10.3 - Commutative and Associative Properties

Front

What is the associative property of addition?

Back

The associative property of addition states that the way in which numbers are grouped when adding does not change the sum. For example, (a + b) + c = a + (b + c).

Front

What is the commutative property of addition?

Back

The commutative property of addition states that the order in which two numbers are added does not change the sum. For example, a + b = b + a.

Front

What is the associative property of multiplication?

Back

The associative property of multiplication states that the way in which numbers are grouped when multiplying does not change the product. For example, (a × b) × c = a × (b × c).

Front

What is the commutative property of multiplication?

Back

The commutative property of multiplication states that the order in which two numbers are multiplied does not change the product. For example, a × b = b × a.

Front

Provide an example of the associative property of addition.

Back

An example of the associative property of addition is (2 + 3) + 4 = 2 + (3 + 4).

Front

Provide an example of the commutative property of multiplication.

Back

An example of the commutative property of multiplication is 4 × 5 = 5 × 4.

Front

What does it mean if an operation is associative?

Back

If an operation is associative, it means that the grouping of the numbers does not affect the result of the operation.

Front

What does it mean if an operation is commutative?

Back

If an operation is commutative, it means that the order of the numbers does not affect the result of the operation.

Front

Which property is shown in the equation (x + y) + z = x + (y + z)?

Back

This equation demonstrates the associative property of addition.

Front

Which property is shown in the equation 5 x 2 = 2 x 5?

Back

This equation demonstrates the commutative property of multiplication.