The commutative property is stating that if we change the order of the terms in addition or multiplication, it will not change our outcome.
You may remember this easily as “commute” means to travel or move.
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There will be many times in algebra when we have to simplify expressions.
The properties of real numbers are providing tools to help us to simplify complicated expressions. Algebra’s commutative property is often used for the simplification of algebraic expressions.
The commutative property of addition is stating that when we add two numbers, we can change the order of those numbers without affecting their sum.
Example: 30 + 25 has exactly the same sum as 25 + 30.
30 + 25 equals 55
25 + 30 equals 55
Multiplication is behaving in the same way.
The commutative property of multiplication states that when we multiply 2 (two) numbers, we are able to change their order and this will not affect the product. For example, 7 • 12 gives us the exact same product as will 12 • 7.
7 • 12 = 84
12 • 7 = 84
The Commutative Property of Addition:
For the real numbers, a and b counts: a + b equals b + a.
The Commutative Property of Multiplication:
For the real numbers, a and b counts: a • b equals b • a.
Please note that Subtraction is not commutative.
Example: 4 − 7 is not having the same difference as 7 − 4 has.
The − sign means subtraction here.
Just as subtraction doesn’t come commutative, neither does division.
Example: 4 ÷ 2 doesn’t have the same quotient as 2 ÷ 4.