1. 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

2. Problem of the Day
Daniel usually buys 6 bottles of water and 3 apples when he goes to the grocery store. Next time he goes, he will buy three times as many of each. How many items will Daniel buy? 27

3. Learn how to identify properties of numbers and use them to simplify numerical expressions.

4. Vocabulary Commutative Property Associative Property Identity Property
Distributive Property

8. Tell which property is represented. A. (2  6)  1 = 2  (6  1)
Additional 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 factors is 0.
Identity Property
7 + 9 = 9 + 7
The order of the numbers is switched.
Commutative Property

9. Tell which property is represented. A. 7  1 = 7
Check It Out: Example 1
Tell which property is represented.
A. 7  1 = 7
B = 4 + 3
C. (5  1)  2 = 5  (1  2)
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

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. Check It Out: Example 2A & B
Simplify each expression. Justify each step. A
B. 12  3  5 =
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

12. 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.

13. 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. =
= 324
Subtract.

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 Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems

16. 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

17. Lesson Quiz for Student Response Systems
1. Identify the property that is represented.
( ) + 7 = 21 + (16 + 7)
A. Identity Property
B. Associative Property
C. Commutative Property
D. Distributive Property

18. Lesson Quiz for Student Response Systems
2. Identify the property that is represented.
17 · 9 = 9 · 17
A. Associative Property
B. Commutative Property
C. Distributive Property
D. Identity Property

19. Lesson Quiz for Student Response Systems
3. Simplify the expression 20 · 11 · 5. Then identify the correct justification for each step.
A. 20 · 11 · 5 = 20 · 5 · 11 Commutative Property
= (20 · 5) · 11 Associative Property
= 100 · Multiply.
= 1,100
B. 20 · 11 · 5 = 11 · 20 · 5 Commutative Property
= (11 · 20) · 5 Associative Property
= 110 · Multiply.
= 550

20. Lesson Quiz for Student Response Systems
4. Simplify the expression 53 + (11 + 7). Then identify the correct justification for each step.
A (11 + 7) = 11 + (53 + 7) Associative Property
= ( ) Commutative Property
= Add.
= 67
B (11 + 7) = 53 + (7 + 11) Commutative Property
= (53 + 7) Associative Property
= Add.
= 71

21. Lesson Quiz for Student Response Systems
5. Use the Distributive Property to identify the product of 8(20 + 2).
A. 196
B. 113
C. 176
D. 85