Main Idea and New Vocabulary Key Concept: Distributive Property

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Presentation transcript:

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 Lesson Menu

Apply the Distributive Property to rewrite algebraic expressions. equivalent expressions Main Idea/Vocabulary

Key Concept

Evaluate Numerical Expressions Use the Distributive Property to evaluate the expression 7(3 + 12). 7(3 + 12) = 7 • 3 + 7 • 12 Distributive Property = 21 + 84 or 105 Multiply. Then add. Answer: 105 Example 1

Use the Distributive Property to evaluate the expression 4(9 + 3). C. 4 • 9 + 4 • 3; 48 D. 4 • 9 • 3; 108 Example 1 CYP

Evaluate Numerical Expressions Use the Distributive Property to evaluate the expression (8 – 5)11. (8 – 5)11 = 8 • 11 – 5 • 11 Distributive Property = 88 – 55 or 33 Multiply. Then subtract. Answer: 33 Example 2

Use the Distributive Property to evaluate the expression (10 – 3)7. C. 10 • 7 – 3 • 7; 49 D. 10 • 7 – 3; 67 Example 2 CYP

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. Example 3

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 Example 3 CYP

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

Use the Distributive Property to rewrite the expression (d – 6)5. A. 5d – 6 B. 5d – 30 C. 5d + 6 D. d – 30 Example 4 CYP

Simplify Algebraic Expressions Use the Distributive Property to rewrite the expression 8(3 – t). 8(3 – t) = 8[3 + (–t)] Rewrite 3 – t as 3 + (–t). = 8(3) + 8(–t) Distributive Property = 24 + (–8t) Simplify. = 24 – 8t Definition of subtraction Answer: 24 – 8t Example 5

Use the Distributive Property to rewrite the expression 4(9 – a). A. 36 – a B. 36 – 4a C. 9 – 4a D. 36 + 4a Example 5 CYP