Properties A property is something that is true for all situations.

Six Properties of Addition and Multiplication 1.Distributive 2.Commutative 3.Associative 4.Identity 5.Inverse 6.Multiplicative Property of Zero

Distributive Property A(B + C) = AB + AC 4(3 + 5) =

Commutative Property of addition and multiplication Order doesn’t matter A B = B A A + B = B + A CO = Change Order

Associative Property of multiplication and Addition Addition  (a + b) + c = a + (b + c) Example: (6 + 4) + 3 = 6 + (4 + 3) Multiplication  (a · b) · c = a · (b · c) Example: (6 · 4) · 3 = 6 · (4 · 3) SO = Same Order

Identity Properties If you add 0 to any number, the number stays the same. A + 0 = A or = 5 If you multiply any number times 1, the number stays the same. A 1 = A or 5 1 = 5

Inverse Properties Addition: a + -a = 0 or =0 Multiplication: a 1 = 1 or 5 1 = 1 a 5

Multiplicative Property of Zero Any number times zero will give you the product of 0 (zero) a 0 = = 0 or 0 4=0

(2 + 1) + 4 = 2 +(1 + 4) Associative Property of Addition

3 + 7 = Commutative Property of Addition

8 + 0 = 8 Identity Property of Addition

6 4 = 4 6 Commutative Property of Multiplication

17 + (-17) = 0 Inverse Property of Addition

2(5) = 5(2) Commutative Property of Multiplication

3(2 + 5) = Distributive Property

6(78) = (67)8 Associative Property of Multiplication

5 1 = 5 Identity Property of Multiplication

(6 – 3)4 = 64 – 34 Distributive Property

1(-9) = -9 Identity Property of Multiplication

3 + (-3) = 0 Inverse Property of Addition

1 + [-9 + 3] = [1 + (-9)] + 3 Associative Property of Addition

-3(6) = 6(-3) Commutative Property of Multiplication

= -8 Identity Property of Addition

37 – 34 = 3(7 – 4) Distributive Property

6 + [(3 + (-2)] = (6 + 3) +(- 2) Associative Property of Addition

7 + (-5) = Commutative Property of Addition

(5 + 4)9 = Distributive Property

-3(5 4) = (-3 5)4 Associative Property of Multiplication

-8(4) = 4(-8) Commutative Property of Multiplication

ab = ba Commutative Property of Multiplication

a + 0 = a Identity Property of Addition

a(bc) = (ab)c Associative Property of Multiplication

a1 = a Identity Property of Multiplication

a +b = b + a Commutative Property of Addition

a(b + c) = ab + ac Distributive Property

a +(b + c) = (a +b)+ c Associative Property of Addition

a + (-a) = 0 Inverse Property of Addition