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Expressions Chapter Problems
Exponents
Classwork
1. What is the base and exponent in the
following expressions?
Homework
12. What is the base and exponent in the
a. 53
following expressions?
b. 89
a. 35
c. 112
b. 58
c. 153
2. 62 = 36, what does this have to do with a
square?
13. 72 = 49, what does this have to do with a
square?
3. 63 = 216, what does this have to do with a
cube?
14. 73 = 343, what does this have to do with
a cube?
Write the following in expanded form and
Write the following in expanded form and
evaluate:
evaluate:
4. 32 =
15. 12 =
5. 42 =
16. 72 =
6. 52 =
17. 82 =
7. 23 =
18. 73 =
8. 63 =
19. 43 =
9. 74 =
20. 83 =
10. 84 =
21. 105 =
11. 35 =
22. 55 =
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Order of Operations
Classwork
Homework
23. 9 + 3 x 3 + 10 -1 =
37. 10 – 2 + 9 + 3 x 5 =
24. 3 – 3 + 1 + 3 x 12 =
38. 5 x 8 + 2 – 2 + 12 x 5 + 10 =
25. 7 + 63 ÷ 3 =
39. 6 x 3 + 32 – 6 =
26. (7 – 4)2 x 3 =
40. 43 – 6 ÷ 3 x 5 =
27. 72 – 82 ÷ 23 + 3 x 5 =
41. 4+ 43 x 2 ÷ 4 -6 =
28. (1 + 4) ÷ 5 =
42. (9 – 3) x 6 =
29. 5 – (3 – 1) =
43. (8 + 4) ÷ 3 – 2 =
30. (8 + 8) x 3 =
44. (2 + 8) x (7 – 3) =
31. (7 – 4) x 2 ÷ (5 – 3) =
45. 36 – (52 + 4 ÷ 2) =
32. [(6 – 3) x 2] ÷ 3 =
46. [20 – (10 – 4)] ÷ (8 – 1) =
33.
47.
a. Simplify the expression: 5 x 6 – 6 =
a. Simplify the expression: 3 + 12 ÷ 3 =
b. Add parentheses to the expression so
b. Add parentheses to the expression so
that it simplifies to a different
that it simplifies to a different
answer.
answer.
34.
48.
a. Simplify the expression: 9 ÷ 1 + 9 =
a. Simplify the expression: 22 – 6 x 2 =
b. Add parentheses to the expression so
b. Add parentheses to the expression so
that it simplifies to a different
that it simplifies to a different
answer.
answer.
49. A landscaping company charges $75 for
35. Your brother buys 3 shirts for $9 each.
spring yard clean-up and then $25 each
He also buys a pair of jeans for $25.00
time the grass is cut. If you plan on
that gets a $4.00 discount. How much
having the yard cleaned up in the spring,
does he spend?
plus the lawn cut 11 times, how much will
it cost?
36. The repairman charged $36 for parts
50. At the clothing store you buy 3 pairs of
and $12 per hour for labor to repair a
jeans for $22 each and 4 shirts for
bicycle. If he spent 3 hours repairing the
$8.50 each. You also have a $20 off
bike, what will the total repair bill be?
coupon. How much do you spend?
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Vocabulary, Equations & Expressions
Classwork
Homework
51. Circle the constant and underline the
58. Circle the constant and underline the
coefficient for each expression below
coefficient for each expression below
a. 5x – 3
a. 3x – 5
b. 2x + 7
b. 2x - 1
c. 2 – 4x
c. 7 – 8x
d. x + 3
d. x + 2
52. Create an algebraic expression with a
coefficient of 7 and a constant of 4.
53. Create an algebraic expression with a
coefficient of -1 and a constant of -12.
54. Create an equation that contains a
coefficient of 6.
59. Create an algebraic expression with a
coefficient of 17 and a constant of 3.
60. Create an algebraic expression with a
coefficient of -1 and a constant of -1.
61. Create an equation that contains a
coefficient of 4.
55. Create an equation that contains a
coefficient of -13.
constant of -12.
56. What is the difference between an
algebraic expression and an equation?
57. Which are algebraic expressions?
5x – 2
8x
14 + 5x
2w – 6
62. Create an equation that contains a
63. What is the difference between an
algebraic expression and an equation?
64. Which are algebraic expressions?
w
17m
9w + 4 = 12
8 – 3z
12 + 7t
4x – 8 = 9
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Translating between Words & Expressions
Classwork
Translate the words into an algebraic expression.
65. 4 times x
73. The quotient of 300 and the quantity of
66. The sum of x and 6
x times 2
67. The product of 9 and y
74. x less than 32
68. w less than 8
75. The quotient of 35 and the quantity of x
69. 5 more than x
minus 7
70. The difference of 6 and x
76. The product of 7 and x, minus the
71. 9 times the product of x and 4
quantity of 4 less than y
72. The product of 5 and y, divided by 3
77. The quantity of 9 more than x divided by
the quantity of 12 less than y
78. Adult ticket prices are $3 more than child ticket prices. Determine the adult ticket price,
given the child ticket price.
