1. 1-8 Distributive Property Mrs. Robertson Grade 6 Sem/CL 2011

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

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

9. Page  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.