1. Chapter 1 Operations with Whole Numbers

2. 1-1: Mathematical Expression

3. Variable A variable is a symbol used to represent one or more numbers. The number that the variable represents is called the value of the variable. Examples:  b + 90  3 X n  18 – m  y ÷ 24

4. Variable and Numerical Expressions An expression such as b + 90 Is called a variable expression. An expression such as 3 X 2 Is called a numerical expression.

5. Multiplication Symbols We can used a raised dot as a multiplication symbol. 9 x 7 can be written as 9·7 2 x a x b can be written as 2·a·b In a variable expression we can use the raised dot or omit the multiplication symbol. 3 x n can be written as 3·n 3·n can be written as 3n 2 x a x b can be written as 2·a·b 2·a·b can be written as 2ab

6. Equation When a mathematical sentence uses an equal sign, it is called an equation. An equation tells us that two expressions name the same number. The expression to the left of the equal sign is the left side of the equation. The expression to the right of the equal sign is called the right side. 5 ̶ 5 = 0 4 + 5 = 9 18 ÷ 9 = 2 2 · 4 = 8

7. An Equation is like a balance scale. Everything must be equal on both sides. 10 5 + 5 =

8. An Equation is like a balance scale. Everything must be equal on both sides. 12 6 + 6 =

9. An Equation is like a balance scale. Everything must be equal on both sides. 7 n + 2 =

10. An Equation is like a balance scale. Everything must be equal on both sides. 7 n + 2 = 5

11. Substitution When a number is substituted for a variable in a variable expression and the operation is carried out, we say that the variable has been evaluated. If n = 6, evaluate 3 · n If n = 6, 3 · 6 = 18 If x = 2, evaluate 3 + x If x = 2, 3 + 2 = 5 If y = 9, evaluate 18 ÷ y If y = 9, 18 ÷ 9 = 2

12. x = 10; y = 20. Evaluate 1.x ̶ 5 2.y ̶ x + 50 3.50 ̶ x + y 4.50 + y ̶ x 5.y ̶ 10 6.xy 10 ̶ 5 = 5 20 ̶ 10 + 50 = 60 50 ̶ 10 + 20 = 60 50 + 20 ̶ 10 = 60 20 ̶ 10 = 10 10 · 20 = 200

13. 1-2: Properties of Addition and Multiplication

14. The Set of Numbers Counting numbers 1, 2, 3, 4, 5,... Whole numbers 0, 1, 2, 3, 4,...

15. Commutative Property of Addition and Multiplication The order in which two whole numbers are added or multiplied does not change their sum or their product. 3 + 4 = 7 and 4 + 3 = 7 3 x 4 = 12 and 4 x 3 = 12 a + b = b + a a x b = b x a

16. Associative Property of Addition and Multiplication Add 6 + 5 + 7 = 1.(6 + 5) + 7 = 2.6 + (5 + 7) = 3.(6 + 7) + 5 = Multiply 9 x 2 x 5 = 1.(9 x 2) x 5 = 2.9 x (2 x 5) = 3.(9 x 5) x 2 = 18 90 18 90

17. Exercise Simplify Using the Commutative and Associative Properties 1.13 + 8 + 7 2.5 x 7 x 2

18. Addition Property of Zero 7 + 0 = a + 0 = 8 + 0 = c + 0 = 2 + 0 = 7 a 8 c 2

19. Multiplication Property of One 7 x 1 = a x 1 = 8 x 1 = c x 1 = 2 x 1 = 7 a 8 c 2

20. Multiplication Property of Zero 7 x 0 = a x 0 = 8 x 0 = c x 0 = 2 x 0 = 0 0 0 0 0

21. 1-4: The Distributive Property

22. The fee for each person entering the state park is $4. If the person rents a bicycle, he has to pay an additional $2. How much will a group of 12 people have to spend if each will enter the park and each will rent a bicycle? 12 · (4 + 2) Two Methods: = 12 · 6 = 72 = (12 · 4) + (12 · 2) = 48 + 24 = 72

23. The fee for each person entering the state park is $4. If the person has a coupon, he gets a $2 discount. How much will a group of 12 people have to spend if each will enter the park with a coupon? 12 · (4 ̶ 2) Two Methods: = 12 · 2 = 24 = (12 · 4) ̶ (12 · 2) = 48 ̶ 24 = 24

