Name
LESSON
Date
Class
Problem Solving
11-2 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.
b
b
c
a
b
c
a
Figure 1
2. Figure 2 is a square swimming pool.
Write and simplify an expression for
the perimeter of the pool.
3. Write and simplify an expression for
the combined perimeter of the
garden and the pool.
Figure 2
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.
Choose the letter for the best answer.
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?
A d 23
C d 23
D 23 d
B 23d
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.
F $20.60
H $515.00
G $200
J $206.00
7. What is the perimeter of a triangle
with sides the following lengths:
2a 4c, 3c 7, and 6a 4.
Simplify the expression.
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.
F 6x 6y
G6xy
H 6x y
J 6xy
A
B
C
D
8a
6a
8a
8a
11c
7c 3
7c 3
7c 11
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Holt Mathematics
Problem Solving
LESSON
11-2 Simplifying Algebraic Expressions
Challenge
LESSON
11-2 Matching Terms
Write the correct answer. Use the figures
for Problems 1–3.
Draw a line from each set of terms in Column A to its
equivalent combination in Column B. Then circle each letter in
Column B that does not have a matching term. Unscramble
those letters to answer the riddle.
Column A
1. Figure 1 shows the length of each
side of a garden. Write and simplify
an expression for the perimeter of
the garden.
Column B
1. 2x 7 5x 4 x
A. 5y 9x 12
2. 5 7x 2x 3 6
B. 12y 6x 24
3. x y 4x 3x 2y 3y
C. 15
4. 3x 2 5x 17 6x 20
D. 9x 8
2
E. 4
6. 12y 12x 12 6x 12
F. 6x 3
7. 12y 4 x 7y 8 8x
G. 11x y 7
8. 5x x 2 2x 5 4 x 2
H. x 2 6x 8
11. 5x 4 3x 5 2x 9
K. 3x 2
L. 3x 2
M. 6x
14. 2y 2x 8 6 x 2y
N. x 2 3x
24 columns
Choose the letter for the best answer.
O. 6x 6y 1
16. 3x 2 4x 2x 2 3x 2x
P. 12x 2 14x
17. 8x 4 4 4x x
Q. 7x 1
18. y 5x 6y 9 6
R. x 2
19. x 2 3 2x 2 4 7
S. 5x 7y 3
2
20. 5y 3 7x 2 x y
T. 0
U. 2x 6y
V. 3x y 5
X. 5x
Riddle: What can be a word, a number, a period of time, or a variable?
T
A
E
R
Holt Mathematics
variables
m
12
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.
F 6x 6y
G6xy
H 6x y
J 6xy
11c
7c 3
7c 3
7c 11
18
Holt Mathematics
Puzzles, Twisters & Teasers
LESSON
11-2 In Other Words. . .
Write each verbal expression as an algebraic expression. Then
use the answer key to solve the riddle.
An algebraic expression is made up of parts called terms.
1
2
7. What is the perimeter of a triangle
with sides the following lengths:
2a 4c, 3c 7, and 6a 4.
Simplify the expression.
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All rights reserved.
Reading Strategies
LESSON
11-2 Organization Patterns
3.2
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.
F $20.60
H $515.00
G $200
J $206.00
M
17
constants
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?
A d 23
C d 23
D 23 d
B 23d
A 8a
B 6a
C 8a
D 8a
W. 11x 7y 6
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All rights reserved.
n n n 3n; 3(8) 24
2a 6b 2c
2
15. 4x 6y 6 7x y
n
2
x
2
y
3
4x
20t
1. the product of 20 and t
constants and variables
s
3m2
4n 2
2. the sum of 4 times a number and 2
A coefficient is a value multiplied by a variable.
7p
3. the product of 7 and p
Term
Value of Coefficient
Meaning
7x
7
7•x
y
1
x
3
1
3
4. the sum of six times a number and 1
6n 1
1•y
5. the sum of 5 and a number
5n
1
• x
3
6. the quotient of a number and 8
This expression has 6 terms:
Term
2x
Term
5b
7
n
8
m6
7. m plus 6
Term
Term
Figure 2
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.
I. 4x
13. 4x 5 7x 2y 2 y
b
c
4b
J. 3x 2 11x 3
12. 4x 2y 8 3 y x
b
a
Figure 1
3. Write and simplify an expression for
the combined perimeter of the
garden and the pool.
10. 12x 6 8x 4x 3 12
2
a
2a 2b 2c
2. Figure 2 is a square swimming pool.
Write and simplify an expression for
the perimeter of the pool.
5. 4x x 12 4 2x
9. 5x 2 8x 7x 2 6x
b
c
b
Term
3x
Term
2x 2
• Reorganize the terms: 2x 3x 5b b 7 2x 2.
• Combine like terms: 5x 4b 7 2x 2.
8. t less than 23
23 t
9. the quotient of 100 and the amount 6 plus w
100
(6 w)
Answer Key
Answer each question.
1. How many terms are there in this expression:
6b b 2 5 2b 3f?
5 terms
2. 6b and b 2 are unlike terms. Explain why.
In b 2, b is raised to the second power, but it is not in 6b.
SH
LB
N
GA
CI
What’s worse than raining cats and dogs?
3. How many terms are there in this expression:
5a 2 6b a 3 2a 2 3b 2?
6
H
A
I
L
I
N
G
C
A
B
S
4. Reorganize these terms so like terms are next to each other.
a 3 5a 2 2a 2 6b 3b 2
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All rights reserved.
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Copyright © by Holt, Rinehart and Winston.
All rights reserved.
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Copyright © by Holt, Rinehart and Winston.
All rights reserved.
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