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
HWK: p 6

2. EQ: How do I identify properties of rational numbers and use them to simplify numerical expressions?
M7P1c Adapt and apply a variety of
appropriate strategies to solve problems

3. Vocabulary Commutative Property Associative Property Identity Property
Distributive Property

7. 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
Associative Property
Identity Property
Commutative Property

8. 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)
Identity Property
Commutative Property
Associative Property

9. 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

10. 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

11. 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.

12. 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.

13. 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.

14. TOTD Identity Property Associative Property Commutative Property 1,200
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

15. 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