24. Simplify using the distributive property. 1.(11 · 4) + (11 · 6) =11 · (4 + 6) = 11 · 10 = 110 1.13 · 15 = (13 · 10) + (13 · 5) = 130 + 65 = 195

25. Simplify using the distributive property. 1.6 ( 20 + 4) 2.4 ( 80 – 6) 3.(4 x 12) + (4 x 8) 4.(33 x 90) + (33 x 10) 5.(23 x 104) – (23 x 4) 6.(56 x 11) – (6 x 11) 7.35 (10 + 2) 8.33 ( 100 – 3) 9.12 x 22 10.32 x 8 11.9 x 120 12.7 x 896 144 304 80 3300 2300 550 420 3201 264 256 1080 6272

26. Test: 1-1, 1-2, 1-3, 1-4

27. 1-5: Order of Operations

28. Grouping Symbols: Show which operations need to be performed first. [ ] ( ) When one pair of grouping symbols is enclosed in another, we ALWAYS perform the operation enclosed in the INNER pair of symbols FIRST. (14 + 77) ÷ 7 [3 + (4 · 5)] · 10

29. Simplify (14 + 77) ÷ 7 91 ÷ 7 13

30. Simplify [3 + (4 · 5)] · 10 20 ] · 10 23 [3 + · 10 230

31. For expressions that are written without grouping symbols like, 8 + 3 – 9 x 2 ÷ 3 Rule 1.Do all multiplication and divisions in order from left to right. 2.Then do all additions and subtractions in order from left to right.

32. Simplify 72 – 24 ÷ 3 8 72 – 64 Rule 1.Do all multiplication and divisions in order from left to right. 2.Then do all additions and subtractions in order from left to right.

33. Simplify 8 + 3 – 9 x 2 ÷ 3 18 8 + 3 – – Rule 1.Do all multiplication and divisions in order from left to right. 2.Then do all additions and subtractions in order from left to right. ÷ 3 6 5 11

34. Solve 1.12 ( 18 + 36) 2.(100 – 16) ÷ 7 3.4[(6 + 17)2]

35. 1-6: A Problem Solving Model

36. Plan for Solving Word Problems 1.Read the problem carefully. Make sure you understand what it says. You may need to read it more than once. 2.Use questions like these in planning the solution: a.What is asked for? b.What facts are given? c.Are enough facts given? If not, what else is needed? d.Are unnecessary facts given? If so, what are they? e.Will a sketch or diagram help? 3.Determine which operations or operations can be used to solve the problem. 4.Carry out the operations carefully. 5.Check your results with the facts given in the problem. Give the answer.

37. The Golden Gate Bridge has a span of 4200 feet. The Brooklyn Bridge has a span of 1595 feet. How much longer is the span of the Golden Gate Bridge? a.What number or numbers does the problem ask for? b.Are enough facts given? If not, what else is needed? c.Are unnecessary facts given? If so, what are they? d.What operation or operations would you use to find the answer?

38. How many 30-second ads can a politician buy with $528,000? a.What number or numbers does the problem ask for? b.Are enough facts given? If not, what else is needed? c.Are unnecessary facts given? If so, what are they? d.What operation or operations would you use to find the answer?

39. Paula washed 5 cars and Jim washed 4. Paula charged $3 for each car. Jim charged $4. How much money did Paula earn? a.What number or numbers does the problem ask for? b.Are enough facts given? If not, what else is needed? c.Are unnecessary facts given? If so, what are they? d.What operation or operations would you use to find the answer?

40. Mike can type a page in 7 min. How many pages can he type in 45 min? a.What number or numbers does the problem ask for? b.Are enough facts given? If not, what else is needed? c.Are unnecessary facts given? If so, what are they? d.What operation or operations would you use to find the answer?

41. 1-7: Problem Solving Applications

42. During the four quarters of a basketball game, the Hoopsters scored 16 points, 21 points, 19 points, and 17 points. How many points did the Hoopsters score during the game? a.What number or numbers does the problem ask for? b.Are enough facts given? If not, what else is needed? c.Are unnecessary facts given? If so, what are they? d.What operation or operations would you use to find the answer?

43. Simon had $165 in his checking account. He wrote checks for $32, $19, and $47. How much did Simon have left in his account? a.What number or numbers does the problem ask for? b.Are enough facts given? If not, what else is needed? c.Are unnecessary facts given? If so, what are they? d.What operation or operations would you use to find the answer?

