Holt CA Course 1

1-4 Properties of Numbers

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Holt CA Course 1

1-4 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

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Holt CA Course 1

1-4 Properties of Numbers

Holt CA Course 1

1-4 Properties of Numbers

VocabularyCommutative PropertyAssociative PropertyIdentity PropertyDistributive Property

Holt CA Course 1

1-4 Properties of Numbers

Holt CA Course 1

1-4 Properties of Numbers

Holt CA Course 1

1-4 Properties of Numbers

Holt CA Course 1

1-4 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.

Holt CA Course 1

1-4 Properties of NumbersAdditional 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 addends is 0. Identity Property

7 + 9 = 9 + 7 The order of the numbers is switched. Commutative Property

Holt CA Course 1

1-4 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.

Holt CA Course 1

1-4 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)

Holt CA Course 1

1-4 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

Holt CA Course 1

1-4 Properties of NumbersCheck It Out! Example 2

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.

Holt CA Course 1

1-4 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)

Holt CA Course 1

1-4 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