1. Chapter 6
Algebra: Use Multiplication and Division
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2. Algebra: Use Multiplication and Division
6
Lesson 6-1 Multiplication and Division
Expressions
Lesson 6-2 Problem-Solving Strategy: Work
Backward
Lesson 6-3 Order of Operations
Lesson 6-4 Algebra: Solve Equations Mentally
Lesson 6-5 Problem-Solving Investigation:
Choose a Strategy
Lesson 6-6 Algebra: Find a Rule
Lesson 6-7 Balanced Equations

3. 6-1 Multiplication and Division Expressions
Five-Minute Check (over Chapter 5)
Main Idea
California Standards
Example 1
Example 2
Example 3

4. 6-1 Multiplication and Division Expressions
• I will write and find the value of multiplication
and division expressions.

5. 6-1 Multiplication and Division Expressions
Standard 4AF1.1 Use letters, boxes, or other
symbols to stand for any number in simple
expressions or equations (e.g., demonstrate an
understanding and the use of the concept of a
variable).

6. 6-1 Multiplication and Division Expressions
Jake had 4 boxes of apples. There are 6 apples
in each box. Find the value of 4 × n if n = 6.
4×n Write the expression.

7. 6-1 Multiplication and Division Expressions
4×6 Replace n with 6.
24 Multiply 4 and 6.

8. 6-1 Multiplication and Division Expressions
Marian has 5 CD cases. Each CD case has 2 CDs
inside. Find the value of 5 × n if n = 2.
A. 7
B. 10
C. 5
D. 2

9. 6-1 Multiplication and Division Expressions
Find the value of x ÷ (3 × 2) if x = 30.
In Lesson 3-1, you learned that you need to perform
the operations inside parentheses first.
x ÷ (3 × 2) Write the expression.
30 ÷ (3 × 2) Replace x with 30.
30 ÷ 6, or 5 Find (3 × 2) first. Then find 30 6.
Answer: So, the value of x (3 2) if x = 30 is 5.

10. 6-1 Multiplication and Division Expressions
Find the value of 45 (x × 1) if x = 5.
A. 9
B. 45
C. 5
D. 1

11. 6-1 Multiplication and Division Expressions
Judy has d dollars to buy bottles of water that cost
$2 each. Write an expression for the number of
bottles of water she can buy.
Words Dollars divided by cost
Variable Let d = dollars.
Expression dollars divided by cost
d ÷ $7
Answer: So the number of bottles of water Judy can
buy is d 2.

12. 6-1 Multiplication and Division Expressions
Toby has d dollars to spend on discounted books
that cost $3 a piece. Write an expression for the
number of books he can buy.
A. d ÷ 3
B. d – 3
C. d + 3
D. d × 3

14. 6-2 Problem-Solving Strategy: Work Backward
Five-Minute Check (over Lesson 6-1)
Main Idea
California Standards
Example 1: Problem-Solving Strategy

15. 6-2 Problem-Solving Strategy: Work Backward
• I will solve problems by working backward.

16. 6-2 Problem-Solving Strategy: Work Backward
Standard 4MR1.1 Analyze problems by
identifying relationships, distinguishing relevant
from irrelevant information, sequencing and
prioritizing information, and observing patterns.

17. 6-2 Problem-Solving Strategy: Work Backward
Standard 4NS3.0 Students solve problems
involving addition, subtraction, multiplication, and
division of whole numbers and understand the
relationships among the operations.

18. 6-2 Problem-Solving Strategy: Work Backward
Currently, there are 25 students in the chess
club. Last October, 3 students joined. Two
months before that, in August, 8 students
joined. How many students were in the club
originally?

19. 6-2 Problem-Solving Strategy: Work Backward
Understand
What facts do you know?
• Currently, there are 25 students in the club.
• 3 students joined in October.
• 8 students joined in August.
What do you need to find?
• The number of students that were in the club
originally.

20. 6-2 Problem-Solving Strategy: Work Backward
Plan
Work backward to solve the problem.

21. 6-2 Problem-Solving Strategy: Work Backward
Solve
Work backward and use inverse operations. Start
with the end result and subtract the students who
joined the club.
25
– 3
22

22. 6-2 Problem-Solving Strategy: Work Backward
Solve
22
– 8
14
Answer: So, there were 14 students in the club
originally.

