Properties of Addition and Multiplication

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) 5 + 4 = 3 + 6 9 = 9

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

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

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

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

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

Distributive Property a(b + c) = ab + ac a(b – c) = ab - ac 3(4 + 2) = 3 ∙ 4 + 3 ∙ 2 3(6) = 12 + 6 18 = 18

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 ∙ 5 + 3 ∙ 2 3 ∙ 9 = 9 ∙ 3 Commutative Property of Multiplication 5 ∙(3 ∙ 1) = (5 ∙ 3) ∙ 1 Associative Property of Multiplication