The commutative property applies to addition and multiplication. It states that the order of the numbers does not change the result of the operation.

a + b = b + a

For example, 3 + 4 = 4 + 3

a * b = b * a

For example, 2 * 5 = 5 * 2

The associative property also applies to addition and multiplication. It states that the grouping of the numbers does not change the result of the operation.

(a + b) + c = a + (b + c)

For example, (2 + 3) + 4 = 2 + (3 + 4)

(a * b) * c = a * (b * c)

For example, (2 * 3) * 4 = 2 * (3 * 4)

- Understand the commutative property for addition and multiplication.
- Understand the associative property for addition and multiplication.
- Practice identifying examples of the commutative and associative properties in simple arithmetic problems.
- Create your own examples to demonstrate the commutative and associative properties.
- Apply these properties to solve more complex math problems.

Study GuideCommutative/Associative Properties Worksheet/Answer key

Commutative/Associative Properties Worksheet/Answer key

Commutative/Associative Properties Worksheet/Answer key

Commutative/Associative Properties Worksheet/Answer keyCommutative/Associative Properties

Number and Operations (NCTM)

Understand meanings of operations and how they relate to one another.

Use the associative and commutative properties of addition and multiplication and the distributive property of multiplication over addition to simplify computations with integers, fractions, and decimals.

Connections to the Grade 6 Focal Points (NCTM)

Algebra: Students use the commutative, associative, and distributive properties to show that two expressions are equivalent. They also illustrate properties of operations by showing that two expressions are equivalent in a given context (e.g., determining the area in two different ways for a rectangle whose dimensions are x + 3 by 5). Sequences, including those that arise in the context of finding possible rules for patterns of figures or stacks of objects, provide opportunities for students to develop formulas.