Properties

1. Commutative Property Commutative Property of Addition and Multiplication- -changing the order in which you add does not change the sum or product.

Commutative Property of Addition = a + b = b + a

Commutative Property of Multiplication 4  3 = 3  4 a  b = b  a

Why isn’t there a commutative property of subtraction or division? 4 – 3  3 – 4 1  –1 2  1 1 2

2. Associative Property Associative Property of Addition and Multiplication - -changing the way the numbers are grouped does not change the sum or product.

Associative Property of Addition (3 + 4) + 5 = 3 + (4 + 5) (a + b) + c = a + (b + c) () () =

Associative Property of Multiplication (3 4) 5 = 3 (4 5) (a b) c = a (b c) () = ()

3. Identity Property Identity Property of Addition-- if you add zero to a number, you get the same number! NOTE: 0 is called the identity of addition

Identity Property of Addition = 6 x + 0 = x

Identity Property of Multiplication 6 1 = 6 x 1 = x

Zero Property of Multiplication 6 0 = 0x 0 = 0

4. Zero Property (of Multiplication) Any number multiplied by 0 equals 0!

5. Inverse Property Additive Inverse Property--a number plus its opposite equals 0.

Inverse Property of Multiplication- -a number multiplied by its reciprocal equals 1.

1.) Commutative for Addition =

2.) (6 + 2) + 4 = 6 + (2 + 4) Associative for Addition

3.) Commutative for Multiplication 7xy = 7yx

4.) Multiplication by Zero Property 5 0 = 0

5.) Associative for Multiplication a(bc) = (ab)c

6.) Identity for Multiplication 2 1 = 2

7.) (1 + 2) + 3 = (2 + 1) + 3 Commutative for Addition

8.) Identity for Addition x + 0 = x

9.) Commutative for Multiplication 5(6) = 6(5)

10.) Associative for Multiplication (3a)(b) = 3(ab)

11.) Rewrite using the commutative property y + 5x5x + y =

12.) Rewrite using the associative property (3 5)x3(5x) =