1. PRE-ALGEBRA

2. Lesson 2-2 Warm-Up

3. PRE-ALGEBRA

5. The Distributive Property: When multiplying two numbers together, one can calculate the answer by making one of the numbers into an addition or subtraction problem in parenthesis, multiplying each of these addend or subtractands separately by the number outside of the parenthesis, and adding those “partial products” together. a (b + c) = ab + ac Example: 5 (26) = 130 5 (26) = 5 (20 + 6) = 5(20) + 5(6) = 100 + 30 = 130 5 (26) = 5 (25 + 1) = 5(25) + 5(1) = 125 + 5 = 130 a (b - c) = ab - ac Example: 5 (26) = 130 5 (26) = 5 (30 - 4) = 5(30) - 5(4) = 150 - 20 = 130 5 (26) = 5 (28 - 2) = 5(28) - 5(2) = 140 - 10 = 130 What is the “Distributive Property”? “The Distributive Property” (2-2)

6. PRE-ALGEBRA (b + c)a = ba + ca Example: 5 (26) = 130 (2 + 3) 26 = 2(26) + 3(26) = 52 + 78 = 130 (4 + 1) 26 = 4(26) + 1(26) = 104 + 26 = 130 (b + c)a = ba + ca Example: 5 (26) = 130 (10 - 5) 26 = 10(26) - 5(26) = 260 - 130 = 130 (6 - 1) 26 = 6(26) - 1(26) = 156 - 26 = 130 “The Distributive Property” (2-2)

7. PRE-ALGEBRA Use the Distributive Property to find 15(110) mentally. 15(110) = 15(100 + 10)Write 110 as (100 + 10). = 15 100 + 15 10 Use the Distributive Property. = 1,500 + 150Multiply. = 1,650Add. The Distributive Property LESSON 2-2 Additional Examples

8. PRE-ALGEBRA Ms. Thomas gave 5 pencils to each of her 37 students. What is the total number of pencils she gave to the students? (37)5 = (40 – 3)5Write 37 as (40 – 3). = 40 5 – 3 5Use the Distributive Property. = 200 – 15Multiply. = 185Subtract. Ms. Thomas gave the students 185 pencils. The Distributive Property LESSON 2-2 Additional Examples

9. PRE-ALGEBRA Simplify 11(23) + 11(7). 11(23) + 11(7) = 11(23 + 7)Use the Distributive Property. = 11(30)Work within grouping symbols. = 330Multiply. The Distributive Property LESSON 2-2 Additional Examples

10. PRE-ALGEBRA How can you model the Distributive Property? H To model the Distributive Property, model the excpression inside parenthesis as many times as the number outside the parenthesis. Then, use the Commutative Property of Addition to regroup the numbers. Example: Use a model to multiply 3 (2x + 5). 3(2x + 5) = 3 2x + 3 5 = 6x + 15 “The Distributive Property” (2-2)

11. PRE-ALGEBRA Use a model to multiply 4(3x – 4). So 4(3x – 4) = 12x – 16. Model four groups of 3x – 4. Use the Commutative Property of Addition to regroup. The Distributive Property LESSON 2-2 Additional Examples

12. PRE-ALGEBRA Multiply. a. –9(2 – 8y) = –18 – (–72y)Multiply. = –18 + 72ySimplify. b. (5m + 6)11 = 55m + 66Multiply. –9(2 – 8y) = –9(2) – (–9)(8y)Use the Distributive Property. (5m + 6)11 = (5m)11 + (6)11Use the Distributive Property. The Distributive Property LESSON 2-2 Additional Examples

13. PRE-ALGEBRA Use the Distributive Property to simplify or solve mentally. 1.15(203) 2.7(180) 3.6(26) – 6(16) 4.(8a – 4)9 5.2(14 + y) 60 3,0451,260 28 + 2y 72a – 36 The Distributive Property LESSON 2-2 Lesson Quiz