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Algebra 1 Interactive Chalkboard
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3. Lesson 2-1 Rational Numbers on the Number Line
Lesson 2-2 Adding and Subtracting Rational Numbers
Lesson 2-3 Multiplying Rational Numbers
Lesson 2-4 Dividing Rational Numbers
Lesson 2-5 Statistics: Displaying and Analyzing Data
Lesson 2-6 Probability: Simple Probability and Odds
Lesson 2-7 Square Roots and Real Numbers
Contents

4. Example 1 Identify Coordinates on a Number Line
Example 2 Graph Numbers on a Number Line
Example 3 Absolute Value of Rational Numbers
Example 4 Expressions with Absolute Value
Lesson 1 Contents

5. Name the coordinates of the points graphed on the number line.
The dots indicate each point on the graph.
Answer: The coordinates are {–9, –7, –6, –3}.
Example 1-1a

6. Name the coordinates of the points graphed on the number line.
The bold arrow on the graph indicates that the graph continues infinitely in that direction.
Answer: The coordinates are {11, 12, 13, 14, …}.
Example 1-1b

7. Name the coordinates of the points graphed on each number line.
Answer: {6, 9, 11, 12}
Answer: {–0.5, 0, 0.5, 1, 1.5, …}
Example 1-1c

8. Graph .
Answer:
Example 1-2a

9. Graph {–1.5, 0, 1.5, …}.
Answer:
Example 1-2b

10. Graph {integers less than –6 or greater than or equal to 1}.
Answer:
Example 1-2c

11. Graph each set of numbers. a. {–5, 2, 3, 5}
Answer:
Answer:
Example 1-2d

12. c. {integers less than or equal to –2 or greater than 4}
Answer:
Example 1-2e

13. unit from 0 in the negative direction.
Find .
unit from 0 in the negative direction.
Answer:
Example 1-3a

14. 0.25 is 0.25 unit from 0 in the positive direction.
Find .
0.25 is 0.25 unit from 0 in the positive direction.
Answer:
Example 1-3b

15. Find each absolute value. a.
Answer:
Answer: 6.3
Example 1-3c

16. Replace y with 12.
Simplify.
Answer:
Example 1-4a

17. Answer: 10
Example 1-4b

18. End of Lesson 1

19. Example 1 Use a Number Line to Add Rational Numbers
Example 2 Add Rational Numbers
Example 3 Subtract Rational Numbers to Solve a Problem
Lesson 2 Contents

20. Use a number line to find .–5 +8
Step 1 Draw an arrow from 0 to 8.
Step 2 Then draw a second arrow 5 units to the left to represent adding –5.
Step 3 The second arrow ends at the sum 3.
Answer:
Example 2-1a

21. Use a number line to find .–4 –1
Step 1 Draw an arrow from 0 to –1.
Step 2 Draw a second arrow 4 units to the left.
Step 3 The second arrow ends at the sum –5.
Answer:
Example 2-1b

22. Use a number line to find each sum. a.
Answer: –3
Answer: –9
Example 2-1c

23. Subtract the lesser absolute value from the greater absolute value.
Find .
Subtract the lesser absolute value from the greater absolute value.
Since the number with the greater absolute value is –14, the sum is negative.
Answer:
Example 2-2a

24. Both numbers are negative, so the sum is negative.
Find .
Both numbers are negative, so the sum is negative.
Answer:
Example 2-2b

25. Find each sum. a. b.
Answer: –17
Answer:
Example 2-2c

26. Stocks In the past year, a publishing company’s stock went from $52
Stocks In the past year, a publishing company’s stock went from $52.08 per share to $70.87 per share. Find the change in the price of the stock.
Explore The stock price began at $52.08 per share and ended at $ You need to determine the change in price for the year.
Plan Subtract to find the change in price.
ending price
minus
beginning price
52.08
70.87
Example 2-3a

27. To subtract 52.08, add its inverse.
Solve
To subtract 52.08, add its inverse.
Subtract the absolute values.
The absolute value of is greater, so the result is positive.
Example 2-3b

