The document explains the distributive property, which states that multiplying a sum or difference by a number is equivalent to multiplying each term in the sum or difference by that number. It provides examples of using the distributive property to simplify multiplication problems, including with variables. It also explains using the distributive property "backwards" by first distributing and then combining like terms.

1. Ch. 2, Section 1: Distributive Property Ms. Dewey-Hoffman, 2009

2. To multiply a sum or difference, multiply each number within the parentheses by the number outside the parentheses. Distributive Property B ( N + C ) = B N + B C Always distribute the number outside of the parentheses!

3. Distributive Property Can Look A Lot of Different Ways a(b + c) = ab + ac (b + c)a = ba + ca a(b – c) = ab – ac (b – c)a = ba - ca

4. Use Distributive Property Backwards To make some multiplication problems easier, try doing the Distributive Property Backwards. 20(102) = ? = 20(100 + 2)  100 + 2 = 102, Break 102 into two parts that are easier to work with. = 20(100) + 20(2)  Distribute the 20 = 2,000 + 40  PEMDAS, Multiplication = 2,040  PEMDAS, Addition 20(102) = 2,040 Here we added two numbers to get 102. Don’t forget that you can subtract too!

5. Distributive Property Backwards Find the product of 9 and 199. 9(199) = = 9(200 – 1)  200 – 1 = 199 = 9(200) – 9(1)  Distribute the 9. = 1,800 – 9  PEMDAS, Multiplication. = 1,791  PEMDAS, Subtraction. 9(199) = 1,791

6. Word Problem: Use The Distributive Property Lego Robotics Class sold toy robotics for $7 each at a fundraiser. The class sold 204 robots. How much money did they raise? 7(204) = = 7(200 + 4)  broke down to be easier = 7(200) + 7(4)  distributed. = 1,400 + 28  PEMDAS, multiplied. = 1,428  PEMDAS, addition. 7(204) = $1,428 The Lego Robotics Class made $1,428 off of selling toy robots.

7. More Backward Distributive Property 12(52) – 12(62) = = 12(52 – 62)  Pull out 12 and combine the 52 – 62 = 12(-10)  PEMDAS, Simplify in the parentheses 12(52) – 12(62) = -120  PEMDAS, Multiply. Try This one : (16)7 – (11)7 = = (16 – 11)7  Pull out 7 and combine 16 – 11 = (5)7  PEMDAS, Simplify in the parentheses = 35  PEDMAS, Multiply

8. Distributive Property and Variables 4(2x – 3) = Represents x Represents 1 Represents –1 4(2x – 3) = 8x - 12 Reorganize

9. More Distributive Property Multiply: -5 (4x – 3) = = -5 (4x) – (-5) (3)  Distribute –5 = -20x – (-15)  PEMDAS, Multiply. = -20x + (+15)  Add the Opposite. = -20x + 15  Simplify, this is your answer! Try This One: (2x + 5)7 = = 2x(7) + 5(7)  Distribute 7. = 14x + 35  PEMDAS, Multiply.

10. #12 Page 76-77: 1-49 odd. YOU MUST SHOW YOUR WORK!!!!!!!!! When it says to Use the Distributive Property to Simplify, break up the big number and show steps. Example: #6: 5(18) = 5(20 – 2) = 5(20) – 5(2) = 100 – 10 = 90