44. The temperature was 15°C at 8am. By noon, the temperature had increased by 13°. What was the temperature at noon? a.What number or numbers does the problem ask for? b.Are enough facts given? If not, what else is needed? c.Are unnecessary facts given? If so, what are they? d.What operation or operations would you use to find the answer?

45. Test: 1-5, 1-6, 1-7 Next: Chapter 11

46. Chapter 11 Operations with Integers

47. 11-1: Negative Numbers Objective: To represent negative numbers on the number line. HW: P. 368: 1-39 ODD; 40-43 ALL; Read 11-2

48. The Number Line Natural Numbers = {1, 2, 3, …} Whole Numbers = {0, 1, 2, …} Integers = {…, -2, -1, 0, 1, 2, …} -505

49. Definition Positive number – a number greater than zero. 0123456

50. Definition Negative number – a number less than zero. 0123456-2-3-4-5-6

51. Put the appropriate sign: > OR < OR = 1.– 6 ____ 9 2. 2 ____ – 1 3.12 ____ – 9 4.– 12 ___ 9

52. Use a number line and arrow to represent each integer. 1.3, starting at 0 2.– 3, starting at 0 3.3, starting at – 1 4.– 3 starting at 2

53. Negative Numbers Are Used to Measure Temperature

54. 0 10 20 30 -10 -20 -30 -40 -50 Negative Numbers Are Used to Measure Under Sea Level

55. Negative Numbers Are Used to Show Debt Let’s say your parents bought a car but had to get a loan from the bank for $5,000. When counting all their money they add in –$5,000 to show they still owe the bank.

56. Temperature Sea Level $ Slope of a Line Football Directions on a # Line Cold Example+─ -5 -4 -3 -2 -1 0 1 2 3 4 5 Below Debt Downhill Yards Lost Left Hot Above Profit Uphill Yards Gained Right

57. Definition Opposite Numbers – numbers that are the same distance from zero in the opposite direction 0123456-2-3-4-5-6

58. Hint If you don’t see a negative or positive sign in front of a number it is positive. 9 +

59. Absolute Value: Absolute value is the distance from zero. The absolute value of 2 is 2 because 2 is 2 units away from 0. The absolute value of – 2 is 2 because – 2 is 2 units away from 0. 02-2 Absolute value is ALWAYS a POSITIVE number.

60. Absolute Value Bars are used to show absolute value. l -2 l = 2 l 2 l = 2

61. 11-2: Adding Integers Objective: To add positive and negative integers. HW P. 373: 9 – 34 ALL (Tonight) P. 374: 1-7 ALL; Read 11-3 (Tomorrow Night)

62. The Number Line Natural Numbers = {1, 2, 3, …} Whole Numbers = {0, 1, 2, …} Integers = {…, -2, -1, 0, 1, 2, …} -505

63. One Way to Add Integers Is With a Number Line 0123456-2-3-4-5-6 When the number is positive, count to the right. When the number is negative, count to the left. +–

64. One Way to Add Integers Is With a Number Line 6789101112543210 + +6 + (+ 4) =+ 10 + The sum of two positive integers is a positive integer.

65. One Way to Add Integers Is With a Number Line -6-5-4-3 -2 0-7-8-9-10-11-12 – – 6 + (– 4) =– 10 – The sum of two negative integers is a negative integer.

66. 0123456-2-3-4-5-6 + – +6 + (– 4) =+2 The sum of a positive and a negative integer is: 1.Positive if the positive number has the greater absolute value. 2.Negative if the negative number has that greater absolute value. 3.Zero if both number have the same absolute value.

67. 0123456-2-3-4-5-6 + – +3 + (–5) =–2 The sum of a positive and a negative integer is: 1.Positive if the positive number has the greater absolute value. 2.Negative if the negative number has that greater absolute value. 3.Zero if both number have the same absolute value.

68. 0123456-2-3-4-5-6 + – +6 + (– 6) = 0 The sum of a positive and a negative integer is: 1.Positive if the positive number has the greater absolute value. 2.Negative if the negative number has that greater absolute value. 3.Zero if both number have the same absolute value.

69. SHORT CUT Adding integers with the same sign Positive + Positive: Add and make the sign 6 + 4 = 10 6789101112543210 + + positive.