Child Ticket Price Adult Ticket Price
$5
$7
$10
$12
79. Write an expression that represents the adult price, if the child price is “x”
80. For NJASK testing, 25 students are placed in each classroom. Determine the number of
classrooms needed, given the number of students testing.
Number of Students Testing Number of Classroom Needed
250
325
400
520
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81.
Write an expression that represents the number of classrooms needed, if the number of
students testing is “x”
82. Mary has ½ the amount of money that Jim has. Determine the amount of money that Mary
has, given Jim’s amount of money.
Jim’s Amount of Money Mary’s Amount of Money
$50
$100
$175
$220
83. Write an expression that represents the amount of money Mary has, given the amount of
Jim’s money.
84. Each person running in the race paid $20. Determine the amount of money collected, given
the amount of people running in the race.
Number of People Running Amount of Money Collected
150
230
410
520
85. Write an expression that represents the amount of money collected, given the number of
people running in the race.
Write an expression for each of the following situations.
86. Bob weighs 7 more pounds than Jack. Jack weighs x pounds. Bob’s weight:
87. Tiffany has 6 dollars less than Jessica. Jessica has x dollars. Tiffany’s money:
88. Samantha has 12 more stickers than Mike. Mike has x stickers. Samantha’s sticker
amount:
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89. The recipe calls for twice the amount of sugar than flour. There is f amount of flour in
the recipe. Amount of sugar:
90. Mark’s quiz grade is one more than twice Ted’s quiz grade. Ted’s quiz grade is x. Mark’s
quiz grade:
91.
Laura paid x dollars for her prom dress. Beth paid four dollars less than Laura. Beth’s
prom gown price:
92. David ran the 5k in x minutes. Harry ran the same race in five minutes less than double
David’s time. Harry’s time:
93. The beans grew k inches. The tomatoes grew 3 inches more than triple the height of the
beans. Tomato height:
Create a scenario for the following expressions:
94. x + 5
95. 2(x – 3)
Homework
Translate the words into an algebraic expression.
96. The product of 14 and x
104.
97. The quotient of x and 5
The quotient of 100 and the sum of x
and 2
98. The sum of 19 and w
105.
x less than 2
99. w less than 8
106.
The product of 5 and the quantity of
100.
7 less than x
x less than 7
101.
The difference of 16 and y
102.
9 times the quotient of x and 20
103.
The product of 6 and x, less 3
107.
The product of 27 and y, divided by
the quantity of 4 more than y
108.
The quantity of 6 less than x divided
by the quantity of 2 more than y
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109.
Child ticket prices are $3 less than adult ticket prices. Determine the child ticket price,
given the adult ticket price.
Adult Ticket Price Child Ticket Price
$10
$15
$20
$25
110.
Write an expression that represents the child price, if the adult price is “x”
111.
For busing, 40 students are assigned to each bus. Determine the number of buses
needed, given the number of students riding.
Number of Students Riding Number of Buses Needed
240
320
400
500
112.
Write an expression that represents the number of buses needed, if the number of
students riding is “x”
113.
The farm always has four times the number of chicks as hens. Determine the number of
chicks, given the number of hens.
Number of Hens Number of Chicks
20
40
50
60
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114.
Write an expression that represents the number of chicks, given the number of hens.
115.
Each person running in the race will eat two hotdogs. Determine the number of hotdogs
needed, given the amount of people running in the race.
Number of People Running Number of Hotdogs needed
150
230
410
520
116.
Write an expression that represents the number of hotdogs needed, given the number of
people running in the race.
Write an expression for each of the following situations.
117.
Bob weighs 17 pounds less than Jack. Jack weighs x pounds. Bob’s weight:
118.
Tiffany has 50 dollars more than Jessica. Jessica has x dollars. Tiffany’s money:
119.
Samantha has 12 times as many stickers than Mike. Mike has x stickers. Samantha’s
sticker amount:
120.
The recipe calls for triple the amount of sugar than flour. There is f amount of flour in
the recipe. Amount of sugar:
121.
Mark’s quiz grade is six more than double Ted’s quiz grade. Ted’s quiz grade is x. Mark’s
quiz grade:
122.
Laura paid x dollars for her prom dress. Beth paid 16 dollars more than Laura. Beth’s
prom gown price:
123.
David ran the 5k in x minutes. Harry ran the same race in half the time that David ran
the race. Harry’s time:
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124.
The beans grew k inches. The tomatoes grew triple the height of the beans, less 2
inches. Tomato height:
Create a scenario for the following expressions:
125.
2(x + 3)
126.
x-4
Evaluating Expressions
Classwork
Evaluate the expression for the given
value
127.
a.
b.
c.
d.
e.
f.
g.
h.
i.
j.
k.
l.
m.
n.
