1-2 Properties of Numbers

Warm UpWarm Up

Lesson PresentationLesson PresentationProblem of the DayProblem of the Day

Lesson Quizzes

1-2 Properties of Numbers

Warm UpEvaluate.

1. 2 + 5 3 – 72. 5(3 – 1) ÷ (3 + 2)3. (4 + 1)2 – 8 ÷ 24. 12 ÷ 3 6 – 20

10

2214

1-2 Properties of Numbers

Problem of the DayDaniel 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

1-2 Properties of Numbers

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

1-2 Properties of Numbers

VocabularyCommutative PropertyAssociative PropertyIdentity PropertyDistributive Property

1-2 Properties of Numbers

1-2 Properties of Numbers

1-2 Properties of Numbers

1-2 Properties of NumbersAdditional Example 1: Identifying Properties of Addition

and MultiplicationTell 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 numbers is switched.Commutative Property

1-2 Properties of NumbersCheck 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

1-2 Properties of NumbersAdditional Example 2: Using Properties to Simplify

ExpressionsSimplify 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.

= 46Add.

20 9 5 = 20 5 9 Commutative Property.= 20 (5 9)= 20 45

Associative Property.

= 900Multiply.

1-2 Properties of NumbersCheck 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.

= 34Add.

12 3 5 = 3 5 12 Commutative Property.= 3 (5 12)= 3 60

Associative Property.

= 180Multiply.

1-2 Properties of Numbers

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.

1-2 Properties of NumbersAdditional Example 3: Using the Distributive Property

to Multiply MentallyUse 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)

1-2 Properties of NumbersCheck 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)

1-2 Properties of Numbers

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

1-2 Properties of NumbersLesson Quiz

Tell which property is represented.

1. 17 1 = 172. (12 + 14) + 5 = 12 + (14 + 5)3. 2 16 = 16 2

Simplify each expression. Justify each step.4. 4 12 255. 48 + (15 + 2)

Use the Distributive Property to find each product.6. 6 (12 + 5)7. (20 – 7) 9

Identity PropertyAssociative Property

Commutative Property

1,20065

102117

1-2 Properties of Numbers

1. Identify the property that is represented.(21 + 16) + 7 = 21 + (16 + 7)

A. Identity PropertyB. Associative PropertyC. Commutative PropertyD. Distributive Property

Lesson Quiz for Student Response Systems

1-2 Properties of Numbers

2. Identify the property that is represented.17 · 9 = 9 · 17

A. Associative PropertyB. Commutative PropertyC. Distributive PropertyD. Identity Property

Lesson Quiz for Student Response Systems

1-2 Properties of Numbers

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 · 11 Multiply.= 1,100

B. 20 · 11 · 5 = 11 · 20 · 5 Commutative Property= (11 · 20) · 5 Associative Property= 110 · 5 Multiply.= 550

Lesson Quiz for Student Response Systems

1-2 Properties of Numbers4. Simplify the expression 53 + (11 + 7). Then

identify the correct justification for each step.

A. 53 + (11 + 7) = 11 + (53 + 7) Associative Property

= (11 + 53) + 7 Commutative Property

= 60 + 7Add.

= 67B. 53 + (11 + 7) = 53 + (7 + 11) Commutative

Property= (53 + 7) + 11 Associative

Property= 60 + 11

Add.= 71

Lesson Quiz for Student Response Systems

1-2 Properties of Numbers

5. Use the Distributive Property to identify the product of 8(20 + 2).

A. 196B. 113C. 176D. 85

Lesson Quiz for Student Response Systems