Definition
Commutative property
The commutative property says swapping addends or factors does not change the sum or product.
Continue from this idea into connected AXIO math.
Defining relationship
Swap the order; keep the answer.
For addition, a + b = b + a. For multiplication, a × b = b × a. The property changes order, not grouping, and does not hold generally for subtraction or division.
- 1
original order
- 2
swap the addends
- The addends trade places
- The sum stays 8
- No regrouping is needed
What it means
You can switch the two numbers in an addition or multiplication and get the same result. This lets you place numbers in an order that is easier to think about.
Remember it
Swap the order; keep the answer.
Example
4 × 13 = 52, and 13 × 4 = 52. The factors changed places, but the product did not.
Watch for
Subtraction is different: 9 − 4 = 5, but 4 − 9 = −5.
Common mix-up
Changing order is commutative; changing parentheses is associative.
Exact meaning
For addition, a + b = b + a. For multiplication, a × b = b × a. The property changes order, not grouping, and does not hold generally for subtraction or division.