The Distributive Property of Multiplication over Addition

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The Distributive Property of Multiplication over
Addition!!!

• What is this Distributive Business Anyway??

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Heres the setup
Bobs Classmates
Bob
Rachael
Jill
Brian
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Bob has candy or maybe its gum
Gum
What should he do with all that gum??
Bob
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Well? What should he do?
Rachael
Jill
Brian
Bob
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His mom always told him to share!
One for Brian
One for Jill
One for Rachael
Rachael
Jill
Brian
Bob
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Bob has Distributed the gum.
Rachael
Jill
Brian
Bob
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Lets look at that again
Extra gum
)
(

Heres Bob
Rachael
Jill
Brian
Bobs gum
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)
(
Rachael
Jill
Brian
The box tells us what is going to be distributed.
The gum is outside.
The Parentheses tell us who will get the gum. The
classmates are inside.
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Bob has distributed the gum.
Rachael, Jill and Brain each have a pack of gum.
)
(
Rachael
Jill
Brian
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• Lets add that all up

(
)


Rachael
Jill
Brian
Thats Rachael has gum Jill
has gum Brian has gum.
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So whats the big deal??

• Anyone can hand out gum to their friends.
• But what about the Algebra??
• Algebra takes obvious, everyday things and
  disguises them with a secret code.
• If you know the code its not such a big
  secret, is it?

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)
(
Rachael
Jill
Brian
The box contains what Bob wants to
Distribute. The Parentheses tell us who Bob
wants to distribute it to.
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One More Time !!!
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Secret Codes
)
(
Rachael
Jill
Brian
R is for Rachael
g is for gum
B is for Brian
J is for Jill
We already know the Parentheses tell us
who gets the gum!
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This is what we just did
(
)





Here it is in code
Means
g ( R J B ) gR gJ gB
Rachael has gum
Jill has gum
Brian has gum
and
and
Distribute gum to Rachael, Jill and Brian
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What does this mean??
3(4)
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Multiplication!!
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We knew that !!
Duh!
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Ok, so whats Multiplication got to do with
distributing gum, anyway?!
Well, Ill tell you
If you can keep a secret!!
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Algebra doesnt really care what you distribute,
only how many (and that everyone in the
parentheses gets one).
So Parentheses means that everyone gets one.
But parentheses also mean multiplication.
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Right, you are!!
Meow
Lets do it!
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3(4)
Means
take 4 three times
Duh!
Meow Wheres the kibble?
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Well, if youre so smart, Kitten, you tell me!!
Ok, I will!
Owl for lunch? Hmmm
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Right-Oh!!
We dont just have 3(4) We have something like
3(2 3 4) Or theres nothing to distribute
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The Distributive property of Multiplication over
Addition.
You just multiply the number on the outside of
the parentheses by EVERYTHING inside the
parentheses.
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3( 2 3 4 ) 3(2) 3( 3) 3(4)
Lets check!
Do YOU think thats true? Yeah! You out there
reading this!!
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3( 2 3 4 ) 3(2) 3( 3) 3(4)

• You mean
• 3(9) 6 9 12.
• Hmmm
• 15 12 27 Right!!

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That owl is Sooo lunch!!
Look out!
Wet!! Yuck!! Water!
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The Distributive Property of Multiplication
over Addition
For any Real Numbers, a, b and c
a( b c)
ab ac

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Examples
1. 4( 2 7)

4(2) 4(7)
Check it out!
4(9) 8 28
or
36 36
2. 5( 2 6)

5(2) 5(6)
5(-4) 10 30
or
-20 -20
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You try it!!
Just Distribute

• 3( 7 6)
• -3 ( 2 5)
• 7 ( 4 2)
• 5 ( 2 3 4)
• -4( 1 4 5 3)
• 2( 3 5 7 - 9 11)

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Hey! Anyone got any gum?
Now, Class!!
Meow, Wet Feet!!
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• 3(7) 3(6)
• -3(2) (-3)(6)
• 7(4) 7(2)
• 5(2) 5(3) 5(4)
• (-4)(1) (-4)(4) (-4)(5) (-4)(3)
• 2(3) 2(5) 2(7) 2(9) 2(11)

Is this what you got??