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Commutative & Associative Properties


“Commute” ative Property

Commutative Property

  

True for addition True for multiplication Changing the order or direction does not affect the sum (addition) or the product (multiplication).

Commutative Property


Example 1: Addition

Example 2: Multiplication

5 + 7 = 12 7 + 5 = 12

5 * 7 = 35 7 * 5 = 35

Example 3: Subtraction

Example 4: Division

7–5=2 5 – 7 = -2

7 ÷ 5 = 7/5 5 ÷ 7 = 5/7

Notice that the Commutative Property is not applicable to subtraction and division where order and direction are critical.

Commutative Property


Who am I grouped with?

Associative Property

  

True for addition True for multiplication Changing how they are grouped does not affect the sum (addition) or the product (multiplication).

Associative Property


Example 1: Addition

(3 + 5) + 7 8+7 15

Example 2: Multiplication

3 + (5 + 7) 3 + 12 15

Example 3: Subtraction

(10 – 7) – 4 3–4 -1

10 – (7 – 4) 10 – 3 7

(4 * 5) * 6 20 * 6 120

4 * (5 * 6) 4 * 30 120

Example 4: Division

(8 ÷ 4) ÷ 2 2÷2 1

8 ÷ (4 ÷ 2) 8÷2 4

Notice that the Associative Property is not applicable to subtraction and division where order and direction are critical.

Associative Property


Wrap Up

Commutative Property Applies to: •Addition •Multiplication

Does not apply to: •Subtraction •Division

Associative Property Applies to: •Addition •Multiplication

Does not apply to: •Subtraction •Division

Commutative and Associative Properties  

Students will understand how to apply the Commutative and Associative Properties

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