70. SHORT CUT Adding integers with the same sign Negative + Negative: Add and make the sign – 6 + ( – 4) = – 10 negative. -6-5-4-3 -2 0-7-8-9-10-11-12 – –

71. Adding Integers with the Same Sign 1.-7 + -9 = 2.4 + 7 = 3.-6 + -7 = 4.5 + 9 = 5.-9 + -9 = -16 -18 14 -13 11

72. SHORT CUT Adding integers with the different signs Subtract and take the sign of the absolute value. 6 + ( – 4 ) = 2 LARGER 0123456-2-3-4-5-6 + –

73. SHORT CUT Adding integers with the different signs Subtract and take the sign of the absolute value. 3 + ( – 7 ) = – 4 LARGER 0123456-2-3-4-5-6 + –

74. SHORT CUT Adding integers with the different signs Subtract and take the sign of the absolute value. 3 + ( – 5 ) = – 2 LARGER 0123456-2-3-4-5-6 + –

75. 1) – 4 + 5 4) 7 + (– 1) 3) – 33 + 7 6) 2 + (–15) + (– 2) 2) 12 + – 15 5) – 8 + 3 1– 3– 26 6– 5– 15 Adding Integers with Different Signs

76. 1.-7 + 9 = 2.4 + (-7) = 3.(-3) + (+4) = 4.6 + -7 = 5.5 + -9 = 6.-9 + 9 = 2 0 - 4 1 - 3- 3

77. Additive Inverse The sum of any number and its additive inverse is 3 + ( – 3 ) = 0 zero. 0123456-2-3-4-5-6 + –

78. 11-3: Subtracting Integers Objective: To subtract positive and negative integers. HW: P. 376: 1-21 ODD; 23 – 30 ALL; Read 11-4

79. Subtracting Integers 3 ̶ 5 When you subtract 5, it is like adding its opposite, ̶ 5. 3 + ( ̶ 5 ) = 0123456-2-3-4-5-6 + – ̶ 2

80. ̶ 1 ̶ ( ̶ 4 ) When you subtract ̶ 4, it is like adding its opposite, 4. ̶ 1 + 4 = Subtracting Integers 0123456-2-3-4-5-6 – + 3

81. Subtracting Integers Keep, Change, Change 1.Keep the first number 2.Change subtraction sign to addition 3.Change the second number’s sign to its opposite. 4.Follow the addition rules. 9 + (– 9) – 5 4–4== (– 10) + 10 17 7–7==

82. Subtract Positive Integers Find 2 – 15. 2 – 15= 2 + (–15) = –13 Keep, Change, Change 1.Keep the first number 2.Change subtraction sign to addition 3.Change the second number’s sign to its opposite. 4.Follow the addition rules.

83. A.A B.B C.C D.D A.–34 B.–8 C.8 D.34 Find 13 – 21.

84. Subtract Positive Integers Find –13 – 8. –13 – 8=–13 + (–8) =–21 Keep, Change, Change 1.Keep the first number 2.Change subtraction sign to addition 3.Change the second number’s sign to its opposite. 4.Follow the addition rules.

85. 1.A 2.B 3.C 4.D A.–20 B.–2 C.2 D.20 Find –9 – 11.

86. Find 12 – (–6). 12 – (–6)=12 + 6 =18 Keep, Change, Change 1.Keep the first number 2.Change subtraction sign to addition 3.Change the second number’s sign to its opposite. 4.Follow the addition rules.

87. 1.A 2.B 3.C 4.D A.–13 B.–5 C.5 D.13 Find 9 – (–4).

88. Find –21 – (–8). Subtract Negative Integers –21 – (–8)=–21 + 8 =–13 Keep, Change, Change 1.Keep the first number 2.Change subtraction sign to addition 3.Change the second number’s sign to its opposite. 4.Follow the addition rules.

89. A.A B.B C.C D.D A.–23 B.–11 C.11 D.23 Find 17 – (–6).

90. ALGEBRA Evaluate g – h if g = –2 and h = –7. Evaluate an Expression g – h=–2 – (–7)Replace g with –2 and h with –7. =–2 + 7To subtract –7, add 7. =5Simplify.

