Course 2
1-6 Properties1-6 Properties
Course 2
Warm UpWarm Up
Problem of the DayProblem of the Day
Lesson PresentationLesson Presentation
Course 2
1-6 Properties
Warm UpEvaluate.
1. 2 + 5 3 – 7
2. 5(3 – 1) ÷ (3 + 2)
3. (4 + 1)2 – 8 ÷ 2
4. 12 ÷ 3 6 – 20
10
2
21
4
Course 2
1-6 Properties
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
Course 2
1-6 Properties
Learn how to identify properties of rational numbers and use them to simplify numerical expressions.
Course 2
1-6 Properties
VocabularyCommutative PropertyAssociative PropertyIdentity PropertyDistributive Property
Course 2
1-6 Properties
Course 2
1-6 Properties
Course 2
1-6 Properties
Course 2
1-6 Properties
Additional Example 1: Identifying Properties of Addition and Multiplication
Tell which property is represented.
A. (2 6) 1 = 2 (6 1)
B. 3 + 0 = 3
C. 7 + 9 = 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 variables is switched.Commutative Property
Course 2
1-6 Properties
Check It Out: Example 1
Tell which property is represented.
A. 7 1 = 7
B. 3 + 4 = 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
Course 2
1-6 Properties
Additional Example 2: Using Properties to Simplify Expressions
Simplify each expression. Justify each step.
A. 21 + 16 + 9
B. 20 9 5
21 + 16 + 9 = 16 + 9 + 21 Commutative Property.
= 16 + (9 + 21)
= 16 + 30
Associative Property.
= 46
Add.
20 9 5 = 20 5 9 Commutative Property.
= 20 (5 9)
= 20 45
Associative Property.
= 900
Multiply.
Course 2
1-6 Properties
Check It Out: Example 2A & B
Simplify each expression. Justify each step.
A. 17 + 14 + 3
B. 12 3 5
17 + 14 + 3 = 14 + 17 + 3 Commutative Property.
= 14 + (17 + 3)
= 14 + 20
Associative Property.
= 34
Add.
12 3 5 = 3 5 12 Commutative Property.
= 3 (5 12)
= 3 60
Associative Property.
= 180
Multiply.
Course 2
1-6 Properties
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.
Course 2
1-6 Properties
Additional Example 3: Using the Distributive Property to Multiply Mentally
Use the Distributive Property to find 6(54).
Method 1:
Method 2:
= (6 50) + (6 4)
Rewrite 54 as 50 + 4.
= 300 + 24
= 324
Use the Distributive Property.
Multiply.
6(54) = 6(60 – 6) Rewrite 54 as 60 – 6.
= (6 60) – (6 6)
= 360 - 36
Use the Distributive Property. Multiply.
= 324 Subtract.
Add.
6(54) = 6(50 + 4)
Course 2
1-6 Properties
Check It Out: Example 3
Use the Distributive Property to find 8(19).
Method 1:
Method 2:
= (8 10) + (8 9)
Rewrite 19 as 10 + 9.
= 80 + 72
= 152
Use the Distributive Property.
Multiply.
8(19) = 8(20 – 1) Rewrite 19 as 20 – 1.
= (8 20) – (8 1)
= 160 – 8
Use the Distributive Property. Multiply.
= 152 Subtract.
Add.
8(19) = 8(10 + 9)
Course 2
1-6 Properties
Lesson QuizTell which property is represented.
1. 17 1 = 17
2. (12 + 14) + 5 = 12 + (14 + 5)
3. 2 16 = 16 2
Simplify each expression. Justify each step.
4. 4 12 25
5. 48 + (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
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