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
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