Expressions Chapter Questions
1. Explain how distribution can simplify a problem.
2. What are like terms?
3. How do you combine like terms?
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Expressions Chapter Problems
Mathematical Expressions
Classwork
1)
In each expression below, identify the coefficient, constant, and variable.
a. 7x + 9
b. 6y – 5
c. 4.5 – 2.7z
d. –9w – 22
2)
Determine if each statement is True or False. If False, determine what needs to be changed in
order to make the statement True.
a. In 5x – 8, 5 is the constant.
b. In x – 6.5, x is the variable.
c. In 9y + 38, 38 is the constant.
d. In 2 – 7z, 7 is the coefficient.
e. In –9 – 3w, –9 is the coefficient.
Homework
3) In each expression below, identify the coefficient, constant, and variable.
a. 4v + 7
b. 10u – 8
c. –3.6 – 1.8w
d. –6.1 – 2.2x
4)
Determine if each statement is True or False. If False, determine what needs to be changed in
order to make the statement True.
a. In 3b + 9, 9 is the constant.
b. In c – 2.1, 2.1 is the variable.
c. In 2y + 5, 5 is the coefficient.
d. In 15 – 3z, 3 is the coefficient.
e. In –11 – 4w, –11 is the constant.
Order of Operations
Classwork
5)
Simplify each expression using the Order of Operations.
a. 7 ∙ 23 − 52
b. 6 + 3 − 1 ∙ 6
c. 5 + (3 ∙ 6 + 1)
d. (5 − 1)3 − (3 + 2)2 + 18
e. 52 ∙ 4 − 72 + 6
f. 8 + 6 + 3 ∙ 6
45
g.
− 12
9
h. 75 ÷ 5 + 8 ∙ 40 ÷ 5
i. 21 − [110 ÷ (6 + 5)]
200
j.
−3∙5
2+2
k. 400 − [12 + 6 ∙ 10]
2(4∙5−6)
l.
35÷5
2∙9−3∙2∙1
m.
12−3−1
n. 12(10 − 5) − 40 ÷ (4 + 1)
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o.
75÷5+1
(10+8)÷(4+5)
Homework
6)
Simplify each expression using the Order of Operations.
a. (11 − 7) + 3
b. 4 ∙ 3 + 10 ∙ 2
c. 35 ÷ 7 ∙ 4 − 15 ∙ 8
d. 30 ÷ (12 − 2) + 3
e. 2(6 + 4) ÷ 4
f. 7 − (9 ∙ 3) ∙ 0
g. 2[4 + (9 ÷ 3)]
h. 6(−12 + 7) ÷ 3 − 1
i. 12 ÷ [(12 ÷ 3) ∙ (5 ÷ 5)]
j.
k.
l.
m.
n.
92 −4
(5+2)∙11
32 −6∙2+4
32 −5
4∙2÷8+2∙4÷8
32 +22 +12
2∙4−9(1+1)
12 −3∙2
4∙3−(4+2)
(−3−4−5)÷(4−3)
o. 55 ÷ 52 ÷ 52 ÷ 5
7)
Amy says that the two expressions below are equal.
2 ∙ (8 + 52 ) − 3
92 − 6 ∙ 3 ÷ 2
Is Amy correct when she says that the two expressions have equal values? Explain your answer.
Distributive Property
Classwork
8)
Use the Distributive Property to rewrite the expressions without parentheses
a.
b.
c.
d.
e.
f.
g.
(x + 4)
8(x – 2)
6(x + 4)
-1(x – 4)
(x + 2)8
⅝(4x + 12)
1.2(3x – 7.1)
Homework
9)
Use the Distributive Property to rewrite the expressions without parentheses
a. 5(x + 4)
b. 7(x – 12)
c. 3(x - 14)
d. -1(x – 2)
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e. (x - 2)5
f. ⅔(6x + 12)
g. 2.5(3x – 4.1)
Like Terms
Classwork
10)
Create a like term for the given term.
a. 4x
b. 13y
c. 15x2
d. 16xy
e. X
11) Simplify the expression if possible.
a. 7x + 8x
b. 6x + 8y + 2x
c. 15x2 + 5x2
d. -10y + 4y
e. x + 2x
f. x2 + 5x2
g. 2x + 4x + 3
h. 6y – 3y
i. 9y + 4y – 2y + y
12) Simplify the algebraic expression if possible.
a.
b.
c.
d.
e.
f.
g.
h.
i.
j.
k.
l.
m.
n.
