Associative/Communative

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 the sum or product. For example, a + b = b + a and a × b = b × a.

Front

What is the Associative Property?

Back

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

Front

Example of Commutative Property of Addition: 7 + (6 + 3) = ?

Back

7 + (3 + 6) (This shows that the order of addition does not affect the result.)

Front

Example of Commutative Property of Multiplication: 3 × 4 = ?

Back

4 × 3 (This shows that the order of multiplication does not affect the result.)

Front

What is the Distributive Property?

Back

The Distributive Property states that a(b + c) = ab + ac. It allows you to multiply a number by a sum by distributing the multiplication over each addend.

Front

What is the Inverse Property?

Back

The Inverse Property states that for every number a, there exists an additive inverse (-a) such that a + (-a) = 0, and a multiplicative inverse (1/a) such that a × (1/a) = 1.

Front

If 16 • 4 = ?, what is the equivalent expression using the Commutative Property?

Back

4 • 16 (This shows that the order of multiplication does not affect the product.)

Front

What is an example of the Associative Property of Addition?

Back

(2 + 3) + 4 = 2 + (3 + 4) (This shows that the grouping of numbers does not affect the sum.)

Front

If a + 5 = 5 + 9, what is the value of a?

Back

9 (This shows how to use the Commutative Property to solve for a.)

Front

Find an equivalent expression using the Commutative property: 4 x 3 x 5 = ?

Back

5 x 4 x 3 (This shows that the order of multiplication can be changed.)