Name Class Date 1-5
Simplifying Algebraic Expressions
Going Deeper
Essential question: How do you add, subtract, factor, and multiply
algebraic expressions?
CC.7.EE.1
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video tutor
EXPLORE
Combining Expressions
Jill and Kelly work as consultants and get paid per project. Jill is paid a
project fee of $25 plus $10 per hour. Kelly is paid a project fee of $18 plus
$14 per hour. Write an expression to represent how much a company will
pay to hire both consultants for a project.
A
Write expressions for how much Jill and Kelly each make per project.
Jill: $
B
+$
h
Fee + Rate per hour
+$
h
Fee + Rate per hour
Add both expressions to represent how much the company will pay to hire
both consultants.
Let h represent the number of hours they work together.
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Kelly: $
Combine their pay rates.
= 25 + 18 +
=
+
+
h
Use the Commutative Property.
Combine like terms.
The company will pay their project.
for both Jill and Kelly to work on
TRY THIS!
1a. How much do Jill and Kelly make individually if they work 10 hours?
1b. Combine (​  3x + __​ 12 ​ )​- (​  7x - 4​ __12 ​ )​
[  ​( 7x - 4​ __12 ​ )​ ]​ Subtraction is adding the opposite.
= (​  3x +  __​ 12 ​ )​+ (​   7x
4​ __12 ​ )​ Distribute the negative sign to each term.
= 3x
=
= (​  3x + __​ 12 ​ )​+ ​
Chapter 1
7x + __​ 12 ​
4​ __12 ​ Use the Commutative Property.
Combine like terms.
25
Lesson 5
REFLECT
1c. What are two different ways to calculate how much a company would pay to
hire both Jill and Kelly to work on a 10-hour project?
1d. Explain how the Distributive Property allows you to combine the terms 10h and 14h.
CC.7.EE.1
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EXPLORE
Using the Distributive Property
Marc is selling tickets for a concert. Adult tickets cost $16.60, and
children’s tickets cost $12.20. He gets to keep 25% of the money he
collects from ticket sales. Write an expression to represent how much
Marc gets to keep.
A
Let a represent the number of adult tickets he sells.
Let c represent the number of + 12.20
B
The expression 16.60
C
Write 25% as a decimal. D
Write an expression to represent 25% of the money he collects.
tickets he sells.
represents the ×​
+
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( 
)
 ​
25% of adult ticket and children ticket
sales sales
E
Use the Distributive Property to simplify the expression.
( 
0.25​
=
a+
( 
)
  ​+ 0.25​
)
 ​
c
TRY THIS!
2.
How much does Marc get to keep if he sells 20 adult tickets and
40 children’s tickets?
Chapter 1
26
Lesson 5
A factor is a number that is being multiplied by another number to get a
product. To factor is the process of writing a number or an algebraic expression
as a product.
CC.7.EE.1
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explore
Factoring Expressions
Factor 4x + 8.
A
Model the expression with algebra tiles.
Use positive x tiles and positive one tiles.
B
Arrange the tiles to form a rectangle. The total area represents 4x + 8.
C
Since the length multiplied by the width equals area, the length and the width of the
­rectangle are the factors of 4x + 8. Find the length and width.
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The width is
tiles‚ or
.
The length is
x tile and
ones tiles‚ or
.
D
ones
×
+ + + +
+
+ + + +
+
+
+ + + +
+ + + +
Use the expressions from the length and width of the rectangle to write
the area of the ­rectangle, 4x + 8, in factored form.
TRY THIS!
Factor each expression.
3a. 2x + 2
3b. 3x + 9
3c. 5x + 15
3d. 4x + 16
Chapter 1
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Lesson 5
REFLECT
3e. How could you use the Distributive Property to check your factoring?
3f. What If? How would the model and factors change if the original expression was 4x – 8?
pr a c t i c e
Add or subtract each expression.