28. Answer: The price of the stock changed by $18.79.
Examine The problem asks for the change in a stock’s price in the past year. Since the change in price was positive, the price increased. This makes sense since the ending price is more than the beginning price.
Example 2-3c

29. Stocks The stock in a company went from $46. 98 to $35
Stocks The stock in a company went from $46.98 to $35.09 over a one-month period. Find the change in price for the stock.
Answer: –$11.89
Example 2-3d

30. End of Lesson 2

31. Example 1 Multiply Integers Example 2 Simplify Expressions
Example 3 Multiply Rational Numbers
Example 4 Multiply Rational Numbers to Solve a Problem
Example 5 Evaluate Expressions
Lesson 3 Contents

32. same signs  positive product
Find (–8)(–6).
same signs  positive product
Answer: 48
Example 3-1a

33. different signs  negative product
Find (10)(–11).
different signs  negative product
Answer: –110
Example 3-1b

34. Find each product. a. (–4)(8) Answer: –32 b. (–6)(–12) Answer: 72
Example 3-1c

35. Simplify the expression
Associative Property ()
Substitution
Distributive Property
Simplify.
Answer:
Example 3-2a

36. Simplify the expression
Answer: 3x
Example 3-2b

37. same signs  positive product
Find
same signs  positive product
Answer:
Example 3-3a

38. Find
Answer:
Example 3-3b

39. different signs  negative product
Stocks The value of a company’s stock dropped by $1.25 per share. By what amount did the total value of the company’s stock change if the company has issued 500,000 shares of stock?
To find the change in the total value of the company’s stock, multiply the price lost per share by the number of shares.
different signs  negative product
Answer: The total value of the company’s stock changed by –$625,000.
Example 3-4a

40. Construction A construction project is stopped by a winter storm
Construction A construction project is stopped by a winter storm. For every day that they are unable to work, the company loses $35,000. If the storm keeps them from working for 4 days, how much money do they lose?
Answer: –$140,000
Example 3-4b

41. same signs  positive product
Substitution
Answer:
same signs  positive product
Example 3-5a

42. Answer:
Example 3-5b

43. End of Lesson 3

44. Example 1 Divide Integers Example 2 Simplify Before Dividing
Example 3 Divide Rational Numbers
Example 4 Divide Rational Numbers to Solve a Problem
Example 5 Simplify Algebraic Expressions
Example 6 Evaluate Algebraic Expressions
Lesson 4 Contents

45. Find .
Answer:
positive quotient
Example 4-1a

46. Find .
Divide.
negative quotient
Answer:
Example 4-1b

47. Find each quotient. a. b.
Answer: 20
Answer: –15
Example 4-1c

48. Simplify the numerator first.
Multiply.
Answer:
different signs  negative quotient
Example 4-2a

49. Simplify
Answer: 3
Example 4-2b

50. Answer: Use a calculator. different signs  negative quotient
Find .
Answer: Use a calculator. different signs  negative quotient
Example 4-3a

51. Multiply by the reciprocal of
Find .
Multiply by the reciprocal of
Answer:
same signs  positive quotient
Example 4-3b

52. Find each quotient. a. b.
Answer: 15.3
Answer:
Example 4-3c

53. same signs  positive quotient
Baseball The perimeter of a square baseball diamond is 360 feet. Find the length of one side of the diamond.
To find the length of one side, divide the perimeter by the number of sides.
same signs  positive quotient
Answer: The length of one side is 90 feet.
Example 4-4a

54. The perimeter of a triangular building is 450 feet
The perimeter of a triangular building is 450 feet. Find the length of each side.
Answer: 150 feet
Example 4-4b

55. The fraction bar indicates division.
Simplify
The fraction bar indicates division.
Multiply by the reciprocal of 13.
Example 4-5a

56. Distributive Property.
Answer: Simplify.
Example 4-5b

57. Simplify
Answer:
Example 4-5c

58. Evaluate if w = 2, x = –9.1 and y = 4.
Replace w with 2, x with –9.1 and y with 4.
Find the numerator and denominator separately.
Answer: Use a calculator. different signs  negative quotient
Example 4-6a

