Fillable Algebraic Expressions 7th Grade Worksheets | Worksheet 1 (City of Oakland)

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Algebraic Expressions 7th Grade Worksheets | Worksheet 1 (City of Oakland)

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WWW.CUEMATH.COM
1. . Identify the algebraic expression among the following.
a)
b)
23x −
c)
1
3
2
x =
d)
2xy=
2. Classify the following algebraic expressions into monomials,
binomials, and trinomials.
a)
2
3x yz
b)
x y z+−
c)
22
xy−
3. Simplify the following algebraic expressions by combining like
terms.
a)
b)
1
73
2
xx−−
4. Mia’s piggy bank has only dimes and quarters. Write an
expression for the amount of money (in dollars) in her piggy
bank if
x
is the number of dimes and
y
is the number of quarters.
2 3 0x+=
Algebraic Expressions 7th Grade Worksheets
WWW.CUEMATH.COM
5. Find the sum.
a)
(3.2 ) ( 10 2.5)xx− + − +
b)
11
57
32
mm
− + +
6. Find the algebraic expression that corresponds to the
perimeter of the following rectangle.
7. Find the difference.
a)
( 3 8) (5 12)gg− + − +
b)
3
52
44
5
1xx
+ − − +
8) Simplify the following using distributive property.
79
(3 6) 2 5
22
yy

− − + −


9) Subtract
2
54xx−+
from the sum of
2
25xx−
and
2
72x −
.
10) What should be added to
22
3x xy y++
to get
22
33xy−
?
11) What should be subtracted from
3 5 10ab−+
in order to get
7 2 5ab− + −
?
12) Factor out the GCF.
a)
16 20xy−
b)
14 21 7mn+−
13) The area of a rectangular shaped swimming pool is
39x −
square units. Find the possible dimensions of the rectangle as
algebraic expressions.
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14) Factor out the coefficient of the variable term.
a)
55
84
k +
b)
7
14
2
m+
15) A square shaped door mat has a perimeter of
8 12x−
units.
Find an expression for the length of the mat.
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1) Option b
2) a) Monomial
b) Trinomial
c) Binomial
3) a) Monomial
b) Trinomial
c) Binomial
4) 0.10x + 0.25y
5) a) 5.7-11x
b) (5/6)m+2
6) 12m+8
7) a) -8g-4
b) 2x-7
8) -39y/2 +31
9)
2
87xx−−
10)
2
4y xy−−
11) 10a-7b+15
12)a)4(4x-5y)
13) 3 units and (x-3)
units
14)a) 5(k+2)/8
b) 7(m+4)/2
15) 2x-3
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1. Identify the algebraic expression among the following.
a)
2 3 0x +=
b)
23x −
c)
1
3
2
x =
d)
2xy=
Solution:
An algebraic expression is a combination of variables and
constants without any “=” symbol. Hence the option is b).
Note: a), c), and d) are called the equations NOT the algebraic
expressions.
2. Classify the following algebraic expressions into monomials,
binomials, and trinomials.
a)
2
3x yz
b)
x y z+−
c)
22
xy−
Solution:
The algebraic expressions are called monomials if they have
one term, binomials if they have two terms, and trinomials if they
have three terms. Hence:
a)
2
3x yz
is a monomial.
b)
x y z+−
is a trinomial.
c)
22
xy−
is a binomial.
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3. Simplify the following algebraic expressions by combining like
terms.
a)
b)
1
73
2
xx−−
Solution:
a) All terms in the given expression are like terms. We know that
3 5 7 1+ − =
.
Hence,
3 5 7 (3 5 7) 1 (or) x x x x x x+ − = + − =
.
b)
1 1 5
7 3 3 7 7
2 2 2
x x x x x
−

