Can someone tell me a step by step explanation on what distributive properties are and also give an example?

- Atsie

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- jamiebookeater

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- skullpatrol

Do you have any ideas?
:-)

- skullpatrol

The distributive properties state that a multiplier can be distributed over terms.
The call it distribut"IVE" because the multiplication CAN be done producing a simplified result.
Consider the expression:
a • ( b + c )
The multiplier "a" can be distributed over the ( b + c ) producing the simplified result:
a • b + a •c

- skullpatrol

Here is an example:
a • ( b + c ) = a • b + a • c
3 • ( 4 + 2 ) = 3 • 4 + 3 • 2
3 • ( 6 ) = 18 also 12 + 6 = 18
18 = 18 so the property is correct

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- Atsie

Finally a response! Thank you!
Now whats funny is I am learning this in Algebra class but I'm given a rather different more simple example of
a (b + c) = ab + ac
and
(b+c) a = ba + ca
and
a (b - c) = ab - ac
and
(b - c) a = ba - ca.
This is about the only example I am given in the book, and there aren't any other examples with more specifics.
So I am thrown into the deep end with a test question stating this:
"Rewrite the expression using the distributive property. 5 ∙ 97"
What are proper steps to solve this?

- anonymous

im here

- anonymous

@Atsie im here :)

- Atsie

ooh, didn't see ya.
I'm sure you've read it over right?

- anonymous

yeah im still

- anonymous

what is your question?

- Atsie

Well, firstly have you learned about Distributive Properties yet? I don't want to burden you if you don't know it.

- anonymous

i have just its kinda rusty in there, but if i read a question im sure ill remember

- Atsie

Well here is the first page of my chapter, maybe you'll get a better idea. :)

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- anonymous

im slowly getting it

- anonymous

sorry im taking long

- Atsie

Its ok. if you need the second page let me know.

- anonymous

yeah i thinnk i do

- Atsie

Here you go

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- anonymous

oh i get it!

- anonymous

ok whats the question?

- Atsie

Rewrite the expression using the distributive property. 5 ∙ 97

- Atsie

I don't know if its just me, but everything in the book seems soo simple to the point of ridculous and then I get this for a question and it seems so complicated

- anonymous

first do 5 x 97

- Atsie

thats 485

- anonymous

ok now the thing it 5(485)

- anonymous

is*

- Atsie

Right, so what is the equation getting to that?

- Atsie

I mean, I'm given these options to choose from....

- Atsie

A. (5 + 90)7
B. 5(100 - 3)
C. (10 - 5)7
D. 5(100 - 17)

- anonymous

is one of the answres 2425?

- anonymous

oh

- anonymous

oh! it is A sorry for direct answere

- anonymous

answer

- Atsie

Ok thats good to know, but how is it that though?
I mean I believe you, but I'm wondering how it makes sense
5 + 90 is 95.
Do I do 95 x 7?

- Atsie

Wait no, that don't even make sense. IF I do that it comes out to 665

- anonymous

dang now im confused again...

- anonymous

yeah

- Atsie

(5 + 90)7
The parentheses mean it leads to a different equation I think. Ugh, I'm lost. You see, this is why the book doesn't seem to be much help to me. I mean its all simple and great in there, but when it comes to actually testing a student on it it just don't make sense!

- anonymous

look at 2nd page it helped me a bit

- anonymous

ohhh it B

- anonymous

becase 5(100 - 3) 100 - 3 is 97 and well its hard to explain

- anonymous

@Atsie

- Atsie

I see you
I'm trying to re-read the second page and make sense outa those examples. 100-3 does equal 97, that sounds more realistic but I'm unsure of what the 5 in that option has to do with it. Or is that just there to give an idea

- anonymous

Sorry.. if you don't trust me its ok, But i really think it is B and it is hard to explain but if you dont believe me.. then.. Ok sorry im not too help full

- Atsie

I believe you, I'm just confused. I sometimes over analyze stuff. I'll go ahead and pick it.

- Atsie

Ugh, I got nine more of these questions left. Oh joy

- anonymous

next one i get it now and its easy

- anonymous

Atsie do you do k12?

- Atsie

Rewrite the expression using the distributive property. 8 ∙ 203
I'm supposed to be in 10th grade but I got held behind. I've never ever been good at math, I'm usually a failure at it heh

- anonymous

ok lemme quikly do it can you put the answeres?

- Atsie

A. 8(20 + 3)
B. (8 + 20)3
C. 8(200 + 3)
D. (800 + 2)3
Its C isn't it?

- anonymous

its C sorry again for direct

- Atsie

Yass, you know what I think you just gave me an idea of what I'm supposed to be doing on this.

- anonymous

Oh, Lol

- Atsie

Ok, I'm stuck again I think

- anonymous

show me the question

- Atsie

Simplify the expression.(4 - 3m) 8
A. 32 - 24m
B. 4 - 24m
C. 24m - 32
D. 24m - 4

- anonymous

im lost..

- Atsie

Is it A

- anonymous

Oh yeah it is!

- Atsie

Cuz 32 - 24 is 8

- anonymous

yeah

- anonymous

next question?

- Atsie

It gets more complicated as I go along
Simplify the expression 4b - 1 + 5b
A. 8b
B. -1b + 1
C. -1b - 1
D. 9b - 1

- anonymous

im lost

- anonymous

sorry but i have to go..

- anonymous

not trying to avoid but i gtg

- anonymous

Bye thanks!

- Atsie

Its ok, I had to go to. Thanks for all your help! I really really appreciate it. I've been stuck for months on end

- skullpatrol

The numerical examples you are struggling with illustrate how you can use the distributive property to simplify mental arithmetic.
They are trying to show that if you want to multiply two numbers together the distributive property allows you to write one of the numbers as a sum or difference and then distibute the other number over the two terms.

- skullpatrol

|dw:1449405669075:dw|

- Atsie

@skullpatrol
You did a nice job of breaking it down, thank you very much! :)

- skullpatrol

Thanks for asking :D

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