Properties and Identities

How can we do what we do

Properties

Commutative Property

• Works for addition or multiplication

• It doesn’t matter what order you put numbers or variables in, as long as they are all addition or all multiplication

• 5 + 3 = 8 3 + 5 = 8 A + B = B + A

• 2 x 3 = 6 3 x 2 = 6 A x B = B x A

Associative Property

• Works for addition or multiplication• It doesn’t matter how you group numbers or variables, as

long as they are all addition or all multiplication

• 2 + (3 + 4) = 9 (2 + 3) + 4 = 9

• (A + B) + C = A + (B + C)

• 2 x (3 x 4) = 24 (2 x 3) x 4 = 24

• (A x B) x C = A x (B x C)

Distributive Property

• Used when there is a common multiple or a common factor

• 2(4 + 3) = (2 x 4) + (2 x 3)

• A(B + C) = AB + AC

Identity

• An Identity is used when the number doesn’t change

• In addition: 6 + 0 = 6 A + 0 = A

• In multiplication 5 x 1 = 5 A x 1 = A