Name: ____________________________
Operations – Properties of Addition
Basic Skills Practice
State whether the example given illustrates
the associative property (A), or commutative
property (C).
_____ (a) x + 9 = 9 + x
1
Date: _______
PreAlgebra
Going Deeper
7
Sheet # 03-02
Explain how you can use the commutative
property and additive inverses to help you
evaluate the following mental math problem.
_____ (b) 100 + (52 + 45) = (100 + 52) + 45
2
 2
 5     6 1
3
 3
_____ (c) 89 + 45 = 45 + 89
_____ (d) x + ( y + 3 ) = x + ( 3 + y )
_____ (e) (6  3)  4  4  (6  3)
2
A
B
Determine which equation illustrates the
commutative property and justify your
answer.
a  b  c  a  b  c 
a  b  c  c  a  b
C
D
a0a
a  (a )  0
8
3
A
B
Determine which equation illustrates the
associative property and justify your
answer.
a  b  c  a  b  c  C a  0  a
a  b  c  c  a  b D a  (a)  0
Alana wants to buy a sweater that costs $38,
sunglasses that costs $14, a pair of jeans that costs
$22, and a T-shirt that costs $16.
Here is an expression for the total cost. You can
rearrange the numbers using the properties of
addition. Look for sums that are multiples of ten.
On the lines provided, write the property used to
write equivalent expressions.
4
Explain the difference between the Commutative
and Associative Properties.
38  14  22  16
Original expression
38  22  14  16
38  22  14  16
60  30
5
Which property is illustrated by the
following?
60  6
A
B
C
D
6
Additive identity
Additive Inverse
Associative Property of Addition
Commutative Property of Addition
Which property is illustrated by the
following?
6  (6)  0
A
B
C
D
Additive identity
Additive Inverse
Associative Property of Addition
Commutative Property of Addition
90
Add
Simplify
H.O.T. Problems Higher Order Thinking
9 What is the value of x in the equation
3 x  0?
Answer _______
10 A property is a statement that is true for any
number. You may wonder if any of the
properties apply to subtraction. If you can
find a counterexample, an example that
shows that a conjecture is false, the property
does not apply.
13 Add or subtract. Write your answer in simplest
form. No Calculator!
A.
D.
B.
E.
State whether the following conjecture is
true or false. If false, provide a
counterexample.
Subtraction of whole numbers is
associative.
11 Describe and correct the error.
12 Describe and correct the error.
C.