91. A.A B.B C.C D.D A.–10 B.–2 C.2 D.10 ALGEBRA Evaluate m – n if m = –6 and n = 4.

92. Use Integers to Solve a Problem GEOGRAPHY In Mongolia, the temperature can fall to –45ºC in January. The temperature in July may reach 40ºC. What is the difference between these two temperatures? To find the difference in temperatures, subtract the lower temperature from the higher temperature. Answer: The difference between the temperatures is 85ºC. 40 – (–45)=40 + 45To subtract –45, add 45. =85Simplify.

93. A.A B.B C.C D.D A.–26 B.–4 C.4 D.26 TEMPERATURE On a particular day in Anchorage, Alaska, the high temperature was 15ºF and the low temperature was –11ºF. What is the difference between these two temperatures for that day?

94. 1) 8 – 13 4) – 25 – 5 3) 4 – (–19) 6) 54 – 14 2) 14 – 7 5) 13 – 7 – 5 23 – 30 640 7 Subtract Integers

95. Adding integers Positive + Positive: Add and make the sign positive. 6 + 4 = 10 Negative + Negative: Add and make the sign negative. – 6 + ( – 4) = – 10 Positive + Negative: Subtract and take the sign of the LARGER absolute value. 6 + ( – 4 ) = 2 Negative + Positive: Subtract and take the sign of the LARGER absolute value. – 3 + 2 = – 1

96. Subtracting Integers Keep, Change, Change 1.Keep the first number 2.Change subtraction sign to addition 3.Change the second number’s sign to its opposite. 4.Follow the addition rules. 9 + (– 9) – 5 4–4== (– 10) + 10 17 7–7==

97. 1) 16 – 14 4) – 12 + 16 7) – 19 – 1 10) 3 – 13 3) 99 + 11 6) – 23 + 15 9) – 447 – 23 12) 39 – 42 2) 9 + 26 5) – 22 + 18 8) – 14 – 16 11) 23 – 8 235110 4 – 4– 8 – 20– 30– 470 – 10– 15– 3 Subtract and Add Integers

98. 1) 23 + 4 4) – 18 + 12 7) – 18 – (–12) 10) 18 + (– 12) + 5 3) 9 – (– 2) 6) 24 + (– 17) 9) – 15 – 0 12) – 14 + 0 + 13 2) – 4 – 2 5) – 24 + (–11) 8) 52 – (–30) 11) – 2 (–10) + 15 27– 611 – 6 – 357 – 682– 15 11– 17– 1 Subtract and Add Integers

99. 1) a + ( – 12) 4) b + c 7) x – 7 10) x – (– z) 3) c + 23 6) a + b 9) y - x 12) x – z – y 2) – 20 + b 5) a + c 8) x - z 11) | y – z | 0– 3513 – 25 2– 3 – 15315 – 1918– 4 a = 12, b = – 15, c = – 10 x = –8, y = 7, z = – 11

100. Test: 11-1, 11-2, 11-3

101. 11-4: Products with one negative number. Objective To multiply a positive number and a negative number. HW P. 379: 1-25 ODD; 26-33 ALL; Read 11-5

102. Multiplying Integers Same sign always has a positive answer. Different sign always has a negative answer. When multiplying by zero, you get zero, no matter what the sign is. 9 ● 3 = 27 – 9 ● (– 3) = 27 9 ● (– 3) = – 27 – 9 ● 3 = – 27 9 ● 0 = 0 – 9 ● 0 = 0

103. Lesson 6 Ex1 Multiply Integers with Different Signs Find 5(–4). Answer: –20 5(–4)=–20The integers have different signs. This product is negative.

104. A.A B.B C.C D.D Lesson 6 CYP1 A.–15 B.–2 C.2 D.15 Find 3(–5).

105. Lesson 6 Ex2 Multiply Integers with Different Signs Find –3(9). Answer: –27 –3(9)=–27The integers have different signs. This product is negative.

106. Lesson 6 CYP2 1.A 2.B 3.C 4.D A.–35 B.2 C.12 D.35 Find –5(7).

107. Lesson 6 Ex3 Multiply Integers with the Same Sign Find –6(–8). Answer: 48 –6(–8)=48The integers have the same sign. This product is positive.

108. 1.A 2.B 3.C 4.D Lesson 6 CYP3 A.–28 B.–11 C.11 D.28 Find –4(–7).

109. Lesson 6 Ex4 Find (–8) 2. Answer: 64 Multiply Integers with the Same Sign (–8) 2 =(–8)(–8)There are two factors of –8. =64The product is positive.

