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Chapter 2, Section 2: Distributive Property

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Chapter 2, Section 2: Distributive Property

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Chapter 2, Section 2: Distributive Property

  1. 1. Ch. 2, Section 1: Distributive Property Ms. Dewey-Hoffman, 2009
  2. 2. <ul><li>To multiply a sum or difference, multiply each number within the parentheses by the number outside the parentheses. </li></ul>Distributive Property B ( N + C ) = B N + B C Always distribute the number outside of the parentheses!
  3. 3. Distributive Property Can Look A Lot of Different Ways <ul><li>a(b + c) = ab + ac </li></ul><ul><li>(b + c)a = ba + ca </li></ul><ul><li>a(b – c) = ab – ac </li></ul><ul><li>(b – c)a = ba - ca </li></ul>
  4. 4. Use Distributive Property Backwards <ul><li>To make some multiplication problems easier, try doing the Distributive Property Backwards. </li></ul><ul><li>20(102) = ? </li></ul><ul><li>= 20(100 + 2)  100 + 2 = 102, Break 102 into two parts that are easier to work with. </li></ul><ul><li>= 20(100) + 20(2)  Distribute the 20 </li></ul><ul><li>= 2,000 + 40  PEMDAS, Multiplication </li></ul><ul><li>= 2,040  PEMDAS, Addition </li></ul><ul><li>20(102) = 2,040 </li></ul><ul><li>Here we added two numbers to get 102. </li></ul><ul><li>Don’t forget that you can subtract too! </li></ul>
  5. 5. Distributive Property Backwards <ul><li>Find the product of 9 and 199. </li></ul><ul><li>9(199) = </li></ul><ul><li> = 9(200 – 1)  200 – 1 = 199 </li></ul><ul><li> = 9(200) – 9(1)  Distribute the 9. </li></ul><ul><li>= 1,800 – 9  PEMDAS, Multiplication. </li></ul><ul><li>= 1,791  PEMDAS, Subtraction. </li></ul><ul><li>9(199) = 1,791 </li></ul>
  6. 6. Word Problem: Use The Distributive Property <ul><li>Lego Robotics Class sold toy robotics for $7 each at a fundraiser. The class sold 204 robots. How much money did they raise? </li></ul><ul><li>7(204) = </li></ul><ul><li>= 7(200 + 4)  broke down to be easier </li></ul><ul><li>= 7(200) + 7(4)  distributed. </li></ul><ul><li>= 1,400 + 28  PEMDAS, multiplied. </li></ul><ul><li>= 1,428  PEMDAS, addition. </li></ul><ul><li>7(204) = $1,428 </li></ul><ul><li>The Lego Robotics Class made $1,428 off of selling toy robots. </li></ul>
  7. 7. More Backward Distributive Property <ul><li>12(52) – 12(62) = </li></ul><ul><li>= 12(52 – 62)  Pull out 12 and combine the 52 – 62 </li></ul><ul><li>= 12(-10)  PEMDAS, Simplify in the parentheses </li></ul><ul><li>12(52) – 12(62) = -120  PEMDAS, Multiply. </li></ul><ul><li>Try This one : </li></ul><ul><li>(16)7 – (11)7 = </li></ul><ul><li>= (16 – 11)7  Pull out 7 and combine 16 – 11 </li></ul><ul><li>= (5)7  PEMDAS, Simplify in the parentheses </li></ul><ul><li>= 35  PEDMAS, Multiply </li></ul>
  8. 8. Distributive Property and Variables <ul><li>4(2x – 3) = </li></ul><ul><li>Represents x </li></ul><ul><li>Represents 1 </li></ul><ul><li>Represents –1 </li></ul>4(2x – 3) = 8x - 12 Reorganize
  9. 9. More Distributive Property <ul><li>Multiply: </li></ul><ul><li>-5 (4x – 3) = </li></ul><ul><li> = -5 (4x) – (-5) (3)  Distribute –5 </li></ul><ul><li> = -20x – (-15)  PEMDAS, Multiply. </li></ul><ul><li> = -20x + (+15)  Add the Opposite. </li></ul><ul><li> = -20x + 15  Simplify, this is your answer! </li></ul><ul><li>Try This One: </li></ul><ul><li>(2x + 5)7 = </li></ul><ul><li> = 2x(7) + 5(7)  Distribute 7. </li></ul><ul><li> = 14x + 35  PEMDAS, Multiply. </li></ul><ul><li> </li></ul>
  10. 10. #12 <ul><li>Page 76-77: 1-49 odd. </li></ul><ul><li>YOU MUST SHOW YOUR WORK!!!!!!!!! </li></ul><ul><li>When it says to Use the Distributive Property to Simplify, break up the big number and show steps. </li></ul><ul><li>Example: </li></ul><ul><li>#6: 5(18) = 5(20 – 2) </li></ul><ul><li> = 5(20) – 5(2) </li></ul><ul><li> = 100 – 10 </li></ul><ul><li> = 90 </li></ul>

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