1. Objective The student will be able to:
recognize and use the commutative, associative, distributive and identity properties for addition and multiplication in Algebra.

2. **The commutative property does not work for subtraction or division.
Commutative means that the order does not make any difference.
a + b + c = b + c + a
a • b • c = b • a • c
Examples
4 + x + 5= x
z • 3 • ½ = 3 • ½ • z
**The commutative property does not work for subtraction or division.

3. ** The associative property does not work for subtraction or division.
Associative means that the grouping does not make any difference.
(a + b) + c = a + (b + c)
(ab) c = a (bc)
Examples
(1 + 2) + 3 = 1 + (2 + 3)
(2 • 3) • 4 = 2 • (3 • 4)
** The associative property does not work for subtraction or division.

4. When any number is multiplied by 1, it does not change its identity.
Identity Property
When any number is multiplied by 1, it does not change its identity.
a x 1 = a
1 x a = a
Example:
45 x 1 = 45
1 x 123 = 123

5. Distributive Property
the number outside of the parentheses is distributed (multiplied) to the numbers within the parentheses.
2(a + b) = 2a + 2b

6. Distributive Property: with a negative
the negative number outside of the parentheses is distributed (multiplied) to the numbers within the parentheses.
-(a + b) = (-a) + (-b)
-2(a + b) = (-2a + -2b)
-a(2 + b) = -2a + -ab

7. Name the property 1) 5a + (6 + 2a) = 5a + (2a + 6)
commutative (switching order)
2) 5a + (2a + 6) = (5a + 2a) + 6
associative (switching groups)
3) 2(3 + a) = 6 + 2a
distributive

8. Which property would justify rewriting the following expression without parentheses? 3(2x + 5y)
Associative property of multiplication
Distributive property
Addition property of zero
Commutative property of multiplication

9. Which property would justify the following statement? 8x + 4 = 4 + 8x
Associative property of addition
Distributive property
Addition property of zero
Commutative property of addition

10. Which property would justify the following statement
Associative property of addition
Distributive property
Addition property of zero
Commutative property of addition