Commutative Properties
Commutative Property of Addition: if
a and
b are real numbers, then
a+b=b+a
Commutative Property of Multiplication: if
a and
b are real numbers, then
a⋅b=b⋅a
The commutative properties have to do with order. If you change the order of the numbers when adding or multiplying, the result is the same.
example
Use the commutative properties to rewrite the following expressions:
1.
−1+3=
2.
4⋅9=
Solution:
1. |
|
|
−1+3= |
Use the commutative property of addition to change the order. |
−1+3=3+(−1) |
2. |
|
|
4⋅9= |
Use the commutative property of multiplication to change the order. |
4⋅9=9⋅4 |
example
Use the associative properties to rewrite the following:
1.
(3+0.6)+0.4=
2.
(−4⋅52)⋅15=
Answer:
Solution:
1. |
|
|
(3+0.6)+0.4= |
Change the grouping. |
(3+0.6)+0.4=3+(0.6+0.4) |
Notice that
0.6+0.4 is
1, so the addition will be easier if we group as shown on the right.
2. |
|
|
(−4⋅52)⋅15= |
Change the grouping. |
(−4⋅52)⋅15=−4⋅(52⋅15) |
Notice that
52⋅15 is
6. The multiplication will be easier if we group as shown on the right.
example
Use the Associative Property of Multiplication to simplify:
6(3x).
Answer:
Solution:
|
6(3x) |
Change the grouping. |
(6⋅3)x |
Multiply in the parentheses. |
18x |
Notice that we can multiply
6⋅3, but we could not multiply
3⋅x without having a value for
x.