1. Properties for Addition and Multiplication only
Algebraic Properties
Properties for Addition
and Multiplication only

2. Commutative Property of Addition
The order changes, but not the sum
ex: = 7 + 4
For any number a and b:
a + b = b + a

3. Commutative Property of Multiplication
The order changes, but not the product
ex: 6 • 9 = 9 • 6
For any number a and b:
a • b = b • a

4. Will the Commutative Property work for Subtraction?
How about Division?
Give an example why.

5. Associative Property of Addition=
The way numbers are grouped does not change the sum.
ex: ( ) + 3 = 12 + ( 7 + 3)
For any numbers a, b, and c:
( a + b ) + c = a + ( b + c )

6. Associative Property of Multiplication=
The way numbers are grouped does not change the product.
ex: ( 6 • 2 ) • 5 = 6 • ( 2 • 5)
For any numbers a, b, and c:
( a • b ) • c = a • ( b • c )

7. Will the Associative Property work for Subtraction?
How about Division?
Give an example why.

8. Identity Property of Addition
The sum of zero and any given number will equal that given number.
ex: = 9
For any number a:
a + 0 = a

9. Identity Property of Multiplication
The product of any given number and one will equal that given number.
ex: 9 • 1 = 9
For any number a:
a • 1 = a

10. Will the Identity Property work for Subtraction?
How about Division?
Give an example why.

11. Distributive Property of Multiplication
Distributing multiplication over addition or subtraction
ex: 3( ) = 3(10) + 3(7)
(multiply the number outside the parentheses to each number inside the parentheses)
For any numbers a, b, and c:
a( b + c ) = a(b) + a(c)

12. Multiplicative Property of Zero
The product of zero and any number is…
ZERO
ex: 3 • 0 = 0
For any number a:
a • 0 = 0