Commutative Property of Addition
The Commutative Property of Addition teaches Grade 4 students that the order of addends does not change the sum. In Saxon Math Intermediate 4, this foundational rule is expressed as a + b = b + a, meaning 5 + 6 equals 6 + 5 — both give 11. Students learn to use this property to rearrange problems for easier mental math, verify their work, and understand why swapping addends does not affect the total. The property applies to addition and multiplication but not subtraction or division, making it a critical distinction to master early in the curriculum.
Key Concepts
Property When we add two numbers, either number may be first. The order of the addends does not change the sum. For any numbers $a$ and $b$, $a + b = b + a$.
Examples Adding five and six gives the same result as adding six and five: $5 + 6 = 11$ and $6 + 5 = 11$. You can even shuffle three numbers: $1 + 2 + 3 = 6$ is the same as $3 + 2 + 1 = 6$. For this picture of dots, you can write two number sentences: $4 + 5 = 9$ and $5 + 4 = 9$.
Explanation This property is like making a sandwich! It does not matter if you put the cheese on first or the ham on first; the final sandwich still tastes the same. In addition, changing the order of the numbers you are adding together will not change the final answer, which is super helpful for checking your work.
Common Questions
What is the Commutative Property of Addition?
It states that changing the order of addends does not change the sum. For any numbers a and b, a + b = b + a. For example, 5 + 6 = 11 and 6 + 5 = 11.
How can the Commutative Property help with mental math?
If you find it easier to add 10 + 2 than 2 + 10, you can rearrange the addends to use the simpler order. The answer will always be the same.
Does the Commutative Property work for subtraction?
No. Subtraction is not commutative. For example, 10 - 4 = 6, but 4 - 10 = -6. The property only applies to addition and multiplication.
How do you use the Commutative Property to fill in a blank like 28 + 45 = __ + 28?
The blank must be 45. Since a + b = b + a, swapping the positions of 28 and 45 gives 45 + 28, which equals the same sum as 28 + 45.
Can the Commutative Property extend to three numbers?
Yes. For example, 1 + 2 + 3 = 6 is the same as 3 + 2 + 1 = 6. You can shuffle any set of addends and the sum stays the same.