− − = − − = −


4. Mia’s piggy bank has only dimes and quarters. Write an
expression for the amount of money (in dollars) in her piggy
bank if
x
is the number of dimes and
y
is the number of quarters.
Solution:
The number of dimes is
x
and each dime is of worth $0.10. So
the total worth of dimes is 0.10
x
.
The number of quarters is
y
and each quarter is of worth $0.25.
So the total worth of quarters is 0,25
x
.
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So the algebraic expression that represents the total money in
the piggy bank is
0.10 0.25xy+
dollars.
5. Find the sum.
a)
(3.2 ) ( 10 2.5)xx− + − +
b)
11
57
32
mm
− + +
Solution:
a) We will find the sum by combining the like terms.
(3.2 ) ( 10 2.5) (3.2 2.5) ( 10 )
5.7 11
x x x x
x
− + − + = + + − −
=−
b) We will find the sum by combining the like terms.
1 1 1 1
5 7 ( 5 7)
3 2 3 2
5
2
6
m m m m
m
− + + = + + − +
=+
6. Find the algebraic expression that corresponds to the
perimeter of the following rectangle.
Solution:
The length of the rectangle is
45lm=+
The width of the rectangle is
21wm=−
The perimeter is,
2( ) 2(4 5 2 1)
2(6 4)
12 8
l w m m
m
m
+ = + + −
=+
=+
WWW.CUEMATH.COM
7. Find the difference.
a)
( 3 8) (5 12)gg− + − +
b)
3
52
44
5
1xx
+ − − +
Solution:
a) We will just distribute the minus sign and perform the usual
addition.
( 3 8) (5 12) 3 8 5 12
( 3 5 ) (8 12)
84
g g g g
gg
g
− + − + = − + − −
= − − + −
= − −
b) Here also, we will just distribute the minus sign and perform
the usual addition.
( )
3 5 3 5
5 12 5 12
4 4 4 4
35
5 12
44
27
x x x x
xx
x
+ − − + = + + −

= + + −


=−
8) Simplify the following using distributive property.
79
(3 6) 2 5
22
yy

− − + −


Solution:
The distributive property is
()a b c ab ac+ = +
.
7 9 21
(3 6) 2 5 21 10 9
2 2 2
21
9 (21 10)
2
39
31
2
y
y y y
y
y
y

− − + − = − + + −



= − − + +


= − +
9) Subtract
2
54xx−+
from the sum of
2
25xx−
and
2
72x −
.
Solution:
Using the given instruction,
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( ) ( ) ( )
( )
2 2 2
22
2
2 5 7 2 5 4
9 5 2 5 4
87
x x x x x
x x x x
xx

− + − − − +

= − − − + −
= − −
10) What should be added to
22
3x xy y++
to get
22
33xy−
?
Solution:
Here, the sum is
22
33xy−
and one of the addends is
22
3x xy y++
.
To find the other addend, we have to subtract the given addend
from the sum.
( ) ( )
2 2 2 2
2 2 2 2
2
3 3 3
3 3 3
4
x y x xy y
x y x xy y
y xy
− − + +
= − − − −
= − −
11) What should be subtracted from
3 5 10ab−+
in order to get
7 2 5ab− + −
?
Solution:
Here the difference is
7 2 5ab− + −
and the minuend is
3 5 10ab−+
.
To get the subtrahend, we subtract difference from the minuend.
(3 5 10) ( 7 2 5)
3 5 10 7 2 5
10 7 15
a b a b
a b a b
ab
− + − − + −
= − + + − +
= − +
12) Factor out the GCF.
a)
16 20xy−
b)
14 21 7mn+−
Solution:
a) The GCF of 16 and 20 is 4. So
16 20 4(4 5 )x y x y− = −
b) The GCF of 14, 21, and -7 is 7. So
14 21 7 7(2 3 )m n m n+ − = + −
13) The area of a rectangular shaped swimming pool is
39x −
square units. Find the possible dimensions of the rectangle as
algebraic expressions.
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Solution:
The area of the given swimming pool =
3 9 3( 3) Length Widthxx− = − =
So the possible dimensions are 3 units and
( 3)x −
units.
14) Factor out the coefficient of the variable term.
a)
55
84
k +
b)
7
14
2
m+
Solution:
a) Here, the variable is
k
and its coefficient is
5
8
.
( )
5 5 5
2
8 4 8
kk+ = +
b) Here, the variable is
m
and its coefficient is
7
2
.
77
14 ( 4)
22
mm+ = +
15) A square shaped door mat has a perimeter of
8 12x−
units.
Find an expression for the length of the mat.
Solution:
The perimeter of the mat =
8 12 4(2 3)xx− = −
.
If we divide it by 4, we get its length.
So the length of the mat =
4(2 3)
(2 3)
4
x
x
−
=−
units.
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Algebraic Expressions 7th Grade Worksheets Worksheet 1 (City of Oakland)

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