&KDSWHU
1-7
Properties
Objective To identify properties of addition and multiplication
These properties are true for operations with any integers.
Let a, b,and c represent any integers.
Changing the orderof the addends
does notchange the sum.
abba
Example: 6 (2) 2 6
4 4 Tr u e
Commutative Property of Addition
Changing the orderof the factors
does notchange the product.
abba
Example: 6(2) 2(6)
12 12 Tr u e
Commutative Property of Multiplication
Changing the groupingof the addends
does not change the sum.
(ab)ca(bc)
Example: ( 6 2) 3 6 (2 3)
4 3 6 5
1 1 Tr u e
Associative Property of Addition
Changing the groupingof the factors
does not change the product.
(ab)ca(bc)
Example: (6 • 2)3 6(2 • 3)
(12)3 6(6)
36 36 Tr u e
Associative Property of Multiplication
Adding 0 and any number does not
change the value of the number.
a 0 a or 0aa
Examples:
6 0 6
or
0 (6) 6
Identity Property of Addition
Multiplying 1 and any number does not change
the value of the number.
a• 1aor 1• aa
Examples:
6(1) 6
or
1(6) 6
Identity Property of Multiplication
The sum of any integer and
its additive inverse is 0.
a(a) 0
Example: 3 (3) 0
Inverse Property of Addition
The product of 0 and
any number is 0.
0 • a0 or a• 0 0
Example: 0(3) 0 or (3)0 0
Zero Property of Multiplication
Think
“order”
Think
“grouping”
Think
“same number”
identity element
of addition
Think
3 and 3 are opposites.
Think
n• 0 0
identity element
of multiplication