59. Evaluate if s = 2.3, t = 5 and u = –4.
Answer: –14.375
Example 4-6b

60. End of Lesson 4

61. Example 1 Create a Line Plot
Example 2 Use a Line Plot to Solve a Problem
Example 3 Create a Stem-and-Leaf Plot
Example 4 Back-to-Back Stem-and-Leaf Plot
Example 5 Analyze Data
Example 6 Determine the Best Measure of Central Tendency
Lesson 5 Contents

62. Draw a line plot for the data.
11 – –
Step 1 The values of the data range from –2 to 11, so construct a number line containing these values.
Step 2 Then place an  a number for each time it occurs.
Example 5-1a

63. 3 5 7 6 0 –4 6 4 7 0 0 –2 3 7 Draw a line plot for the data. Answer:
– –
Answer:
Example 5-1b

64. Traffic The highway patrol did a radar survey of the speeds of cars along a stretch of highway for 1 minute. The speeds (in miles per hour) of the 20 cars that passed are listed below.
Make a line plot of the data.
The lowest value is 64 and the highest value is 79, so use a scale that includes those values. Place an  above each value for each occurrence.
Example 5-2a

65. Answer:
Example 5-2b

66. Which speed occurs the most frequently?
Answer: Looking at the line plot, we can easily see that 72 miles per hour occurs most frequently.
Example 5-2c

67. Family Size Students in Mrs
Family Size Students in Mrs. Barrett’s class listed the number of family members in their households below.
a. Make a line plot of the data.
b. Which family size occurs the most frequently?
Answer:
Answer: 4
Example 5-2d

68. Use the data below to make a stem-and-leaf plot.
The greatest common place value is tens, so the digits in the tens place are the stems.
Example 5-3a

69. Stem 7 8 9 10 11 12 13
Leaf
1 1 2
Answer:
Example 5-3b

70. Use the data below to make a stem-and-leaf plot.
Stem 1 2 3
Leaf
3 5 7
1 1 5
2 7
Answer:
Example 5-3c

71. High Temperature Dallas Atlanta
Weather Monique wants to compare the monthly average high temperatures of Dallas and Atlanta before she decides to which city she wants to move. The table shows the monthly high temperatures (F) for both cities.
Monthly Average
High Temperature
Dallas
Atlanta
Example 5-4a

72. Make a stem-and-leaf plot to compare the data.
To compare the data we can use a back-to-back stem-and-leaf plot. Since the data represent similar measurements, the plot will share a common stem.
Answer:
Dallas Stem Atlanta
Example 5-4b

73. What is the difference between the highest average temperatures in each city?
Answer: 95 – 88 or 7°
Example 5-4c

74. Which city has higher average temperatures?
Answer: Looking at the temperatures of 80 and above, we can see that Dallas has a higher number of average temperatures above 80°.
Example 5-4d

75. Ms. Smith wants to compare the final grades for two of her classes
Ms. Smith wants to compare the final grades for two of her classes. The table shows the scores for both classes.
Class A
Class B 87 96 99 76 81 51 62 57 92 98 77 83 75 72 85 71 64 69 91
Example 5-4e

76. a. Make a back-to-back stem-and-leaf plot to compare the data.
Answer:
Class A Stem Class B
1 5 7
Example 5-4f

77. b. What is the difference between the highest score in each class?
c. Which class scored higher overall for the grading period?
Answer: 1 point
Answer: Class A
Example 5-4g

78. Which measure of central tendency best represents the data?
Stem 4 5 6 7 8
Leaf
2 5 7
3 9 1
Example 5-5a

79. Determine the mean, median, and mode.
The mean is about 5.5. Add the data and divide by 15.
The median is 4.8. The middle value is 4.8.
The mode is 4.4. The most frequent value is 4.4.
Answer: Either the median or the mode best represent the set of data since both measures are located in the center of the majority of the data. In this instance, the mean is too high.
Example 5-5b

