Splash Screen. Lesson Menu Main Idea and Vocabulary Key Concept: Distributive Property Example 1:Write Sentences as Equations Example 2:Write Sentences.

Main Idea and Vocabulary

Key Concept: Distributive Property

Example 1: Write Sentences as Equations

Example 2:Write Sentences as Equations

Example 3:Real-World Example

Concept: Summary: Real Number Properties

Example 4:Use Properties to Evaluate Expressions

• equivalent expressions

• properties

• Use Commutative, Associative, Identity, and Distributive properties to solve problems.

Write Sentences as Equations

Use the Distributive Property to evaluate the expression 8(5 + 7).

Answer: 96

8(5 + 7) = 8(5) + 8(7) Distributive Property

= 40 + 56 Multiply.

= 96 Add.

A. 9

B. 12

C. 27

D. 36

Use the Distributive Property to evaluate the expression 4(6 + 3).

Write Sentences as Equations

Use the Distributive Property to evaluate the expression 6(9) + 6(2).

Answer: 66

6(9) + 6(2) = 6(9 + 2)Distributive Property

= 6(11) Add.

= 66Multiply.

A. 8

B. 26

C. 56

D. 105

Use the Distributive Property to evaluate the expression (5 + 3)7.

VACATIONS Mr. Harmon has budgeted $150 per day for his hotel and meals during his vacation. If he plans to spend six days on vacation, how much will he spend?

You can find how much Mr. Harmon will spend over the six-day period by finding 6 × 150. You can use the Distributive Property to multiply mentally.

6(150) = 6(100 + 50) Rewrite 150 as 100 + 50.

Answer: Mr. Harmon will spend about $900 on a six-day vacation.

= 6(100) + 6(50) Distributive Property

= 600 + 300 Multiply.

= 900 Add.

A. $2.50

B. $62.50

C. $150

D. $162.50

COOKIES Heidi sold cookies for $2.50 per box for a fundraiser. If she sold 60 boxes of cookies, how much money did she raise?

Find 5 ● 13 ● 20 mentally. Justify each step.

Answer: 1,300

Use Properties to Evaluate Expressions

5 ● 13 ● 20 = 5 ● 20 ● 13 Commutative Property of Multiplication

= (5 ● 20) ● 13 Associative Property of Multiplication

= 100 ● 13 or 1,300 Multiply 100 and 13 mentally.

A. Associative Property of Addition

B. Commutative Property of Addition

C. Identity Property of Addition

D. A and B

Name the property shown by the statement 4 + (6 + 2) = (4 + 6) + 2.