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Basic College Math The Distributive Property
Getting ready for algebra! <ul><li>Now that we’re ready to study algebra, we’re going to need more than just the order of ...
A brand new property! <ul><li>We’re going to need a new property called the </li></ul><ul><li>distributive property  of mu...
What will we learn? <ul><li>We are going to see how the property works with a  numerical example . </li></ul><ul><li>We’re...
Remember the order of operations? <ul><li>If you have a problem like 5( 6 + 8 ), the order of operations tells you to do w...
The Distributive Property of Multiplication  over Addition tells us . . . <ul><li>If we have something that is multiplying...
Practical Example <ul><li>Suppose you hire the neighbor’s daughter for $5.00 an hour to help you rake leaves. She is all e...
Raking in the profits <ul><li>Day 1, she works 6 hours  </li></ul><ul><ul><li>that’s $5(6) or $30 toward her stereo. </li>...
Paying the bill <ul><li>You go to the bank to get the cash to pay her. </li></ul><ul><li>All you care about is that she wo...
Some algebraic examples <ul><li>5( x  +  2) = 5( x )  +  5( 2 ) = 5x  +  10 </li></ul><ul><li>2( 3x  –  6 ) = 2( 3x )  -  ...
A more complicated problem <ul><li>Take the problem - 5( x + 7 ) + 30 </li></ul><ul><li>You first distribute and then comb...
Pitfall 1:  Negative numbers <ul><li>If the number in front of the parentheses is negative, you must multiply each item in...
Pitfall 2:  Oops - forgot the second guy! <ul><li>5( x + 7 ) = 5x +  7   WRONG! </li></ul><ul><li>You get the 5x right bec...
Pitfall 3:  Over enthusiasm <ul><li>5(x + 7) – 30 = 5( x ) + 5( 7 )  – 5( 30 )   </li></ul><ul><li>5x + 35 – 150 = 5x - 11...
Pitfall 4:  It’s backwards! <ul><li>( x + 7 )( 5 )  What the heck? </li></ul><ul><li>The  commutative property of multipli...
Let me tell you a story . . . <ul><li>The first time I ever went to Sea World, my friends and I decided to go to the Shamu...
THE SEATS WERE GREAT! <ul><li>We could see Shamu swimming around through the windows in the side of his tank. </li></ul><u...
Perfect! <ul><li>. . .  and then he re-entered the water  . . . </li></ul>
 
. . . and that is how Shamu can help you remember the rules. <ul><li>When you are simplifying an expression like   </li></...
The End <ul><li>Splash photo courtesy of Mike Sandells www.mikejs.com   </li></ul>
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Shamu3

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Transcript of "Shamu3"