110. A.A B.B C.C D.D Lesson 6 CYP4 A.–25 B.–10 C.10 D.25 Find (–5) 2.

111. Lesson 6 Ex5 Find –2(–5)(–6). Answer: –60 Multiply Integers with the Same Sign –2(–5)(–6)=[–2(–5)](–6)Associative Property = 10(–6)–2(–5) = 10 =–60The product is negative.

112. A.A B.B C.C D.D Lesson 6 CYP5 A.84 B.–14 C.14 D.–84 Find –7(–3)(–4).

113. Explain what Product means.

114. 1) 8 (–12) 4) –6 (–6) 3) –6 (–5) 6) –9 (1)(–5) 2) 25 (–2) 5) –4 (–2)(–8) – 96– 5030 36– 6445 Multiply Integers

115. Lesson 6 Ex6 Use Integers to Solve a Problem MINES A mine elevator descends at a rate of 300 feet per minute. How far below the earth’s surface will the elevator be after 5 minutes? If the elevator descends 300 feet per minute, then after 5 minutes, the elevator will be 300(5) or 1,500 feet below the surface. Thus, the elevator will descend to 1,500 feet below the earth’s surface. Answer: After five minutes, the elevator will be 1,500 feet below the earth’s surface.

116. A.A B.B C.C D.D Lesson 6 CYP6 A.–$468 B.$468 C.–$84 D.$84 RETIREMENT Mr. Rodriguez has $78 deducted from his pay every month and placed in a savings account for his retirement. What integer represents a change in his savings account for these deductions after six months?

117. Lesson 6 Ex7 ALGEBRA Evaluate abc if a = –3, b = 5, and c = –8. Answer: 120 Evaluate Expressions abc=(–3)(5)(–8)Replace a with –3, b with 5, and c with –8. =(–15)(–8)Multiply –3 and 5. =120Multiply –15 and –8.

118. A.A B.B C.C D.D Lesson 6 CYP7 A.–48 B.–4 C.0 D.48 ALGEBRA Evaluate xyz if x = –6, y = –2, and z = 4.

119. End of Lesson 6

120. Lesson 7 Menu Five-Minute Check (over Lesson 2-6) Main Idea California Standards Example 1:Look For a Pattern

121. Lesson 7 MI/Vocab Solve problems by looking for a pattern.

122. Look For a Pattern HAIR Lelani wants to grow an 11-inch ponytail to cut off and donate to a program that makes wigs for children with cancer. She has a 3-inch ponytail now, and her hair grows about one inch every two months. How long will it take for her ponytail to reach 11 inches? ExploreYou know the length of Lelani’s ponytail now. You know how long Lelani wants her ponytail to grow and you know how fast her hair grows. You need to know how long it will take for her ponytail to reach 11 inches. PlanLook for a pattern. Then extend the pattern to find the solution.

123. Lesson 7 Ex1 Look For a Pattern SolveAfter the first two months, Lelani’s ponytail will be 3 inches + 1 inch, or 4 inches. Her hair grows according to the pattern below. 3 in.4 in.5 in.6 in.7 in.8 in.9 in.10 in.11 in. Answer: 16 months +1 It will take eight sets of two months, or 16 months total, for Lelani’s ponytail to reach 11 inches. CheckLelani’s ponytail grew from 3 inches to 11 inches, a difference of eight inches, in 16 months. Since one inch of growth requires two months and 8 × 2 = 16, the answer is correct.

124. A.A B.B C.C D.D Lesson 7 CYP1 A.3.5 mi B.15 mi C.16.5 mi D.19.5 mi RUNNING Samuel ran 2 miles on his first day of training to run a marathon. On the third day, Samuel increased the length of his run by 1.5 miles. If this pattern continues for every other day, how many miles will Samuel run on the 27th day?

