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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

Commutative and Associative Properties  

Students will understand how to apply the Commutative and Associative Properties

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