1. 1.2 Commutative, Identity, and Associative Properties
We will write equivalent expressions using the properties

2. Vocabulary: Equivalent Expression:
Expressions that have equal values for the same replacement values of their variables

3. Commutative Properties
Multiplication Rule: Ex:
Addition Rule: Ex:

4. To commute means to move
The news talks about the daily commute on the freeway.
Think about how the cars move this will help you to remember commutative property is when the numbers move!

5. Write an equivalent expression using the commutative prop
7 + 11
3 +x 5y

6. Why is the Commutative Property helpful?
It can help you to do more simple calculations

7. For Example:
264
200

8. Mental Math 72 8

9. Multiplication Rule: Ex:
Identity Properties
Addition
Rule: a + 0 = a
Ex: = 7
Multiplication Rule: Ex:

10. Identity is who you are
Same with numbers. We want to be able to do an operation (such as +0 or mult by 1) and get the same thing back, its identity

11. Equivalent Expressions
(Using the Identity Property of Multiplication)
Do you reduce this???

12. Answer is: NO!!!! Usually we reduce everything!
We reduce when the directions say to:
Simplify
Evaluate
Solve
Calculate (add, sub, mult, divide)
When the directions say to write an equivalent expression we do not reduce

13. Equivalent Expressions

14. (Parenthesis) around different pairs of numbers
The Associative Property
Of Addition
(Parenthesis) around different pairs of numbers
Rule: (a + b) + c = a + (b + c)
Ex: (5 + 2) + 3 = 5 + (2 + 3)

15. (Parenthesis) around different pairs of numbers
The Associative Property
Of Multiplication
(Parenthesis) around different pairs of numbers
Rule: (a • b) • c = a • (b • c)
Ex: (2 • 3) • 5 = 2 • (3 • 5)

16. Associative: To associate( ) + + + ( ) +

17. Use the Commutative and Associative Property to write three equivalent expressions
(b+a) +2
a+ (b+2)
2+ (a+b)

18. Assignment: Page 14 (1 – 14 ) all Page 22 (31-34) all Page 22 (36-42) even