Associative, Commutative and Distributive Properties
Associative Property of Addition and Multiplication
The grouping of numbers can be changed, yet the result will be the same.
Ex: (1 + 9) + 7 = 1 + (9 + 7)
(1 + 9) + 7 = 17
1 + (9 + 7) = 17
(1 x 9) x 7 = 1 x (9 x 7)
(1 x 9) x 7 = 63
1 x (9 x 7) = 63
Commutative Property of Addition and Multiplication
The order of numbers in an expression can change, yet the result will be the same
Ex: 7 + 3 = 3 + 7
7 + 3 = 10
3 + 7 = 10
6 x 5 = 5 x 6
6 x 5 = 30
5 x 6 = 30
Distributive Property
With the distributive property you multiply a sum by multiplying each addend separately and then adding the products
Ex: 7 x (4 + 3) = (7 x 4) + (7 x 3)
7 x (4 + 3) = 7 x 7 = 49
(7 x 4) + (7 x 3) = 28 + 21 = 49
3 x 27 = (3 x 20) + (3 x 7)
3 x 27 = 81
(3 x 20) + (3 x 7) = 60 + 21 = 81