23. 6-2 Problem-Solving Strategy: Work Backward
Check
Look back at the problem. A total of 3 + 8 or 11
students joined the club. So, if there were 14 students
originally, there would be 14 + 11 or 25 students in the
club now.
The answer is correct.

25. 6-3 Order of Operations
Five-Minute Check (over Lesson 6-2)
Main Idea and Vocabulary
California Standards
Key Concept: Order of Operations
Example 1
Example 2

26. 6-3 Order of Operations
• I will use the order of operations to find the value
of expressions.
• order of operations

27. 6-3 Order of Operations
Standard 4AF1.2 Interpret and evaluate
mathematical expressions that now use
parentheses.
Standard 4AF1.3 Use parentheses to
indicate which operation to perform first when
writing expressions containing more than two
terms and different operations.

28. 6-3 Order of Operations

29. 6-3 Order of Operations
Find the value of 12 – (4 + 2) ÷ 3.
12 – (4 + 2) ÷ 3 Write the expression.
12 – 6 ÷3 Parentheses first. (2 + 4) = 6
12 – 2 Multiply and divide from left to right.
6÷3=2
10 Add and subtract from left to right.
12 – 2 = 10

30. 6-3 Order of Operations
Find the value of 21 (3 + 4) + 5.
A. 16
B. 1
C. 8
D. 12

31. 6-3 Order of Operations
Find the value of 4x + 3y ÷ 2, when x = 7 and y = 2.
Follow the order of operations.
4x + 3y ÷ 2 = 4 7+3×2÷2 Replace x with 7 and
y with 2.
= 28 + 3 Multiply and divide from
left to right.
= 31 Add.
Answer: 31

32. 6-3 Order of Operations
Find the value of 3x – 2y + 12 when x = 5 and y = 3.
A. 19
B. 11
C. 21
D. 12

34. 6-4 Algebra: Solve Equations Mentally
Five-Minute Check (over Lesson 6-3)
Main Idea
California Standards
Example 1
Example 2
Example 3
Multiplication and Division Equations

35. 6-4 Algebra: Solve Equations Mentally
• I will solve multiplication and division equations
mentally.

36. 6-4 Algebra: Solve Equations Mentally
Standard 4AF1.1 Use letters, boxes, or other
symbols to stand for any number in simple
expressions or equations (e.g., demonstrate an
understanding and the use of the concept of a
variable).

37. 6-4 Algebra: Solve Equations Mentally
Mansis’s Used Car Lot has 8 rows of cars with a
total of 32 cars. Solve 8 × c = 32 to find how many
cars are in each row.

38. 6-4 Algebra: Solve Equations Mentally
One Way: Use Models
Step 1 Model the
equation.

39. 6-4 Algebra: Solve Equations Mentally
One Way: Use Models
Step 2 Find the value of c.
8 × c = 32
Answer: So, c = 4.

40. 6-4 Algebra: Solve Equations Mentally
Another Way: Mental Math
8 × c = 32
8 × 4 = 32 You know that 8 × 4 = 32.
Answer: So, c = 4.

41. 6-4 Algebra: Solve Equations Mentally
Kyung has just planted a garden. He has a total of
49 vegetables with 7 vegetables in each row. Solve
7 x = 49 to find how many rows of vegetables
there are.
A. 6
B. 7
C. 8
D. 49

42. 6-4 Algebra: Solve Equations Mentally
Solve 16 ÷ s = 8.
16 ÷ s = 8
16 ÷ 2 = 8
s=2 You know that 16 2 = 8.
Answer: So, the value of s is 2.

43. 6-4 Algebra: Solve Equations Mentally
Solve 36 p = 6.
A. 6
B. 7
C. 8
D. 9

44. 6-4 Algebra: Solve Equations Mentally
Six friends went shopping. They each bought the
same number of t-shirts. A total of 24 t-shirts were
bought. Write and solve an equation to find out how
many t-shirts each person bought.
Write the equation.
Words 6 friends bought 24 t-shirts
Variable Let t = the number of t-shirts bought
per person.
Expression 6 t = 24

45. 6-4 Algebra: Solve Equations Mentally
Solve the equation.
6 t = 24
6 4 = 24
t=4
Answer: So each person bought 4 t-shirts.

