1. Properties of Addition and Multiplication

2. Associative Property of Addition
Changing the grouping of the numbers does not change the sum
(a + b) + c = a + (b + c)
(3 + 2) + 4 = 3 + (2 + 4)
= 3 + 6
9 = 9

3. Associative Property of Multiplication
Changing the grouping of the numbers does not change the product
(a ∙ b) ∙ c = a ∙ (b ∙ c)
(3 ∙ 2) ∙ 4 = 3 ∙ (2 ∙ 4)
6 ∙ 4 = 3 ∙ 8
24 = 24

4. Commutative Property of Addition
The order of numbers does not change the sum
a + b = b + a
4 + 7 = 7 + 4
11 = 11

5. Commutative Property of Multiplication
The order of numbers does not change the product
a ∙ b = b ∙ a
4 ∙ 7 = 7 ∙ 4
28 = 28

6. Identity Property of Addition
The sum of a number and the additive identity, zero, if the number.
a + 0 = a
4 + 0 = 4

7. Identity Property of Multiplication
The product of a number and the multiplicative identity, one, if the number.
a ∙ 1 = a
4 ∙ 1 = 4

8. Distributive Property
a(b + c) = ab + ac
a(b – c) = ab - ac
3(4 + 2) = 3 ∙ ∙ 2
3(6) =
18 = 18

9. Try to figure out which property is represented
8 + 5 = 5 + 8
Commutative Property of Addition
2 ∙ 1 = 2
Identity Property of Multiplication
Associative Property of Addition
7 + (2 + 3) = (7 + 2) + 3
Distributive Property
3(5 + 2) = 3 ∙ ∙ 2
3 ∙ 9 = 9 ∙ 3
Commutative Property of Multiplication
5 ∙(3 ∙ 1) = (5 ∙ 3) ∙ 1
Associative Property of Multiplication