# write the fraction representing the shaded amount, and...

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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

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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

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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

R - 19

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

R - 23

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= − =