## Distributive Property

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New2Math
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### Distributive Property

On this page http://www.purplemath.com/modules/numbprop.htm I found the following example:
Simplify 23 + 5x + 7y – x – y – 27. Justify your steps.

23 + 5x + 7y – x – y – 27 original (given) statement
23 – 27 + 5x – x + 7y – y Commutative Property
(23 – 27) + (5x – x) + (7y – y) Associative Property
(–4) + (5x – x) + (7y – y) simplification (23 – 27 = –4)
(–4) + x(5 – 1) + y(7 – 1) Distributive Property
–4 + x(4) + y(6) simplification
–4 + 4x + 6y Commutative Property
I am lost when I reach the line in red:

(–4) + x(5 – 1) + y(7 – 1) Distributive Property

Where did that (1) come from, please?

-4 + (5) = 1
That is where I can find a 1...not sure how it got put in there, is all.
(And any advice on where to practice this?)

(Edit - this is supposed to be in Arithmetic forum, please move for me)

FWT
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Joined: Sat Feb 28, 2009 8:53 pm

### Re: Distributive Property

y = 1*y

Matt
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### Re: Distributive Property

I am lost when I reach the line in red:

(–4) + (5x – x) + (7y – y) simplification (23 – 27 = –4)
(–4) + x(5 – 1) + y(7 – 1) Distributive Property

Where did that (1) come from, please?
Check it by re-distributing the x and y:

(-4) + x(5 - 1) + y(7 - 1)
(-4) + (x*5 - x*1) + (y*7 - y*1)
(-4) + (5x - x) + (7y - y)

This matches what came it the step before it.

New2Math
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Joined: Thu Oct 11, 2012 9:50 pm
Location: Canada
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### Re: Distributive Property

Ok, thanks I think I understand. Since it is the same x = x * 1 that makes sense to me.

x times (5) minus x (itself) and x replaces the (1) during the multiplication process. I can grasp it but I guess I'm having some issues with my independent thought process when I actually have to do it myself in the process.

I need much-o practice ! Thanks for helping me work this out.

(Edit, I think it is because in the next step I know I have to simplify by taking 1 from 5 when it seems like I've then completely forgotten about the X that was there...and the X is not exactly a (1)! So, it's making my brain hurt a bit to grasp...but I am starting to!)

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