What is the Commutative Property?
The law of mathematics that allows the independence of the ordering of the elements in a problem
The commutative property says that in addition and multiplication, you can change the order of the numbers and still get the same answer. This property is called "commutative" because it’s about switching the order of numbers without changing the result.
Let’s look at the commutative property in action, starting with addition!
The commutative property of addition says that a + b = b + a. This means that 2 + 5 will give us the same result as 5 + 2. Let’s check:
2 + 5 = 5 + 2
7 = 7
We have switched the order of the numbers and still got the same result: 7.
The same is true for multiplication.
The commutative property of multiplication says that a × b = b × a. This means that 2 × 5 = 5 × 2.
2 × 5 = 5 × 2
10 = 10
There we have it: Changing the order of numbers does not change the result in multiplication.
Important Note: Subtraction and division are not commutative. Changing the order will change the result.
When Do Students Learn About the Commutative Property?
Students first learn the commutative property with addition, then apply it to multiplication and later to algebraic expressions.
Grades 1–2 – Commutative Property of Addition
Students see that numbers can be added in any order and still give the same sum.
Grades 3–4 – Commutative Property of Multiplication
Students learn that numbers can be multiplied in any order without changing the product.
Grades 6+ – Commutative Property in Algebra
Students use the commutative property to rearrange variables and simplify algebraic expressions.
