1. Commutative and Associative Properties of Real Numbers

2. Commutative Property of Addition 3 + 2 = 2 + 3 5 = 5 In general, a + b = b + a The order in which you add does not matter.

3. Commutative Property of Multiplication 5∙ 10 = 10 ∙ 5 50 = 50 In general, a ∙ b = b ∙ a The order in which you multiply does not matter.

4. The Commutative Property does not hold for subtraction and division. Look at the following examples: 1) Does 8 – 3 = 3 – 8 ? 5 ≠ -5 No! 2) Does 8 ÷ 4 = 4 ÷ 8 ? 2 ≠ ½ No! If you change the order in a subtraction or division problem, you get a different answer.

5. Summaryof the Commutative Property The Commutative Property has to do with the order of the numbers. Holds true for Addition and Multiplication Does NOT hold true for Subtraction and Division

6. Associative Property of Addition (a + b) + c = a + (b+ c) (2 + 3) + 4 = 2 + (3 + 4) 5 + 4 = 2 + 7 9 = 9 It does not matter how the addends are grouped. It changes the order in which you add them, but the answer is the same. of Multiplication (a ∙ b) ∙ c = a ∙ (b ∙ c) (2 ∙ 3) ∙ 4 = 2 ∙ (3 ∙ 4) 6 ∙ 4 = 2 ∙12 24 = 24 It does not matter how the factors are grouped. It changes the order in which you multiply them, but the answer is the same.

7. The Associative Property does not hold for subtraction and division. Look at the following examples: 1) Does (9 – 5) – 3 = 9 – (5 – 3) ? 4 – 3 = 9 – 2 1 ≠ 7 No! 2) Does (8 ÷ 4 ) ÷ 2 = 8 ÷ (4 ÷ 2) ? 2 ÷ 2 = 8 ÷2 1 ≠ 4 No!

8. Summary of the Associative Property The Associative Property has to do with how the numbers are grouped together and therefore which pair you operate on first. Holds true for Addition and Multiplication Does not hold true for Subtraction and Division

9. Identify the Property Shown 17 + 43 = 43 + 17 (4 ∙ 5) ∙ 2 = 4 ∙ (5 ∙ 2) (8 + 3) + 5 = (3 + 8) + 5 (7 + 2) + 3 = 2 + (7 + 3)