46. 6-4 Algebra: Solve Equations Mentally
Six friends went to a driving range and hit a total of
54 golf balls. If they all hit the same number of golf
balls, how many did each one hit?
A. 7
B. 8
C. 9
D. 10

48. 6-5 Problem-Solving Investigation: Choose a Strategy
Five-Minute Check (over Lesson 6-4)
Main Idea
California Standards
Example 1: Problem-Solving Investigation

49. 6-5 Problem-Solving Investigation: Choose a Strategy
• I will choose the best strategy to solve a problem.

50. 6-5 Problem-Solving Investigation: Choose a Strategy
Standard 4MR1.1 Analyze problems by
identifying relationships, …, and observing
patterns.

51. 6-5 Problem-Solving Investigation: Choose a Strategy
4NS3.0 Students solve problems involving
addition, subtraction, multiplication, and division
of whole numbers and understand the
relationships among the operations.

52. 6-5 Problem-Solving Investigation: Choose a Strategy
MATT: I take 30-minute guitar
lessons two times a week. There are
four weeks in a month. How many
minutes do I have guitar lessons
each month?
YOUR MISSION: Find how many minutes
Matt has guitar lessons each month.

53. 6-5 Problem-Solving Investigation: Choose a Strategy
Understand
What facts do you know?
• Each lesson Matt takes is 30 minutes long.
• He takes lessons two times a week.
• There are four weeks in a month.
What do you need to find?
• Find how many minutes Matt has guitar
lessons each month.

54. 6-5 Problem-Solving Investigation: Choose a Strategy
Plan
You can use the four-step plan along with
addition and multiplication to solve the problem.

55. 6-5 Problem-Solving Investigation: Choose a Strategy
Solve
Find how many minutes Matt has lessons each
week.
30 lesson 1
+ 30 lesson 2
60 minutes per week

56. 6-5 Problem-Solving Investigation: Choose a Strategy
Solve
Find how many minutes Matt has lessons each
week.
60 minutes per week
× 4 weeks per month
240 minutes per month
Answer: So, Matt has lessons 240 minutes
each month.

57. 6-5 Problem-Solving Investigation: Choose a Strategy
Check
Matt has lessons 30 + 30 or 60 minutes each
week. This means he has 60 + 60 + 60 + 60
or 240 minutes of lessons each month.
So, the answer is correct.

59. 6-6 Algebra: Find a Rule
Five-Minute Check (over Lesson 6-5)
Main Idea
California Standards
Example 1
Example 2
Example 3

60. 6-6 Algebra: Find a Rule
• I will find and use a rule to write an equation.

61. 6-6 Algebra: Find a Rule
Standard 4AF1.5 Understand that an
equation such as y = 3x + 5 is a prescription
for determining a second number when a
first number is given.

62. 6-6 Algebra: Find a Rule
Mike earns $10 when he
babysits for 2 hours. He earns
$20 when he babysits for 4
hours. If he babysits for 6
hours, he earns $30. Write a
rule that describes the money
Mike earns.
Put the information in a table.
Then look for a pattern to
describe the rule.

63. 6-6 Algebra: Find a Rule
Pattern: 2 × 5 = 10
4 × 5 = 20
6 × 5 = 30
Rule: Multiply by 5.
Equation: x × 5 = y

64. 6-6 Algebra: Find a Rule
Ricardo earns $16 dollars when he mows 2 lawns
of grass. He earns $32 when he mows 4 lawns, and
$48 when he mows 6 lawns. Write a rule that
describes the money Ricardo earns.
A. 8x = y
B. x+y=8
C. 2x + 8 = y
D. x×8=y

65. 6-6 Algebra: Find a Rule
Use the equation from
Additional Example 1 to find
how much money Mike earns
for babysitting for 8, 9, or 10
hours.

66. 6-6 Algebra: Find a Rule
x×5=y
8 × 5 = $40
40
x×5=y x×5=y
45
9 × 5 = $45 10 × 5 = $50 50
Answer: So, Mike will earn $40, $45, or $50 if he
babysits for 8, 9, or 10 hours.

67. 6-6 Algebra: Find a Rule
Use the equation x 8 = y to find how much money
Ricardo earns for mowing 7 or 8 lawns.
A. $49, $64
B. $15, $16
C. $56, $64
D. $63, $72

68. 6-6 Algebra: Find a Rule
The cost of admission
into a water park is shown
in the table to the right.
Find a rule that describes
the number pattern. Then
use the rule to write an
equation.