1. (4.8x + 15.5) + (2.1x - 12.2) 2. (7x + 8) - (3x + 12)
3. ​( __​ 12 ​x + __​ 34 ​ )​+ (​  __​ 12 ​x - __​ 14 ​ )​
4. Each week, Joey gets paid $10 plus $2 for each chore he does. His sister Julie
gets paid $5 plus $3 per chore.
a. Write an expression for how much their parents pay Joey and Julie
each week if they do the same amount of chores.
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b. If Joey and Julie each do 5 chores, how much do they get paid
individually? How much do their parents pay altogether?
5. A company sets up a food booth and a game booth at the county fair. The fee
for the food booth is $100 plus $5 per day. The fee for the game booth is
$50 plus $7 per day. How much does the company pay for both booths for 5 days?
6. A group of 4 people go out to eat. They decide to split the bill so each person
pays ​ _14 ​of the total price. Appetizers are $6 and main dishes are $9. Write an
expression to show how much each person pays.
Factor each expression.
7. 24 + 36x
8. 5x - 25
9. 12x + 10
10. 10x - 60
Chapter 1
28
Lesson 5
Name Class 1-5
Date Name ________________________________________ Date __________________ Class __________________
Algebraic Practice
Reasoning
Additional
LESSON
5
Practice B: Simplifying Algebraic Expressions
Identify like terms in each list.
1. 3a b2 b3 4b2 4 5a
_________________________________________________________________________________________
2. x
x4
4x
4x 2
4x4
3x2
_________________________________________________________________________________________
3. 6m 6m2 n2 2n 2 4m 5n
_________________________________________________________________________________________
4. 12s 7s4 9s s2 5 5s4 2
_________________________________________________________________________________________
Simplify. Justify your steps using the Commutative,
Associative, and Distributive Properties when necessary.
5. 2p 22q2 p
6. x2 3x2 42
________________________________________
________________________________________
7. n n 3n n n
4
3
8. 4a 4b 2 2a 5b 1
3
________________________________________
________________________________________
10. 2h2 3g 2h2 22 3 4g
________________________________________
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9. 32m2 14n2 12m2 5n 3
________________________________________
11. Write an expression for the perimeter
of the figure at the right. Then
simplify the expression.
________________________________________
12. Write an expression for the combined
perimeters of the figures at the right.
Then simplify the expression.
________________________________________
Chapter 1
29
5
Practice and Problem Solving
Holt McDougal Mathematics
Name ________________________________________ Date __________________ Class __________________
Algebraic
Reasoning
Problem
Solving
LESSON
5
Problem Solving: Simplifying Algebraic Expressions
Write the correct answer. Use the figures
for Problems 1–3.
1. Figure 1 shows the length of each
side of a garden. Write and simplify
an expression for the perimeter of
the garden.
________________________________________
2. Figure 2 is a square swimming pool.
Write and simplify an expression for
the perimeter of the pool.
________________________________________
4. The Pantheon in Rome has n granite
columns in each of 3 rows. Write and
simplify an addition expression to
show the number of columns. Then
evaluate the expression for n 8.
3. Write and simplify an expression for
the combined perimeter of the
garden and the pool.
________________________________________
________________________________________
________________________________________
________________________________________
5. Which is an expression that shows the
earnings of a telemarketer who
worked for 23 hours at a salary of d
dollars per hour?
6. The minimum wage set in 1997 was
$5.15 per hour. Evaluate the
expression 40h where h $5.15 to
find a worker’s weekly salary.
A d 23
C d y 23
F $20.60
H $515.00
B 23d
D 23 y d
G $200
J $206.00
8. A hexagon is a 6-sided figure. Find the
perimeter of a hexagon where all of the
sides are the same length and the
expression x y represents the length
of a side. Simplify the expression.
7. What is the perimeter of a triangle
with sides the following lengths:
2a 4c, 3c 7, and 6a 4.
Simplify the expression.
A 8a 11c
F 6x 6y
B 6a 7c 3
G 6xy
C 8a 7c 3
H 6x y
D 8a 7c 11
J 6xy
Chapter 1
305
Practice
Problem
Solving
Holtand
McDougal
Mathematics
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Choose the letter for the best answer.