  1. 1. Basic College Math The Distributive Property
  2. 2. Getting ready for algebra! <ul><li>Now that we’re ready to study algebra, we’re going to need more than just the order of operations to keep us in line! </li></ul>
  3. 3. A brand new property! <ul><li>We’re going to need a new property called the </li></ul><ul><li>distributive property of multiplication over addition . </li></ul><ul><li>It also has a sister called the </li></ul><ul><li>distributive property of multiplication over subtraction . </li></ul><ul><li>Collectively, they are sometimes just called </li></ul><ul><li>The distributive property . </li></ul>
  4. 4. What will we learn? <ul><li>We are going to see how the property works with a numerical example . </li></ul><ul><li>We’re going to see how it works with some algebraic examples . </li></ul><ul><li>We’re going to map out the potential pitfalls of working with this property. </li></ul><ul><li>We’re going to read a story to help us remember how to use it correctly! </li></ul>
  5. 5. Remember the order of operations? <ul><li>If you have a problem like 5( 6 + 8 ), the order of operations tells you to do what is in parentheses first. </li></ul><ul><li>5( 6 + 8 ) becomes 5( 14 ) which equals 70. </li></ul><ul><li>Remember: the 5 directly against the open parentheses means to multiply by 5. </li></ul>
  6. 6. The Distributive Property of Multiplication over Addition tells us . . . <ul><li>If we have something that is multiplying the sum of two or more numbers like 5( 6 + 8 ). . . </li></ul><ul><li>We have an alternate way to calculate the answer. </li></ul>
  7. 7. Practical Example <ul><li>Suppose you hire the neighbor’s daughter for $5.00 an hour to help you rake leaves. She is all excited about the job because she wants to buy a stereo for her room. </li></ul>
  8. 8. Raking in the profits <ul><li>Day 1, she works 6 hours </li></ul><ul><ul><li>that’s $5(6) or $30 toward her stereo. </li></ul></ul><ul><li>Day 2, she works 8 hours </li></ul><ul><ul><li>that’s another $5(8) or $40 toward her stereo. </li></ul></ul><ul><li>WOW! </li></ul><ul><li>$30 + $40 equals $70 for her stereo! </li></ul>
  9. 9. Paying the bill <ul><li>You go to the bank to get the cash to pay her. </li></ul><ul><li>All you care about is that she worked 14 hours. </li></ul><ul><li>$5(14) = $70. </li></ul><ul><li>You both get the same answer even though you did the problem differently. </li></ul><ul><li>The Distributive Property tells you that it is OK. </li></ul><ul><ul><li>You can multiply and then add (like she did) </li></ul></ul><ul><ul><li>or add and then multiply (like you did). </li></ul></ul>
  10. 10. Some algebraic examples <ul><li>5( x + 2) = 5( x ) + 5( 2 ) = 5x + 10 </li></ul><ul><li>2( 3x – 6 ) = 2( 3x ) - 2( 6 ) = 6x - 12 </li></ul>
  11. 11. A more complicated problem <ul><li>Take the problem - 5( x + 7 ) + 30 </li></ul><ul><li>You first distribute and then combine like terms. </li></ul><ul><li>Answer: - 5( x + 7 ) + 30 = - 5( x ) - 5( 7 ) + 30 </li></ul><ul><li>= - 5x - 35 + 30 </li></ul><ul><li>= - 5x - 5 </li></ul>
  12. 12. Pitfall 1: Negative numbers <ul><li>If the number in front of the parentheses is negative, you must multiply each item in the parentheses by the negative number. </li></ul><ul><li>Watch your signs! </li></ul><ul><li>- 6(x – 4) = - 6( x ) - 6( - 4 ) = - 6x + 24 </li></ul><ul><li>-2(2x + 5) = -2( 2x ) - 2( + 5 ) = -4x -10 </li></ul><ul><li>-3(-3x – 4) = -3( - 3x) - 3(- 4) = 9x + 12 </li></ul>
  13. 13. Pitfall 2: Oops - forgot the second guy! <ul><li>5( x + 7 ) = 5x + 7 WRONG! </li></ul><ul><li>You get the 5x right because it’s staring you in the face. </li></ul><ul><li>In your haste to get the right answer, you forget all about the poor 7. </li></ul><ul><li>5(x + 7) = 5( x ) + 5( 7 ) = 5x + 35 RIGHT! </li></ul>
  14. 14. Pitfall 3: Over enthusiasm <ul><li>5(x + 7) – 30 = 5( x ) + 5( 7 ) – 5( 30 ) </li></ul><ul><li>5x + 35 – 150 = 5x - 115 WRONG </li></ul><ul><li>You get so excited about distributing the 5 that you distribute him to everybody – even the numbers that aren’t in the parentheses! </li></ul><ul><li>5( x + 7 ) – 30 = 5( x ) + 5( 7 ) – 30 </li></ul><ul><li>5x + 35 – 30 = 5x + 5 RIGHT! </li></ul>
  15. 15. Pitfall 4: It’s backwards! <ul><li>( x + 7 )( 5 ) What the heck? </li></ul><ul><li>The commutative property of multiplication tells us that we can re-write the problem because order doesn’t matter when you multiply . </li></ul><ul><li>5 ( x + 7 ) Ah, that’s better! </li></ul>
  16. 16. Let me tell you a story . . . <ul><li>The first time I ever went to Sea World, my friends and I decided to go to the Shamu show. </li></ul><ul><li>When we entered the area, I noticed that there were seats right down at the front that were painted red instead of blue , like the other seats. </li></ul><ul><li>There were no “Reserved” signs on them, so we decided to go sit there and move if we were told we had to. </li></ul>
  17. 17. THE SEATS WERE GREAT! <ul><li>We could see Shamu swimming around through the windows in the side of his tank. </li></ul><ul><li>At last, the show started and Shamu did a mighty leap out of the water right in front of us. </li></ul><ul><li>It was amazing! </li></ul><ul><li>I had my camera out, ready to shoot the picture of a lifetime. . . </li></ul>
  18. 18. Perfect! <ul><li>. . . and then he re-entered the water . . . </li></ul>
  19. 20. . . . and that is how Shamu can help you remember the rules. <ul><li>When you are simplifying an expression like </li></ul><ul><li>5 ( x + 7 ) – 30 </li></ul><ul><li>The 30 is in the blue seats – high and dry and out of harm’s way. </li></ul><ul><li>The x and the 7 are in the red seats – definitely the splash zone! </li></ul><ul><li>And the 5 is Shamu! </li></ul>
  20. 21. The End <ul><li>Splash photo courtesy of Mike Sandells www.mikejs.com </li></ul>
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