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Properties
#10
00
Property
Associative Property
Example
Distributive Property
Commutative Property
4x - 2 = (2x – 1)2
Identity Property of Addition
Identity Property of Multiplication
4+0=4
Addition (Subtraction) Property of Equality
Multiplication (Division) Property of Equality
If 3x + 3 = 4 then 3x + 3 – 3 = 4 – 3
(3 2) 4  3 (2 4)
b cc b
5 1 5
If
1
1
x  3 , then 2 x  3 2
2
2
Inverse Property
Substitution Property
Multiplication Property of Zero
-3 + 3 = 0
If 3x = 9y and x = 6, then 3(6) = 9y.
Reflexive Property
Symmetric Property
Transitive Property
2x = 2x
If 3 = x, then x = 3.
If a + b = c and c = d, then a + b = d.
5 0  0
1. Which is an example of the commutative property
of addition?
2. Which statement is always true?
A 4+a=4a
A 3 + 5m = 3 + (1 + 4)m
B 3 + 5m = 5m + 3
C 3 + 5m = (3 + 5)m
B a + (-4 + 4) = a + 0
C a÷4=4÷a
D 4–a=a–4
D 3 + 5m = 3m + 5
3. What property of real numbers justifies the
following statement?
4x(y + 2) – 3y is equivalent to 4x(y) + 4x(2) – 3y
A The associative property of multiplication
B The commutative property of multiplication
C The distributive property of multiplication over
addition
D The closure property of multiplication
5. Which property justifies the following statement?
If 3a + 3b = 12 then 3(a + b) = 12
A
B
C
D
Commutative property of multiplication
Distributive property for multiplication over addition
Multiplicative identity property
Associative property of addition
4. 6a2 – 2a = 2a(3a – 1)
What property makes this equation true?
A
B
C
D
The reflexive property
The associative property
The commutative property
The distributive property
6.
7. Consider the procedure used below to solve the
given equation.
Given:
3(x – 2) = 17
(1st Step)
3x – 6 = 17
(2nd Step)
3x = 23
(3rd Step)
x = 23/3
Which of the following properties is a justification of the
1st step?
A Associative property of addition
B Commutative property of addition
C Distributive property
D Transitive property of equality
9.
8. While solving an equation, Lenny wrote the
following steps on the board.
(2x + 1) + 5 = 9
2x + (1 + 5) = 9
What property of real numbers guarantees that the second
equation is equivalent to the first?
F Associative property of addition
G Additive inverse property
H Commutative property of addition
J
Distributive property
10. Which property justifies rewriting
3x – 5x as (3 – 5)x?
A Associative property of multiplication
B Distributive property
C Commutative property of multiplication
D Associative property of addition
11. If 2n = 6, what property of equality justifies
writing
p + 2n = 4p + 15
as p + 6 = 4p + 15?
A
B
C
D
Addition property
Transitive property
Symmetric property
Substitution property
12.