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

4 + 3 = 3 + 4a + b = b + a

Commutative Property of Multiplication

4 3 = 3 4a 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!

a 0 a

NOTE: 0 is called the identity of addition

Identity Property of Addition

6 + 0 = 6x + 0 = x

Identity Property of Multiplication

6 • 1 = 6x • 1 = x

Zero Property of Multiplication

6 • 0 = 0x • 0 = 0

4. Zero Property (of Multiplication)

• Any number multiplied by 0 equals 0!a0 0

9 0 0

8,823, 427 0 0

1,000,000 0 0

5. Inverse Property• Additive Inverse Property--a number

plus its opposite equals 0.a ( a) 0

9 ( 9) 0

9.3 9.3 0

5 ( 5) 0

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

2 1

21

1

55 1

3 1

3 1

1.)

Commutative for Addition

96 + 4 = 4 + 96

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) =