Download Properties of Addition and Multiplication

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Properties of Addition and
Multiplication
Commutative Property
Definition:
The order in which two numbers are added or
multiplied does NOT change their sum or
product.
Commutative Property
Examples:
Addition: a + b = b + a
2+4=4+2
Multiplication: a · b = b · a
4·6=6·4
Commutative Property
Associative Property
Definition:
The way in which THREE numbers are grouped
when they are added or multiplied does NOT
change their sum or product
Associative Property
Examples:
Addition: a + (b + c) = (a + b) + c
2 + (3 + 4) = (2 + 3) + 4
Multiplication: a · (b · c) = (a · b) · c
4 · (3 · 2) = (4 · 3) · 2
Associative Property
Identity Property
Definition:
The sum of an addend and 0 is the addend. The
product of a factor and 1 is the Factor
Identity Property
Examples:
Addition: a + 0 = a
15 + 0 = 15
Multiplication: a · 1 = a
7·1=7
Identity Property
Distributive Property
Definition:
To multiply a sum by a number, multiply each
addend by the number outside the parentheses
Distributive Property
Examples:
a(b + c) = ab + ac
2(7 + 4) = 2 · 7 + 2 · 4
14 + 8
22
Think about Angry Birds!!!!
Distributive Property
Working with a variable and Distributive Property:
Using the Distributive Property rewrite 2(x + 3)
2(x + 3) = 2 · x + 2 · 3
2x + 6
YOU ARE DONE---can’t simplify any further unless
you are given what x equals. 
Distributive Property
Factoring Each Expression
We learned this when we discussed GCF !!!!!
1) Find GCF- Goes on the outside of parenthesis
2) Find the remaining factors and put them in
parenthesis
12 + 8
GCF = 4 Remaining Factors 4(3) + 4(2)
4(3 + 2)
Re-Cap of Lesson
Properties Math Rap