Commutative property of addition

Definition

The commutative property of addition states that changing the order of addends does not change their sum. Mathematically, it is expressed as $a + b = b + a$.

5 Must Know Facts For Your Next Test

1. The commutative property applies only to addition and multiplication, not to subtraction or division.
2. It helps simplify algebraic expressions and solve equations more flexibly.
3. This property is fundamental in proving other algebraic properties and theorems.
4. In matrix operations, the commutative property of addition holds for matrices of the same dimensions.
5. $7 + 3 = 3 + 7$ is a simple numerical example illustrating this property.

Review Questions

• What does the commutative property of addition state?
• Does the commutative property apply to subtraction or division?
• Provide an example showing how the commutative property of addition works with algebraic expressions.

Related terms

Associative Property: A property that states the way in which numbers are grouped in an operation does not change their result, e.g., $(a + b) + c = a + (b + c)$.

Distributive Property: A property indicating that multiplying a sum by a number gives the same result as multiplying each addend individually by the number and then adding the products, e.g., $a(b+c)=ab+ac$.

Identity Property: A property stating that any number plus zero is itself $(a+0=a)$ and any number times one is itself $(a \times 1=a)$.