By: Deia Sanders

2e Identify the following properties using variables and apply them in solving problems.

(DOK 1)

• Zero property of multiplication• Inverse operations of addition/subtraction and multiplication/division• Commutative and associative properties of addition and multiplication• Identity properties of addition and multiplication• Distributive properties of multiplication over addition and subtraction

Commutative Property

Change Order

Examples: a + b = b + a

or a • b = b • a or ab = ba

Associative Property

Who you “associate “ with is your GROUP of friends

Examples: a + (b + c) = (a + b) + c

or a • (b • c) = (a • b) • c

or a(bc) = (ab)c

Identity Property

The number keeps it’s identity

Examples: a + 0 = a

or a • 1 = a

Distributive Property

The number outside the parenthesis gets distributed to everything inside

the parenthesis

Examples: a(b + c) = ab + ac

or ab + ac = a(b + c)

Most important

Property!!!

Zero Property of Multiplication

Any number multiplied by zero equals ZERO

Examples: 0(3x + 2y) = 0

or(3 • 0)(2 + 4) = 0 • 6 = 0

Inverse of Addition

Adding opposites equals zero

Examples: 2 – 2 = 0

or -3x + 3x = 0

Inverse of Multiplication

Multiplying by an inverse (reciprocal)

equals 1

Examples: 1

2

12

or

12

3

3

2x

x

Identify the Property

3x(y + 2) = 3xy + 6x Distributive

3x – 3x + 2y = 0 + 2y Inverse of Addition

0 + 2y = 2y Identity of Addition

2(3 + y) + 8 = 6 + 2y + 8 Distributive

6 + 8 + 2y = 8 + 6 + 2yThis simplifies to 14 + 2y Commutative

Identify the Property

1(2x + 3y) = 2x + 3y Identity of Multiplication

(3x)(5x – 2z)(0) = 0 Zero Property of Multiplication

(2x – 4y) + 0 = 2x-4y Identity Property of Addition

3x – 2y + 2y = 3x Inverse Property of Addition

Complete Handout #1

page 73