1. Preview
Warm Up
California Standards
Lesson Presentation

2. Warm Up Evaluate. 1. 2 + 5  3 – 7 2. 5(3 – 1) ÷ (3 + 2) 10
3. (4 + 1)2 – 8 ÷ 2
4. 12 ÷ 3  6 – 20 10 2 21 4

3. AF1.3 Apply algebraic order of operations and the commutative, associative, and distributive properties to evaluate expressions; and justify each step in the process.
California
Standards

4. Vocabulary Commutative Property Associative Property Identity Property
Distributive Property

8. You can use the Distributive Property to multiply numbers mentally by breaking apart one of the numbers and writing it as a sum or difference.

9. Example 1: Identifying Properties of Addition and Multiplication
Tell which property is represented.
A. (2  6)  1 = 2  (6  1)
B = 3
C = 9 + 7
(2  6)  1 = 2  (6  1)
The numbers are regrouped.
Associative Property
3 + 0 = 3
One of the addends is 0.
Identity Property
7 + 9 = 9 + 7
The order of the numbers is switched.
Commutative Property

10. Additional Example 2: Using Properties to Simplify Expressions
Simplify each expression. Justify each step. A
B. 20  9  5 =
Commutative Property
= 16 + (9 + 21)
Associative Property =
Add.
= 46
20  9  5 = 20  5  9
Commutative Property
= 20  (5  9)
Associative Property
= 20  45
Multiply.
= 900

11. Use the Distributive Property to find 6(54). Method 1:
Additional Example 3: Using the Distributive Property to Multiply Mentally
Use the Distributive Property to find 6(54).
Method 1:
Method 2:
6(54) = 6(50 + 4)
Rewrite 54 as
Use the Distributive Property.
= (6  50) + (6  4) =
Multiply.
= 324
Add.
6(54) = 6(60 – 6)
Rewrite 54 as 60 – 6.
= (6  60) – (6  6)
Use the Distributive Property. Multiply.
= 360 – 36
= 324
Subtract.

12. Tell which property is represented. A. 7  1 = 7 *Write in KINB*
Check It Out! Example 1
Tell which property is represented.
A. 7  1 = 7 *Write in KINB*
B = *Write in KINB*
C. (5  1)  2 = 5  (1  2) *Already in KINB*
7  1 = 7
One of the factors is 1.
Identity Property
3 + 4 = 4 + 3
The order of the numbers is switched.
Commutative Property
(5  1)  2 = 5  ( 1  2)
The numbers are regrouped.
Associative Property

13. Simplify each expression. Justify each step. A. 17 + 14 + 3
Check It Out! Example 2
Simplify each expression. Justify each step. A
B. 12  3  5…You try it! =
Commutative Property
= 14 + (17 + 3)
Associative Property =
Add.
= 34
12  3  5 = 3  5  12
Commutative Property
= 3  (5  12)
Associative Property
= 3  60
Multiply.
= 180

14. Use the Distributive Property to find 8(19). Method 1:
Check It Out! Example 3
Use the Distributive Property to find 8(19).
Method 1:
Method 2:
8(19) = 8(10 + 9)
Rewrite 19 as
Use the Distributive Property.
= (8  10) + (8  9) =
Multiply.
= 152
Add.
8(19) = 8(20 – 1)
Rewrite 19 as 20 – 1.
= (8  20) – (8  1)
Use the Distributive Property. Multiply.
= 160 – 8
= 152
Subtract.

15. Lesson Quiz Identity Property Associative Property
Tell which property is represented.
1. 17  1 = 17
2. ( ) + 5 = 12 + (14 + 5)
3. 2  16 = 16  2
Simplify each expression. Justify each step.
4. 4  12  25
(15 + 2)
Use the Distributive Property to find each product.
6. 6  (12 + 5)
7. (20 – 7)  9
Identity Property
Associative Property
Commutative Property
1,200 65
102
117