1. Properties of Operations
Chapter 5.3
Properties of Operations 

2. Objective
Identify and use mathematical properties to simplify algebraic expressions.

3. Vocab Review
Commutative Property 𝑎+𝑏=𝑏+𝑎 𝑎×𝑏=𝑏×𝑎 Associative Property 𝑎+ 𝑏+𝑐 = 𝑎+𝑏 +𝑐 𝑎∙ 𝑏∙𝑐 = 𝑎∙𝑏 ∙𝑐

4. Vocab
Additive Identity - When zero is added to any number, the sum is the number. 𝑎+0=𝑎 9+0=9 Multiplicative Identity – When any number is multiplied by 1, the product is the number. 𝑎×1=𝑎 2×1=2 Multiplicative Property of Zero – When any number is multiplied by zero, the product is 0. 𝑎×0=0 8×0=0

5. Example 1
Name the property shown by the statement. 2∙ 5∙𝑛 =(2∙5)∙𝑛 The grouping (parenthesis) changed Associative Property of Multiplication

6. Got it? Name the property shown by the statement. 42+𝑥+𝑦=42+𝑦+𝑥
3𝑥+0=3𝑥
Commutative Property of Addition
Additive Identity

7. A counterexample is an example that shows that a conjecture is false.

8. Example 2
State whether the following conjecture is true or false. If false, provide a counterexample. Division of whole numbers is commutative. 15÷3=3÷15 15÷3≠3÷15 The conjecture is false. So, division is not commutative.
True or False?

9. Got it?
The difference of two different whole numbers is always less than both of the two numbers. False 8−2=6 6<2

10. Example 3
Alana wants to buy a sweater that costs $38, sunglasses cost $14, a pair of jeans that costs $22, and a T-shirt that costs $16. Use mental math to find the total cost before tax = = 60+30= 90

11. Got it?
Lance made four phone calls from his cell phone today. The calls lasted 4.7, 9.4, 2.3 and 10.6 minutes. Use mental math to find the total amount of time he spent on his phone.
27 minutes

12. Example 4
Simplify each expression. Justify each step. 7+𝑔 +5 = 𝑔+7 +5 =𝑔+ 7+5 =𝑔+12
Commutative Property of Addition
Associative Property of Addition
Simplify

13. Simplify each expression. Justify each step.
Example 5
Simplify each expression. Justify each step.
(𝑚∙11)∙𝑚
= 11∙𝑚 ∙𝑚
=11∙(𝑚∙𝑚)
=11 𝑚 2
Commutative Property of Multiplication
Associative Property of Multiplication
Simplify

14. Simplify each expression. Justify each step.
Got it?
Simplify each expression. Justify each step.
4∙(3𝑐∙2)

15. Properties of Operations
Chapter 5.3
Properties of Operations 

16. Objective
Identify and use mathematical properties to simplify algebraic expressions.

17. Vocab Review
Commutative Property 𝑎+𝑏=𝑏+𝑎 𝑎×𝑏=𝑏×𝑎 Associative Property 𝑎+ 𝑏+𝑐 = 𝑎+𝑏 +𝑐 𝑎∙ 𝑏∙𝑐 = 𝑎∙𝑏 ∙𝑐

18. Vocab
Additive Identity – 𝑎+0=𝑎 9+0=9 Multiplicative Identity – 𝑎×1=𝑎 2×1=2 Multiplicative Property of Zero – 𝑎×0=0 8×0=0

19. Example 1
Name the property shown by the statement. 2∙ 5∙𝑛 =(2∙5)∙𝑛

20. Got it? Name the property shown by the statement. 42+𝑥+𝑦=42+𝑦+𝑥
3𝑥+0=3𝑥

21. Counterexample
A counterexample is an example that shows that a conjecture is false.

22. Example 2
State whether the following conjecture is true or false. If false, provide a counterexample. Division of whole numbers is commutative. 15÷3=3÷15
True or False?

23. Got it?
The difference of two different whole numbers is always less than both of the two numbers.

24. Example 3
Alana wants to buy a sweater that costs $38, sunglasses cost $14, a pair of jeans that costs $22, and a T-shirt that costs $16. Use mental math to find the total cost before tax.

25. Got it?
Lance made four phone calls from his cell phone today. The calls lasted 4.7, 9.4, 2.3 and 10.6 minutes. Use mental math to find the total amount of time he spent on his phone.
27 minutes

26. Example 4
Simplify each expression. Justify each step. 7+𝑔 +5

27. Example 5
Simplify each expression. Justify each step.
(𝑚∙11)∙𝑚

28. Simplify each expression. Justify each step.
Got it?
Simplify each expression. Justify each step.
4∙(3𝑐∙2)