Main Idea and New Vocabulary Key Concept Distributive

Main Idea and New Vocabulary Key Concept: Distributive Property Example 1: Evaluate Numerical Expressions Example 2: Evaluate Numerical Expressions Example 3: Use the Distributive Property Example 4: Simplify Algebraic Expressions Example 5: Simplify Algebraic Expressions

• Apply the Distributive Property to rewrite algebraic expressions. • equivalent expressions

Evaluate Numerical Expressions Use the Distributive Property to evaluate the expression 7(3 + 12) = 7 • 3 + 7 • 12 = 21 + 84 or 105 Answer: 105 Distributive Property Multiply. Then add.

Use the Distributive Property to evaluate the expression 4(9 + 3). A. 4 + 9 + 3; 16 B. 4 • 9 + 3; 39 C. 4 • 9 + 4 • 3; 48 D. 4 • 9 • 3; 108

Evaluate Numerical Expressions Use the Distributive Property to evaluate the expression (8 – 5)11 = 8 • 11 – 5 • 11 = 88 – 55 or 33 Answer: 33 Distributive Property Multiply. Then subtract.

Use the Distributive Property to evaluate the expression (10 – 3)7. A. 10 – 3 • 7; – 11 B. 10 – 3; 7 C. 10 • 7 – 3 • 7; 49 D. 10 • 7 – 3; 67

Use the Distributive Property T-SHIRTS Fifteen students are buying T-shirts that cost $10. 60 each. Use the Distributive Property to find the total cost of the shirts. Rename $10. 60 as $10. 00 + $0. 60. Then use the Distributive Property to find the total cost mentally. 15($10 + $0. 60) = 15 • 10 + 15 • 0. 6 Distributive Property = 150 + 9 Multiply. = 159 Subtract. Answer: The total cost of the shirts is $159.

PHOTOS Twenty volleyball players and coaches are buying a group photo of their championship win. Each photo costs $14. 30. Use the Distributive Property to find the total cost of the photos. A. $206 B. $280. 30 C. $286 D. $396

Simplify Algebraic Expressions Use the Distributive Property to rewrite the expression (a + 9)4 = a(4) + 9(4) = 4 a + 36 Answer: 4 a + 36 Distributive Property Simplify.

Use the Distributive Property to rewrite the expression (d – 6)5. A. 5 d – 6 B. 5 d – 30 C. 5 d + 6 D. d – 30

Simplify Algebraic Expressions Use the Distributive Property to rewrite the expression 8(3 – t) = 8[3 + (–t)] Rewrite 3 – t as 3 + (–t). = 8(3) + 8(–t) Distributive Property = 24 + (– 8 t) Simplify. = 24 – 8 t Definition of subtraction Answer: 24 – 8 t

Use the Distributive Property to rewrite the expression 4(9 – a). A. 36 – a B. 36 – 4 a C. 9 – 4 a D. 36 + 4 a