1. ALGEBRA 1 Lesson 1-7 Warm-Up

2. ALGEBRA 1 Lesson 1-7 Warm-Up

3. ALGEBRA 1 “The Distributive Property” (1-7) What is the Distributive Property? 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

4. ALGEBRA 1 “The Distributive Property” (1-7) (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

5. ALGEBRA 1 Use the Distributive Property to simplify 26(98) mentally. 26(98) = 26(100 – 2)Rewrite 98 as 100 – 2. = 26(100) – 26(2)Use the Distributive Property. = 2600 – 52Simplify. = 2548 The Distributive Property LESSON 1-7 Additional Examples

6. ALGEBRA 1 Find the total cost of 4 CDs that cost $12.99 each mentally using the Distributive Property. 4(12.99) = 4(13 – 0.01)Rewrite 12.99 as 13 – 0.01. = 4(13) – 4(0.01)Use the Distributive Property. = 52 – 0.04Simplify. = 51.96 The total cost of 4 CDs is $51.96. The Distributive Property LESSON 1-7 Additional Examples

7. ALGEBRA 1 Simplify 3(4m – 7). 3(4m – 7) = 3(4m) – 3(7)Use the Distributive Property. = 12m – 21 Simplify. The Distributive Property LESSON 1-7 Additional Examples

8. ALGEBRA 1 Simplify –(5q – 6). –(5q – 6) = –1(5q – 6)Rewrite the expression using –1. = –1(5q) – (-1)(6)Use the Distributive Property. = –5q - (-6)Simplify. The Distributive Property LESSON 1-7 Additional Examples = –5q + 6

9. ALGEBRA 1 “The Distributive Property” (1-7) What is a “term”? What is a “constant”? What is a “coefficient”? What are “like terms”? term: a number, a variable, or the product of a number and variable Examples: 5, x, 5x constant: a term that has no variable Examples: 5, 104 coefficient: the numerical (number) part of a term that has variable Examples: Like terms: terms that have the exact same variable (or variables if there are more than one)

10. ALGEBRA 1 “The Distributive Property” (1-7) How can like terms be combined? Like terms can be combined using the Distributive Property in reverse. Example: 3x – 2x (3 – 2)x = 3x – 2x (1)x = 1x (combine the coefficients) x (Identity Property) Example: -5x 2 and 9x 2 = -5x 2 + 9x 2 (-5 + 9)x 2 = -5x 2 + 9x 2 (4)x 2 = 4x 2 Example: 15x 2 y 3 and 7x 2 y 3 = 15x 2 y 3 + 7x 2 y 3 (15 + 7) x 2 y 3 = 15x 2 y 3 + 7x 2 y 3 (22) x 2 y 3 = 22x 2 y 3

11. ALGEBRA 1 Simplify –2w 2 + w 2. = (–2 + 1)w 2 Use the Distributive Property. = –w 2 Simplify. The Distributive Property LESSON 1-7 Additional Examples –2w 2 + 1w 2 Use the Identity Property to write a “1” in front of w 2. = (–1) w 2 Parenthesis (PEMDAS)

12. ALGEBRA 1 Words: –6 times the quantity 7 minus m Translate: –6 (7 – m) Write an expression for “the product of –6 and the quantity 7 minus m.” –6 (7 – m) The Distributive Property LESSON 1-7 Additional Examples

13. ALGEBRA 1 Simplify each expression. 1. 11(299) 2. 4(x + 8) 3. – 3(2y – 7) 4. –(6 + p) 5. 1.3a + 2b – 4c + 3.1b – 4a 6. Write an expression for the product of and the quantity b minus. 32894x + 32– 6y + 21 – 6 – p –2.7a + 5.1b – 4c 4747 3535 The Distributive Property LESSON 1-7 Lesson Quiz 4747 3535 b –