69. 6-6 Algebra: Find a Rule
Pattern: 6÷6=1
12 ÷ 6 = 2
18 ÷ 6 = 3
Rule: Divide by 6.
Equation: c ÷ 6 = n

70. 6-6 Algebra: Find a Rule
The cost of admission into a basketball game is
shown in the table below. Find a rule that describes
the number pattern. Then use the rule to write an
equation.
A. c÷9=n
B. c+9=n
C. c+n=9
D. c–9=n

71. 6-6 Algebra: Find a Rule
Use the equation from
Additional Example 3 to
find how many people
will be admitted to the
park for $24, $30, and
$36.

72. 6-6 Algebra: Find a Rule
c÷6=n
24 ÷ 6 = 4
c÷6=n c÷6=n
4
30 ÷ 6 = 5 36 ÷ 6 = 6 5
6
Answer: So, $24, $30, and $36 will by 4, 5, and 6
people tickets.

73. 6-6 Algebra: Find a Rule
Use the equation c 9 = n to find how many
people will be admitted to the basketball game
for $45 and $63.
A. 4, 5
B. 5, 6
C. 7,8
D. 5, 7

75. 6-7 Balanced Equations
Five-Minute Check (over Lesson 6-6)
Main Idea
California Standards
Example 1
Example 2
Example 3

76. 6-7 Balanced Equations
• I will balance multiplication and division equations.

77. 6-7 Balanced Equations
Standard 4AF2.2 Know and understand
that equals multiplied by equals are equal.

78. 6-7 Balanced Equations
Show that the equality of 6r = 24 does not change
when each side of the equation is divided by 6.
6r = 24 Write the equation.
6r ÷ 6 = 24 ÷ 6 Divide each side by 6.
r=4 So, r = 4.

79. 6-7 Balanced Equations
Check
6r = 24
6 × 4 = 24
24 = 24

80. 6-7 Balanced Equations
Show that the equality of 3y = 9 does not change
when each side of the equation is divided by 3.
A. 3y ÷ 3 = 9 ÷ 3; 6 = 6
B. 3y ÷ 3 = 9 ÷ 3; 3 = 3
C. 3y ÷ 3 = 9; 9 = 9
D. 3y = 9 ÷ 3; 3 = 9

81. 6-7 Balanced Equations
Show that the equality of q ÷ 7 = 4 does not change
when each side of the equation is multiplied by 7.
q÷7=4 Write the equation.
q÷7×7=4×7 Multiply each side by 4.
q = 28 So, q = 28.

82. 6-7 Balanced Equations
Check
q÷7=4
28 ÷ 7 = 4
4=4

83. 6-7 Balanced Equations
Show that the equality v 5 = 5 does not change
when each side of the equation is multiplied by 5.
A. v 5 5 = 5; 10 = 10
B. v 5 5=5 5; 25 = 25
C. v 5 = 5; 5 = 5
D. v 5 5=5 5; 10 = 10

84. 6-7 Balanced Equations
Find the missing number in 5 × 10 × 4 = 50 × .
5 × 10 × 4 = 50 × Write the equation.
5 × 10 × 4 = 50 × You know that 5 × 10 = 50.
Each side of the equation must be multiplied by
the same number to keep the equation balanced.
Answer: So, the missing number is 4.

85. 6-7 Balanced Equations
Find the missing number in 8 5 3 = 40 .
A. 8
B. 5
C. 3
D. 40

86. 6-7 Balanced Equations
Find the missing number in 2 × 12 ÷ 4 = 24 × .
2 × 12 ÷ 4 = 24 × Write the equation.
2 × 12 ÷ 4 = 24 × You know that 2 × 12 = 24.
Each side of the equation must be divided by the
same number to keep the equation balanced.
Answer: So, the missing number is 4.