80. Which measure of central tendency best represents the data?
Stem 1 2 3 4 5
Leaf
3 7 8 6
4 5 9
Answer: The mean is about 2.9. The median is 2.5. The mode is 1.1. Either the mean or median can be used to represent the data. The mode is too low.
Example 5-5c

81. Politics The number of electoral college votes for the 12 most populous states in the 2000 Presidential election are listed below. Which measure of central tendency best represents the data?
The mean is about Add the data and divide by 12.
The median is The middle value is 21.5.
The mode is 13. The most frequent value is 13.
Answer: Either the mean or median can be used to best represent the data. The mode is too low.
Example 5-6a

82. The number of points scored by the basketball team during each game in the season is listed below. Which measure of central tendency best represents the data?
Answer: Either the mean or the median can be used to best represent the data. The mode is too high.
Example 5-6b

83. End of Lesson 5

84. Example 1 Find Probabilities of Simple Events
Example 2 Odds of an Event
Example 3 Odds Against an Event
Example 4 Probability and Odds
Lesson 6 Contents

85. Find the probability of rolling a number greater than 2 on a die.
There are six possible outcomes. Four of the outcomes are favorable. That is, four of the six outcomes are numbers greater than two.
4 numbers greater than 2
Sample space: 1, 2, 3, 4, 5, 6
6 possible outcomes
Answer:
Example 6-1a

86. There are 6 students with black hair and 20 total students.
A class contains 6 students with black hair, 8 with brown hair, 4 with blonde hair, and 2 with red hair. Find P(black).
There are 6 students with black hair and 20 total students.
number of favorable outcomes
number of possible outcomes
Simplify.
Answer: The probability of selecting a student with black hair is
Example 6-1b

87. number of favorable outcomes
A class contains 6 students with black hair, 8 with brown hair, 4 with blonde hair, and 2 with red hair. Find P(red or brown).
There are 2 students with red hair and 8 students with brown hair. So there are or 10 students with red or brown hair.
number of favorable outcomes
number of possible outcomes
Simplify.
Example 6-1c

88. Answer: The probability of selecting a student with red or brown hair is
Example 6-1d

89. There are 6 + 8 + 2 or 16 students who do not have blonde hair.
A class contains 6 students with black hair, 8 with brown hair, 4 with blonde hair, and 2 with red hair. Find P(not blonde).
There are or 16 students who do not have blonde hair.
number of favorable outcomes
number of possible outcomes
Simplify.
Answer: The probability of selecting a student who does not have blonde hair is
Example 6-1e

90. a. Find the probability of rolling a number less than 3 on a die.
b. A gumball machine contains 40 red gumballs, 30 green gumballs, 50 yellows gumballs, and 40 blue gumballs. Find P(red).
Answer:
Answer:
Example 6-1f

91. c. A gumball machine contains 40 red gumballs, 30 green gumballs, 50 yellows gumballs, and 40 blue gumballs. Find P(green or yellow).
d. A gumball machine contains 40 red gumballs, 30 green gumballs, 50 yellows gumballs, and 40 blue gumballs. Find P(not blue).
Answer:
Answer:
Example 6-1g

92. 2 numbers less than or equal to 2
Find the odds of rolling a number greater than 2.
There are six possible outcomes, 4 are successes and 2 are failures.
4 numbers greater than 2
Sample space: 1, 2, 3, 4, 5, 6
2 numbers less than or equal to 2
Answer: The odds of rolling a number greater than
Example 6-2a

93. Find the odds of rolling a number less than 4.
Answer:
Example 6-2b

94. Answer: The odds against selecting a 2 or 3 are 11:2.
A card is selected at random from a standard deck of 52 cards. What are the odds against selecting a 2 or 3?
There are four 2s and four 3s in a deck of cards, and there are 52 – 4 – 4 or 44 cards that are not a 2 or a 3.
number of ways not to pick a 2 or 3
number of ways to pick a 2 or 3
Answer: The odds against selecting a 2 or 3 are 11:2.
Example 6-3a