126. Lesson 8 MI/Vocab Divide integers.

127. Dividing Integers Same sign always has a positive answer. Different sign always has a negative answer. When you divide 0 by number, no matter what the sign is, you get 0. 27 ÷ 3 = 9 – 27 ÷ (– 3) = 9 27 ÷ (– 3) = – 9 – 27 ÷ 3 = – 9 0 ÷ 3 = 0 0 ÷ (–3) = 0

128. Lesson 8 Ex1 Dividing Integers with Different Signs Find 51 ÷ (–3). Answer: –17 51 ÷ (–3)=–17

129. A.A B.B C.C D.D Lesson 8 CYP1 A.–4 B.4 C.27 D.45 Find 36 ÷ (–9).

130. Lesson 8 Ex2 Dividing Integers with Different Signs Answer: –11 The integers have different signs. The quotient is negative. Find

131. Lesson 8 CYP2 1.A 2.B 3.C 4.D A.–5 B.5 C.36 D.54

132. Lesson 8 KC 2

133. Lesson 8 Ex3 Dividing Integers with Same Sign Find –12 ÷ (–2). Answer: 6 –12 ÷ (–2)=6The integers have the same sign. The quotient is positive.

134. 1.A 2.B 3.C 4.D Lesson 8 CYP3 A.–32 B.–16 C.–3 D.3 Find –24 ÷ (–8).

135. Explain what quotient means.

136. Lesson 8 Ex4 ALGEBRA Evaluate –18 ÷ x if x = –2. Answer: 9 Dividing Integers with Same Sign –18 ÷ x=–18 ÷ (–2)Replace x with –2. =9 Divide. The quotient is positive.

137. A.A B.B C.C D.D Lesson 8 CYP4 A.–63 B.63 C.7 D.–7 ALGEBRA Evaluate g ÷ h if g = –21 and h = –3.

138. 7) 50 ÷ – 5 10) – 26 13 9)– 21 – 7 12) 36 ÷ 4 8) – 100 ÷ (– 10) 11) 84 –12 – 10 3 – 2– 7 9 10 Divide Integers

139. Lesson 8 Ex5 Answer: The car’s acceleration is –4 feet per second squared. Subtract 80 from 40. =–4 Divide. PHYSICS You can find an object’s acceleration with the expression, where S f = final speed, S s = starting speed, and t = time. If a car was traveling at 80 feet per second and, after 10 seconds, is traveling at 40 feet per second, what was its acceleration?

140. A.A B.B C.C D.D Lesson 8 CYP5 A.–20ºF B.–4ºF C.12ºF D.4ºF WEATHER The temperature at 4:00 P.M. was 52ºF. By 8:00 P.M., the temperature had gone down to 36ºF. What is the average change in temperature per hour?

142. Lesson 3 Ex1 Naming Points Using Ordered Pairs Write the ordered pair that names point R. Then state the quadrant in which the point is located. Answer: R is (–2, 4). R is in Quadrant II.

143. A.A B.B C.C D.D Lesson 3 CYP1 A.(–3, –1); Quadrant III B.(2, 1); Quadrant I C.(3, 1); Quadrant I D.(3, –1); Quadrant IV Write the ordered pair that names point M. Then name the quadrant in which the point is located.

144. 1.A 2.B 3.C 4.D Lesson 3 CYP2 Graph and label the point G(–2, –4). A.B. C.D. G G G G

145. Lesson 3 Ex3 GEOGRAPHY Use the map of Utah shown below. In which quadrant is Vernal located. Answer: Quadrant I Locate an Ordered Pair

146. 1.A 2.B 3.C 4.D Lesson 3 CYP3 A.Quadrant I B.Quadrant II C.Quadrant III D.Quadrant IV GEOGRAPHY Use the map of Utah. In which quadrant is Tremonton located.

147. Lesson 3 Ex4 Which of the cities labeled on the map is located in Quadrant IV? Answer: Bluff Identify Quadrants

148. A.A B.B C.C D.D Lesson 3 CYP4 A.Tremonton B.Vernal C.Bluff D.Cedar City Name a city from the map of Utah that is located in Quadrant III.

149. Dave goes to the video store to rent a movie. The cost per movie is $3.50. Make a table that shows the amount Dave would pay for renting 1, 2, 3, and 4 movies.

150. Melanie read 14 pages of a detective novel each hour. Write an equation using two variables to show how many pages p she read in h hours. Let p represent the number of pages read Let h represent the number of hours. Equationp = 14 ● h Equationp = 14 h

151. On an average day, Nancy can pick 2 rows of strawberries per hour. The table shows the number of rows she can pick in a given number of hours. Complete the table. Let t stand for the number of hours worked. Write an expression for the number of rows picked. Let r stand for the number of rows picked. Write an expression for the number of hours worked. 6 8 10 2t r ÷ 2