Section 18 Properties of Real Numbers
Commutative Property of addition
a + b = b + a
Example
:
4 + 6 =
Commutative Property of Multiplication
a
b
b
a
⋅
=
⋅
Example:
=
⋅
8
9
Associative Property of Addition
)
(
)
(
c
b
a
c
b
a
+
+
=
+
+
Example
:
=
+
+
)
5
4
(
3
Associative Property of Multiplication
)
(
)
(
c
b
a
c
b
a
⋅
⋅
=
⋅
⋅
Examples
:
4
)
2
3
(
)
4
2
(
3
⋅
⋅
=
⋅
⋅
Identity Property of Addition
a
a
=
+
0
Examples:
=
+
0
9
Identity Property of Multiplication
a
a
=
⋅
1
Example
:
=
⋅
1
9
Inverse Property of Addition
For every a, there is an additive
inverse –a such that a + (a) = 0
Example:
=

+
)
6
(
6
Inverse Property of Multiplication
For every a
)
0
(
≠
a
, there is a
multiplicative inverse
a
1
such that
1
)
1
(
=
a
a
Example
:
=
⋅
5
1
5
Multiplication Property of Zero
For every real number n,
=
⋅
n
Examples:
=
⋅

253
,
1
Multiplication Property of 1
For every real number n,
n
n

=
⋅

1
Examples:
1)
=
⋅

)
53
(
1
2)
=

⋅

)
32
(
1
Example
Name the property that each equation illustrates.
1)
2
1
2
1

=
+

2)
)
3
4
(
3
)
4
(
⋅
⋅
=
⋅
⋅
d
d
3)
12
4
)
3
(
4

=

x
x
4)
4
1
4

=

⋅
Example
Tell whether the expressions in each pair are equivalent
1)
2
3
+
x
and
x
+
⋅
1
3
2)
c
5
3

and
3
5

c
3)
)
9
4
(


and
4
9

4)
rt
xyz
⋅
and
zrt
y
x
⋅
⋅
Example
Simplify each expression
1)
x
x
6
3
12
+
+
2)
2
1
5
4
2
4
1
5
2
1
4
+

+
Homework #____: p. 56 (110 and 3139)