7y + 8x + 3y + 2x + 9
6x + 8y - 2x – y
4x + 7
x + 5x + x + 12
8x – 3x + 2x + 15
17x + 18x + 3
7y + 8x + 3y + 2x
18 + (x – 4)2 – 4
5x +2(x + 8)
9(x + 5) + 7(x – 3)
8 + (x – 4)2
5x +2(x + 8) + 3
9(x - 5) + 7(x + 3)
12(x +4) –(9x + 3)
Homework
13)
Create a like term for the given term.
a. 6x
b. Y
c. 10x2
d. 14xy
e. -5x
14) Simplify the expression if possible.
a. 15x2 + 5x2 + 2x
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b.
c.
d.
e.
f.
g.
h.
i.
-10y + 4y – 5
x + 2x + x + 5x
6x2 + 5x2
12x + 14x + 3y
6y – 3y + 6xy + 4xy
9y + 4y – 2y + y
x + 5x + x + 12 – 7x
8x – 3x + 2x + 15 – 7x
15) Simplify the algebraic expression if possible.
a.
b.
c.
d.
e.
f.
g.
h.
i.
j.
k.
l.
m.
n.
5x + 4x + 7y + 3y +12
22x + 9y – 14 x - 6y
25x – 15
2x + 42 x + 9x + 13
14x – 12x – 2x -9
23x + 28x + 11
5x + 7y + 4y + 16x
2(x+5) – 8 + 5x
6x + 5(x + 7)
3(4v + 10) + 8(5v + 2)
9 + 2k+ (7 – 2k)5
12j + 3(x + 6) + 19
12(x + 0.5) + 14(x + 2)
5(2t + 4) – (13t – 9)
Translating Words into Expressions
Classwork
16) Translate each phrase into a mathematical expression.
a. Twelve more than a number
b. A number divided by nine
c. Ten decreased by a number
d. Double a number
e. Five less than six times a number
f. The product of four and the sum of a number and seven
g. The quotient of a number and ten increased by eleven
h. The sum of twenty and a number, divided by two
17) Write each phrase/sentence given below as both a “mathematical sentence/phrase” and a
“mathematical expression”
a. The total amount of money that your mother distributes to you and your 2 siblings, if she
gives each person x dollars.
b. Your age if you are x years younger than your 15 year old sister.
c. How many oranges each person gets if starting with 19 oranges, 4 are eaten, and the
rest are divided equally among three friends.
d. My speed if I travel m miles in h hours
e. The amount of money I make if I earn d dollars per hour and I work for 40 hours.
f. The length of my boat if it is 5 feet more than triple the length of my car, which is x feet
long.
g. Mike earned $12 an hour waiting tables plus $200 in tips.
h. Renée’s age if she is three years younger than twice her brother, who is b years old
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Homework
18) Translate each phrase into a mathematical expression.
a. Six less than a number
b. A number multiplied by ten
c. Eight increased by a number
d. Triple a number
e. Fifteen more than eleven times a number
f. The quotient of five and the difference of a number and three
g. The product of a number and twenty decreased by eleven
h. The difference of thirty and a number, multiplied by two
19) Write each phrase/sentence given below as both a “mathematical sentence/phrase” and a
“mathematical expression”
a. The total amount of money that your mother distributes to you and your 4 siblings, if she
gives each person x dollars.
b. Your age if you are x years older than your 8 year old brother.
c. How many bananas each person gets if starting with 11 bananas, 1 is eaten, and the rest
are divided equally among five friends.
d. The length of a rectangle is six inches longer than its width. The width is w inches.
e. A dog weighs four pounds more than triple the weight of a cat, whose weight is c pounds.
f. The length of my boat if it is 7 feet less than quadruple the length of my car, which is x
feet long.
g. Samantha earned $13 an hour waiting tables plus $250 in tips.
h. Nicole ate 3 more brownies than Haley. Sam ate twice as many brownies as Nicole. If x
represents the number of brownies that Haley ate, what is the expression that represents
the number of brownies that Sam ate?
Evaluating Expressions
Classwork
20) Evaluate each expression if a = -3, b = 7 and c = 5
35
a.
+3
𝑐
b. 8𝑎 − 𝑏
c. (𝑎𝑏 − 4) ÷ 5
d. 𝑏 2 − 𝑐 ÷ 5
e. (𝑐 2 − 𝑎3 ) ÷ 2
7−3𝑎
f.
𝑐−1
g. 10 + 3𝑐 − 𝑐 2
𝑏−𝑎+𝑐
h.
𝑎𝑐
Homework
21) Evaluate each expression if a = 4, b = -6 and c = 8
48
a.
+7
𝑏
b. 12𝑎 + 3𝑏
c. 2(11 − 𝑎𝑏) ÷ 𝑎
d. 𝑎2 + 𝑏 + 𝑐
e. 𝑐 2 − 3𝑏 + 4𝑎
𝑐 2 −4
f.
4𝑎−1
g. 𝑏 2 − 𝑎3 − 4𝑐
𝑎+𝑏+𝑐
h.
𝑎+𝑐
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Chapter Review
Determine whether the given terms are like terms. Circle your response.