(2n + 1)2 for n = 3
2(n + 1)2 for n = 4
2n + 22 for n = 3
4x + 3x for x = 5
3(x – 3) for x = 7
8(x + 5)(x – 2) for x = 4
3x2 for x = 2
5x + 45 for x = 6
4x for x = 10
5
4y + x for x = 2 and y = 3
x + 17 for x = 12 and y = 2
y
6x + 8y for x = 9 and y = ¼
x + (2x – 8) for x = 10
5(3x) + 8y for x = 2 and y = 10
Homework
129. Evaluate the expression for the given
value
a. (2n + 1)2 for n = 1
b. 2(n + 1)2 for n = 3
c. 2n + 22 for n = 5
d. 4x + 3x for x = 6
e. 3(x – 3) for x = 3
f. 8(x + 5)(x – 2) for x = 6
g. 3x2 for x = 8
h. 5x + 45 for x = 3
i. 4x for x = 15
5
j. 4y + x for x = 12 and y = 13
k. x + 17 for x = 2 and y = 2
y
l. 6x + 8y for x = 8 and y = ¾
m. x + (2x – 8) for x = 11
n. 5(3x) + 8y for x = 12 and y = 5
Use the distance formula, D = rt, to
find the distance traveled
130.
Use the distance formula, D = rt, to
find the distance traveled
128.
a. Rate: 40 mph; Time: 2 hrs
b. Rate: 60 mph; Time: 5 hrs
c. Rate: 34 mph; Time: ½ hr
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a. Rate: 14 mph; Time: 2 hrs
b. Rate: 60 mph; Time: ¾ hrs
c. Rate: 40 mph; Time: ½ hr
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Distributive Property
Classwork
131.
Use the Distributive Property to rewrite the expressions without parentheses
a.
b.
c.
d.
e.
132.
(x + 4)
8(x – 2)
6(x + 4)
1(x – 4)
(x + 2)8
Use the Distributive Property to rewrite each expression with parentheses.
a.
b.
c.
d.
12x + 15
8x – 20
16y – 24x
18x – 27
133.
Marla did 65 sit-ups each day for one week. Write an expression using the Distributive
Property to find the total number of sit-ups Marla did during the week. Solve the
expression.
134.
Tickets for the school play cost $9 each. Tessa wrote the expression 9 x 26 to find the
cost of 26 tickets to the play. Tessa used the Distributive Property to find the product.
Write Tessa’s expression after she used addition and the Distributive Property.
Homework
135. Use the Distributive Property to rewrite the expressions without parentheses
a.
b.
c.
d.
e.
136.
5(x + 4)
7(x – 12)
3(x - 14)
1(x – 2)
(x - 2)5
Use the Distributive Property to rewrite each expression with parentheses.
a. 24y + 36
b. 12x – 18
c. 15y – 20x
d. 20x – 30
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137.
Coach Brown bought 6 basketballs for $16 each and 6 footballs for $24 each. The
expression 6 x 16 + 6 x 24 gives the total cost in dollars of the basketballs and footballs.
Use the Distributive Property to write this expression another way. Then evaluate.
138.
Jessica took her mother to a movie. She paid $9 each for 2 tickets, $4 each for 2
nachos, and $3 each for 2 bottles of water. Use the Distributive Property to show two
different ways to solve the problem. How much did she spend?
Like Terms
Classwork
139.
Create a like term for the given term.
a. 4x
b. 13y
c. 15x2
d. 16xy
e. x
140. Simplify the expression if possible by
combining like terms.
a.
b.
c.
d.
e.
f.
g.
h.
i.
j.
k.
l.
m.
n.
o.
142.
Simplify the expression if possible by
combining like terms.
7x + 8x
6x + 8y + 2x
15x2 + 5x2
5x +2(x + 8)
10y + 4y
9(x + 5) + 7(x – 3)
8 + (x – 4)2
7y + 8x + 3y + 2x
x + 2x
x2 + 5x2
2x + 4x + 3
6y – 3y
9y + 4y – 2y + y
x + 5x + x + 12
8x – 3x + 2x + 15
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Homework
141.
Create a like term for the given term.
a. 6x
b. y
c. 10x2
d. 14xy
e. -5x
a.
b.
c.
d.
e.
f.
g.
h.
i.
j.
k.
l.
m.
n.
o.
~ 11 ~
17x + 18x + 3
6x + 8y - 2x – y
15x2 + 5x2 + 2x
5x +2(x + 8) + 3
10y + 4y – 5
9(x + 5) + 7(x + 3)
18 + (x – 4)2 – 4
7y + 8x + 3y + 2x + 9
x + 2x + x + 5x
6x2 + 5x2
12x + 14x + 3y
6y – 3y + 6xy + 4xy
9y + 4y – 2y + y + y2
x + 5x + x + 12 – 7x
8x – 3x + 2x + 15 – 7y
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Expressions Chapter Questions
1. How can the order of operations easily be remembered?
2. Why is it important to have an “order” to the operations?
3. What is the difference between an expression and an equation?
4. Can you name 3 words that indicate each operation (addition, subtraction, multiplication and
division)?
5. How do you evaluate an expression?
6. Explain how distribution can simplify a problem.
7. What are like terms?
8. How do you combine like terms?
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