95. A card is selected at random from a standard deck of 52 cards
A card is selected at random from a standard deck of 52 cards. What are the odds against selecting a 5, 6, or 7?
Answer: 10:3
Example 6-3b

96. odds of the plane being on time
Travel Melvin is waiting to board a flight to Washington, D.C. According to the airline, the flight he is waiting for is on time 80% of the times it flies. What are the odds that the plane will be on time?
The probability that the plane will be on time is 80%, so the probability that it will not be on time is 20%.
odds of the plane being on time
Answer: The odds that the plane will be on time are 4:1.
Example 6-4a

97. If the probability that it will snow this weekend is 70%, what are the odds that it will snow?
Answer: 7:3
Example 6-4b

98. End of Lesson 6

99. Example 1 Find Square Roots Example 2 Classify Real Numbers
Example 3 Graph Real Numbers
Example 4 Compare Real Numbers
Example 5 Order Real Numbers
Example 6 Rational Approximation
Lesson 7 Contents

100. represents the positive and negative square roots of
Find .
represents the positive and negative square roots of
Example 7-1a

101. Answer:
Example 7-1b

102. represents the positive square root of 0.0144.
Find .
represents the positive square root of
Answer:
Example 7-1c

103. Find each square root. a. b.
Answer:
Answer: 0.6
Example 7-1d

104. Name the set or sets of numbers to which belongs.
Answer: Because , which is neither a repeating nor terminating decimal, this number is irrational.
Example 7-2a

105. Name the set or sets of numbers to which belongs.
Answer: Because 1 and 6 are integers and , which is a repeating decimal, the number is a rational number.
Example 7-2b

106. Name the set or sets of numbers to which belongs.
Answer: Because this number is a natural number, a whole number, an integer and a rational number.
Example 7-2c

107. Name the set or sets of numbers to which –327 belongs.
Answer: This number is an integer and a rational number.
Example 7-2d

108. Name the set or sets of numbers to which each real number belongs. a.d.
Answer: rationals
Answer: naturals, whole, integers, rationals
Answer: irrationals
Answer: integers, rationals
Example 7-2e

109. Graph .
The heavy arrow indicates that all numbers to the left of 8 are included in the graph. The dot at 8 indicates that 8 is included in the graph.
Example 7-3a

110. Graph .
The heavy arrow indicates that all the points to the right of –5 are included in the graph. The circle at –5 indicates that –5 is not included in the graph.
Example 7-3b

111. Graph each solution set. a.b.
Answer:
Answer:
Example 7-3c

112. Replace the  with <, >, or = to make the sentence true.
Since the numbers are equal.
Answer:
Example 7-4a

113. Replace the  with <, >, or = to make the sentence true.
Answer:
Example 7-4b

114. Replace each  with <, >, or = to make each sentence true.b.
Answer: <
Answer: <
Example 7-4c

115. Write in order from least to greatest. Write each number as a decimal.
or about
Example 7-5a

116. Answer: The numbers arranged in order from least to greatest are
or about
Answer: The numbers arranged in order from least to greatest are
Example 7-5b

117. Write in order from least to greatest.
Answer:
Example 7-5c

118. Multiple-Choice Test Item For what value of x is true?
A –5 B 0 C D 5
Read the Test Item
The expression is an open sentence, and the set of choices is the replacement set.
Example 7-6a

119. Replace x in with each given value.
Solve the Test Item
Replace x in with each given value. A
False; and are not real numbers.
Example 7-6b

120. False; is not a real number.
Example 7-6c

121. C
Use a calculator.
< 1 <
True
Example 7-6d

122. 2.236068 < 1 < 0.447214 D Use a calculator. False
The inequality is true for
Answer: The correct answer is C.
Example 7-6e

123. Multiple-Choice Test Item For what value of x is true?
A 3 B –3 C 0 D
Multiple-Choice Test Item For what value of x is true?
Answer: A
Example 7-6f

124. End of Lesson 7

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