Main Idea and Vocabulary Key Concept Distributive Property

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

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

Write Sentences as Equations Use the Distributive Property to evaluate the expression 8(5 + 7) = 8(5) + 8(7) Distributive Property = 40 + 56 Multiply. = 96 Add. Answer: 96

Use the Distributive Property to evaluate the expression 4(6 + 3). A. 9 B. 12 C. 27 D. 36

Write Sentences as Equations Use the Distributive Property to evaluate the expression 6(9) + 6(2) = 6(9 + 2) Answer: 66 Distributive Property = 6(11) Add. = 66 Multiply.

Use the Distributive Property to evaluate the expression (5 + 3)7. A. 8 B. 26 C. 56 D. 105

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. = 6(100) + 6(50) Distributive Property = 600 + 300 Multiply. = 900 Add. Answer: Mr. Harmon will spend about $900 on a six-day vacation.

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? A. $2. 50 B. $62. 50 C. $150 D. $162. 50

Use Properties to Evaluate Expressions Find 5 ● 13 ● 20 mentally. Justify each step. 5 ● 13 ● 20 = 5 ● 20 ● 13 = (5 ● 20) ● 13 Commutative Property of Multiplication Associative Property of Multiplication = 100 ● 13 or 1, 300 Multiply 100 and 13 mentally. Answer: 1, 300

Name the property shown by the statement 4 + (6 + 2) = (4 + 6) + 2. A. Associative Property of Addition B. Commutative Property of Addition C. Identity Property of Addition D. A and B