22) 3x and -2x
Are Like Terms
Are Unlike Terms
23) 5a and 5b
Are Like Terms
Are Unlike Terms
24) 4y and 5xy
Are Like Terms
Are Unlike Terms
25) x2y and xy2
Are Like Terms
Are Unlike Terms
26) 22 and 14
Are Like Terms
Are Unlike Terms
27) xy and –xy
Are Like Terms
Are Unlike Terms
28) Match the expression 3(-4 + 3) with an equivalent expression.
a)
4(3) + 4(3)
b)
3(-4) + 3(3)
c)
4(3) - 4(3)
d)
3(4) + 3(3)
29) Simplify the expressions:
a. 2x + 3x – 7
b. 17b + 9 – 2b + 16
c. 2x2 + 4x + 13x2 + x2
d. 4(g – 5) + 9g
e. 12h –(6h -5) + 18
30) Determine the constant, coefficient, and variable in the expressions below:
a. 94w + 103
b. 18x – 3
c. -5y – 7
d. 16 – 24z
31) Write an expression to match each phrase given below:
a. The sum of a number and ten
b. Thirteen less than the quotient of nine and a number
c. Nine times the quantity of a number plus four
d. Four more than the product of eleven and a number
32) Simplify each expression using the order of operations
a. 9 + 5(6) − 42 ÷ 6
b. 33 ÷ 3 − 92 + (2 + 5)2
c.
(5+7)2 ÷32 +11∙5−7
196÷49
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33) Evaluate each expression if p = 7, q = -9, and r = 2
a.
63
𝑞
− 𝑟2
b. [(𝑝 + 𝑟)2 + 𝑝𝑟] ÷ 5
c. (𝑞 − 𝑟)2 − 4𝑝𝑞 ÷ 𝑟 + 5
d.
𝑝𝑞−1
+
𝑟
𝑟
34) Translate each sentence/phrase into a mathematical phrase and then a mathematical
expression.
a. When Anna babysits, she gets paid $12 per hour.
b. In order to get internet access in her home, Audra had to purchase a wireless
modem for $50 and pays the cable company $40 per month.
c. The width of a rectangle is 8 feet more than a quarter of the length.
d. How many tomatoes each person gets if starting with 30, 6 are eaten, and the
rest are divided equally among eight friends
35) Write an expression containing three terms that is in simplest form. One of the terms
should be a constant.
36) Simplify: 5 – 2(3x – 4) + x
37) At the video arcade, Jenny buys 25 tokens. She uses two tokens for each game she
plays.
a)
Write an expression for the number of tokens Jenny has left after playing g
games.
b)
Find the number of tokens Jenny has left after playing 1, 4, 6, 10 and 12 games.
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38) Write an expression that has four terms and simplifies to 16x.
a)
Identify the like terms
b)
Identify the coefficients
c)
Identify the constant terms
39) A cell phone company is offering 2 different monthly plans. Each plan charges a
monthly fee plus an additional cost per minute.
Plan A:
$ 40 fee plus $0.45 per minute
Plan B:
$70 fee plus $0.35 per minute
a)
Write an expression to represent the cost of Plan A
b)
Write an expression to represent the cost of Plan B
c)
Which plan would be least expensive for a total of 100 minutes?
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Answer Key
1.
a. 7 = coefficient, 9 = constant, x = variable
b. 6 = coefficient, -5 = constant, y = variable
c. -2.7 = coefficient, 4.5 = constant,
z = variable
d. -9 = coefficient, -22 = constant,
w = variable
2.
a. False; 5 is the coefficient OR
-8 is the constant
b. True
c. True
d. False; -7 is the coefficient
e. False; -9 is the constant OR
-3 is the coefficient
3.
a. 4 = coefficient, 7 = constant, v = variable
b. 10 = coefficient, -8 = constant,
u = variable
c. -1.8 = coefficient, -3.6 = constant,
w = variable
d. -2.2 = coefficient, -6.1 = constant,
x = variable
4.
a. True
b. False; c is the variable OR
-2.1 is the constant
c. False; 5 is the constant OR
2 is the coefficient
d. False; -3 is the coefficient
e. True
5.
a.
b.
c.
d.
e.
f.
g.
h.
i.
j.
k.
l.
m.
n.
o.
31
3
24
57
57
32
4
79
11
35
328
4
3
= 1.5
2
52
8
a.
b.
c.
d.
e.
f.
7
32
-100
6
5
7
14
-11
3
1
1
4
1
l.
7
m. 2
1
n. −
2
o. 1
7. No, Amy is not correct. When you simplify
the expression using the Order of Operations,
the first expression simplifies to:
2(8 + 25) − 3
2(33) − 3
66 − 3
63
and
81 − 6 ∙ 3 ÷ 2
81 − 18 ÷ 2
81 − 9
72
These answers are not equal.
