The Distributive Property of Multiplication over Addition!!! What is this ‘Distributive’ Business Anyway??

Here’s the setup… Bob Bob’s Classmates RachaelJill Brian

Bob has candy… or maybe its gum… Bob Gum

Well? What should he do? RachaelJill Brian Bob

His mom always told him to share! RachaelJill Brian Bob One for Rachael One for Jill One for Brian

Bob has Distributed the gum. RachaelJill Brian Bob

Let’s look at that again: Here’s Bob : Bob’sgum ( RachaelJill Brian ) Extra gum

( RachaelJill 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.

Bob has distributed the gum. ( RachaelJill Brian ) Rachael, Jill and Brain each have a pack of gum.

Let’s add that all up… ( RachaelJill Brian ) ++ That’s Rachael has gum; Jill has gum; Brian has gum.

So what’s 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 – it’s not such a big secret, is it?

( RachaelJill Brian ) The box contains what Bob wants to Distribute. The Parentheses tell us who Bob wants to distribute it to.

Secret Codes… ( RachaelJill Brian ) g is for gum R is for Rachael J is for Jill B is for Brian We already know the Parentheses tell us who gets the gum!

++ () = ++ This is what we just did: Here it is in code: g ( R + J + B ) = gR + gJ + gB Distribute gum to Rachael, Jill and Brian Means Rachael has gum and Jill has gum and Brian has gum

3(4)

We knew that !! Duh!

Ok, so what’s Multiplication got to do with distributing gum, anyway?! Well, I’ll tell you If you can keep a secret!!

Algebra doesn’t 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’.

Meow… Let’s do it!

3(4)Meanstake 4 three times Duh! Meow… Where’s the kibble?

Well, if you’re so smart, Kitten, you tell me!! Ok, I will! ‘Owl’ for lunch? Hmmm…

We don’t just have 3(4)… We have something like 3( ) Or there’s nothing to distribute Right-Oh!!

The Distributive property of Multiplication over Addition. You just multiply the number on the outside of the parentheses by EVERYTHING inside the parentheses.

3( ) = 3(2) + 3( 3) + 3(4) Do YOU think that’s true? Yeah! You out there reading this!! Let’s check!

3( ) = 3(2) + 3( 3) + 3(4) You mean: 3(9) = Hmmm… 27= = 27 Right!!

Wet!! Yuck!! Water! Look out! That owl is Sooo lunch!!

For any Real Numbers, a, b and c a( b + c) = ab + ac

Examples: 1. 4( 2 +7)= 4(2) + 4(7) Check it out!4(9) = 8 +28or36 = ( 2 – 6)= 5(2) – 5(6) 5(-4) = 10 – 30or-20 = -20

You try it!! 1. 3( 7 + 6) = ( 2 + 5) = 3. 7 ( 4 – 2) = 4. 5 ( ) = 5. -4( ) 6. 2( ) Just Distribute

Now, Class!! Hey! Anyone got any gum? Meow, Wet Feet!!

Is this what you got?? 1.3(7) + 3(6) 2.-3(2) + (-3)(6) 3.7(4) – 7(2) 4.5(2) + 5(3) + 5(4) 5.(-4)(1) + (-4)(4) + (-4)(5) + (-4)(3) 6.2(3) + 2(5) +2(7) – 2(9) + 2(11)