Communitive and Associative Properties

Front

What is the Associative Property?

Back

The Associative Property states that the way in which numbers are grouped in addition or multiplication does not change their sum or product. For example, (a + b) + c = a + (b + c) and (a × b) × c = a × (b × c).

Front

What is the Commutative Property?

Back

The Commutative Property states that the order in which two numbers are added or multiplied does not change their sum or product. For example, a + b = b + a and a × b = b × a.

Front

What is the Distributive Property?

Back

The Distributive Property states that a number multiplied by a sum is equal to the sum of the individual products. For example, a(b + c) = ab + ac.

Front

Provide an example of the Associative Property of Addition.

Back

Example: (2 + 3) + 4 = 2 + (3 + 4). Both expressions equal 9.

Front

Provide an example of the Commutative Property of Multiplication.

Back

Example: 4 × 5 = 5 × 4. Both expressions equal 20.

Front

What is the Identity Property of Addition?

Back

The Identity Property of Addition states that adding zero to any number does not change the number. For example, a + 0 = a.

Front

What is the Identity Property of Multiplication?

Back

The Identity Property of Multiplication states that multiplying any number by one does not change the number. For example, a × 1 = a.

Front

Are the expressions 2 • (3 • 7) and (2 • 3) • 7 equivalent?

Back

Yes, because of the Associative Property.

Front

Are the expressions (-2 + 3) + 6 and -2 + (3 + 6) equivalent?

Back

Yes, because of the Associative Property.

Front

What is the result of applying the Distributive Property to -2(x - y)?

Back

-2(x - y) = -2x + 2y.