2. 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

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

4. Key Concept

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

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

7. 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

8. 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

9. 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 $ $0.60. Then use the Distributive Property to find the total cost mentally.
15($10 + $0.60) = 15 • • 0.6 Distributive Property
= Multiply.
= 159 Subtract.
Answer: The total cost of the shirts is $159.
Example 3

10. PHOTOS Twenty volleyball players and coaches are buying a group photo of their championship win. Each photo costs $ Use the Distributive Property to find the total cost of the photos.
A. $206
B. $280.30
C. $286
D. $396
Example 3 CYP

11. 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

12. 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

13. 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

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