87. 6-7 Balanced Equations
Find the missing number in 4 11 2 = 44 .
A. 4
B. 11
C. 44
D. 2

89. Algebra: Use Multiplication and Division
6
Five-Minute Checks
Multiplication and Division Equations

90. Algebra: Use Multiplication and Division
6
Lesson 6-1 (over Chapter 5)
Lesson 6-2 (over Lesson 6-1)
Lesson 6-3 (over Lesson 6-2)
Lesson 6-4 (over Lesson 6-3)
Lesson 6-5 (over Lesson 6-4)
Lesson 6-6 (over Lesson 6-5)
Lesson 6-7 (over Lesson 6-6)

91. Algebra: Use Multiplication and Division
6
(over Chapter 5)
Tell whether 13 is composite, prime, or neither.
A. composite
B. prime
C. neither

92. Algebra: Use Multiplication and Division
6
(over Chapter 5)
Tell whether 26 is composite, prime, or neither.
A. composite
B. prime
C. neither

93. Algebra: Use Multiplication and Division
6
(over Chapter 5)
Tell whether 37 is composite, prime, or neither.
A. composite
B. prime
C. neither

94. Algebra: Use Multiplication and Division
6
(over Chapter 5)
Tell whether 1 is composite, prime, or neither.
A. composite
B. prime
C. neither

95. Algebra: Use Multiplication and Division
6
(over Chapter 5)
Tell whether 21 is composite, prime, or neither.
A. composite
B. prime
C. neither

96. Algebra: Use Multiplication and Division
6
(over Lesson 6-1)
Find the value of each expression if m = 4 and
n = 8.
m 10
A. 18
B. 14
C. 40
D. 80

97. Algebra: Use Multiplication and Division
6
(over Lesson 6-1)
Find the value of each expression if m = 4 and
n = 8.
3 (n m)
A. 1.5
B. 6
C. 12
D. 36

98. Algebra: Use Multiplication and Division
6
(over Lesson 6-1)
Find the value of each expression if m = 4 and
n = 8.
(12 m) n
A. 6
B. 16
C. 24
D. 64

99. Algebra: Use Multiplication and Division
6
(over Lesson 6-1)
Find the value of each expression if m = 4 and
n = 8.
(n m) 2
A. 6
B. 16
C. 24
D. 64

100. Algebra: Use Multiplication and Division
6
(over Lesson 6-2)
Work backward to solve the problem. Lance had 4
granola bars left from his weekend hike. On
Saturday, he ate 2 bars. Before he left for the trip
on Friday, his mother added 5 bars to what he had.
How many bars did he have to start with?
A. 7 bars
B. 5 bars
C. 3 bars
D. 1 bar

101. Algebra: Use Multiplication and Division
6
(over Lesson 6-3)
Find the value of each expression.
4 + (5 2) – 1
A. 6
B. 11
C. 13
D. 14

102. Algebra: Use Multiplication and Division
6
(over Lesson 6-3)
Find the value of each expression.
6+6 3
A. 12
B. 15
C. 24
D. 36

103. Algebra: Use Multiplication and Division
6
(over Lesson 6-3)
Find the value of each expression.
(17 – 3) – (2 4)
A. 6
B. 7
C. 8
D. 22

104. Algebra: Use Multiplication and Division
6
(over Lesson 6-3)
Find the value of each expression.
(21 3) + 3
A. 9
B. 10
C. 21
D. 22

105. Algebra: Use Multiplication and Division
6
(over Lesson 6-4)
Solve each equation mentally.
5 x = 25
A. 4
B. 20
C. 5
D. 6

106. Algebra: Use Multiplication and Division
6
(over Lesson 6-4)
Solve each equation mentally.
56 m=8
A. 8
B. 48
C. 49
D. 7

107. Algebra: Use Multiplication and Division
6
(over Lesson 6-4)
Solve each equation mentally.
r 7=3
A. 21
B. 3
C. 24
D. 7

108. Algebra: Use Multiplication and Division
6
(over Lesson 6-4)
Solve each equation mentally.
k 9 = 36
A. 3
B. 45
C. 4
D. 36

109. Algebra: Use Multiplication and Division
6
(over Lesson 6-5)
Use any strategy to solve. Tell which strategy you
used. Jacobo is 6 years old and his brother is 2
years old. How old will each of them be when
Jacobo is twice his brother’s age?
A. Jacobo will be 12 and his brother will be 6.
B. Jacobo will be 8 and his brother will be 4.
C. Jacobo will be 7 and his brother will be 3.
D. Jacobo will be 10 and his brother will be 6.

110. Algebra: Use Multiplication and Division
6
(over Lesson 6-6)
Find a rule and equation that describes the pattern.
Then use the equation to find the missing number.
A. multiply by 4; x 4 = y;
18
B. add 8; x + 8 = y; 14
C. multiply by 3; x 3 = y;
18
D. multiply by 3; y 3 = x;
18

111. This slide is intentionally blank.