8.
a. x+4
b. 8x-16
c. 6x+24
d. –x+4
e. 8x+16
f. 2 12 x  7 12
g. 3.6x - 8.52
9.
a.
b.
c.
d.
e.
f.
g.
5x + 20
7x – 84
3x – 42
–x + 2
5x – 10
4x +8
7.5x – 10.25
a.
b.
c.
d.
e.
Multiple Answers
Multiple Answers
Multiple Answers
Multiple Answers
Multiple Answers
a.
b.
c.
d.
e.
f.
g.
15x
8x + 8y
20x2
-6y
3x
6x2
6x + 3
10.
11.
6.
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g.
h.
i.
j.
k.
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h. 3y
i. 12y
g.
a. 10x + 10y +9
b. 4x + 7y
c. 4x + 7
d. 7x + 12
e. 7x + 15
f. 35x + 3
g. 10x + 10y
h. 2x + 6
i. 7x + 16
j. 16x + 24
k. 2x
l. 7x + 19
m. 16x – 24
n. 3x + 45
19−4
3
d. m divided by n; 𝑚 ÷ 𝑛
e. d times 40; 40𝑑
f. 3 times x plus 5; 3𝑥 + 5
g. 12 times h plus 200; 12ℎ + 200
h. 3 less than twice b; 2𝑏 − 3
18.
a. 𝑛 − 6
b. 𝑛 ∙ 10
c. 8 + 𝑛
d. 3𝑛
e. 11𝑛 + 15
5
f.
𝑛−3
g. 𝑛 ∙ 20 − 11
h. (30 − 𝑛) ∙ 2
13.
Multiple Answers
Multiple Answers
Multiple Answers
Multiple Answers
Multiple Answers
a.
b.
c.
d.
e.
f.
g.
h.
i.
20x2 + 2x
-6y -5
9x
11x2
26x + 3y
3y + 10xy
12y
12
15
19.
14.
a. 5 times x; 5𝑥
b. 8 plus x; 8 + 𝑥
c. the quantity of 11 minus 1 divided by 5;
11−1
5
d. w plus 6; 𝑤 + 6
e. 3 times c plus 4; 3𝑐 + 4
f. 4 times x minus 7; 4𝑥 − 7
g. 13 times h plus 250; 13ℎ + 250
h. the quantity of h plus 3, multiplied by 2;
2(ℎ + 3)
15.
20.
a. 9x + 10y + 12
b. 8x + 3y
c. 25x -15
d. 53x + 13
e. -9
f. 51x + 11
g. 21x + 11y
h. 7x + 2
i. 11x + 35
j. 52v + 46
k. -8k + 44
l. 12j + 3x + 37
m. 26x + 34
n. -3t + 29
a. 10
b. −31
c. −5
d. 48
e. 26
f. 4
g. 0
h. −1
21.
a. −1
b. 30
35
c.
= 17.5
2
d. 18
e. 98
f. 4
g. −76
1
h. = 0.5
16.
a. 𝑛 + 12
b. 𝑛 ÷ 9
c. 10 − 𝑛
d. 2𝑛
e. 6𝑛 − 5
f. 4(𝑛 + 7)
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+ 11
h.
2
17. Note: phrases may vary
a. 3 times x; 3𝑥
b. x less than 15 OR 15 minus x; 15 − 𝑥
c. the quantity of 19 minus 4 divided by 3;
12.
12.
a.
b.
c.
d.
e.
𝑛
10
20+𝑛
2
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Unit Review
22.
23.
24.
25.
26.
27.
28.
29.
37.
Like terms
Unlike terms
Unlike terms
Unlike terms
Like terms
Like terms
B
a. 5x – 7
b. 15b + 25
c. 16x2 + 4x
d. 13g – 20
e. 6h + 23
a. 25 – 2g
b. 1 23
4 17
6 13
10 5
12 1
38. Answers will vary
39.
a. 40 + .045m
b. 70 + 0.35m
c. Plan A
30.
a. 103 = constant, 94 = coefficient, w =
variable
b. -3 = constant, 18 = coefficient, x =
variable
c. -7 = constant, -5 = coefficient, y =
variable
d. 16 = constant, -24 = coefficient, z =
variable
31.
a. 𝑛 + 10
9
b.
− 13
𝑛
c. 9(𝑛 + 4)
d. 11𝑛 + 4
32.
a. 32
b. –21
c. 16
33.
a.
b.
c.
d.
–11
19
252
–30
34.
a. 12 times h
12ℎ
b. 40 times m plus 50
40𝑚 + 50
c. ¼ times ℓ plus 8
1
ℓ+8
4
d. the quantity of 30 minus 6, divided
by 8
30−6
8
35. Answers will vary
36. -5x + 13
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