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

102117