 to R-8 1.2 Order of Operations and Variable Expressions # answer # answer # answer 1 32 3 49 5 2 33 5⋅ 7 3(1.2) 9 125 11 4096
13 613.1066 15 2764
17 7
19 1 21 1.4142 23 19 25 5
8
27 32 (Exponent) 29 15 2 (Division)÷
31 13 7 (Subtraction)− 33 5 3 (Subtraction)− 35 9 37 38 39 16 41 40 43 2 45 63 47 50 49 3 51 28 53 1
30
55 516
57 14.67 59 0a) 20 C
0b) 100 C 07
90
c) 37
37.78
C
or C
61 2a) 640.88 ft b) 1370.74 sq cm
2c) 37.53m
63 a) 33 b) 7
65 a) 13 b) 14.12
67 a) 1.2 b) 2.1
69 34x + 71 12x −
73 9x − 75 23x + 77 2 x>
79 2 (2)x or x 81 4 x< 83 5x + 85
66x or x ÷
87 1 22 37 − 89 2
3 x−
91 2x 93 7 3x− 95 4( 9)x − 97 7 11x +
Review of Basic Concepts
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Answers to Problems on: p. R-9 to R-12 1.3 Signed Numbers # answer # answer # answer 1 32 ft− 3 282 ft− 5 020 F− 7 $83.27− 9 8 yd−
11
13
15 7 17 12
2
19 4−
21 3 > 1.8 23 4.9 > 0 25 -3 > -10 27 32
5− = -2.6
29 538
− < -3.6 31 5− = 5
33 9− > 4 35 -4.3 < 1.6− 37 4−
39 2.65 41 x− 43 0 45 3x < 47 2.5x > 49 5x ≥ 51 2.75x ≤ 53 37
5x ≤ −
55 1.5 3> −
57 132
x > − 59 3x ≤ 61 a) T
c) T 62 a) T
c) F e) F
63 a) T c) F
64 a) T c) T e) T
65 f 67 d 69 c d e f 71 a b 73 d f 75 a b c d f 77 e f 79 e f
Review of Basic Concepts
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Answers to Problems on: p. R-13 to R-15 1.4 Operations with Signed Numbers # answer # answer # answer 1 14 3 4 5 7 7 13− 9 13 11 28
13 28− 15 7 17 7− 19 9− 21 4 23 7− 25 9− 27 19 29 9− 31 54 33 9
14−
35 65 11154 54or
37 611
39 22 71
15 15or− −
41 2033
43 5 122 2or− −
45 0.325− 47 11.6−
49 0 51 0.05− 53 0.16 55 7.6 57 2.4− 59 undefined 61 25 63 25− 65 81 67 27
64
69 1681
− 71 b
73 c 75 c 77 b 79 7− 81 8 83 36− 85 5
56
87 9 118 8or
89 34
91 17− 93 1 0.25or
95 3−
97 38 99 13−
Review of Basic Concepts
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Answers to Problems on: p. R-16 to R-18 1.5 Properties of Real Numbers # answer # answer # answer 1 20 4+ 3 3x + 5 xy 7 2 13x + 9 12x + 11 12a−
13 5 r− + 15 9x + 17 24a− 19 1r or r 21 9x 23 12 20x y+ 25 12 20x + 27 12 4x y+ 29 10 15 20a b+ − 31 10 ( 35)
10 35x
or x− + −
− −
33 18 ( 24)18 24x
or x+ −
−
35 12 ( 28)12 28x
or x− − −
− +
37 3 ( 15 ) ( 3)3 15 3
x yor x y− − − + −
− + −
39 3 45 5x −
41 7 ( 3)7 3
ror r− + −
− −
43 7 ( 3)7 3
ror r− − −
− +
45 3 15x + 47 6 10a− +
49 6 10a− + 51 b 53 c 55 d 57 a 59 i 61 reciprocal 63 associative 65 opposite 67 addition (or subtraction) 69 2 3A.I. M.I.
3 2= − =
71 1A.I.55M.I. 51or
= −
=
73 1A.I. 5 M.I.5
= − = 75 1A.I. M.I.x
x= − =