My First Algebra Question: Associative Property

[Duckfan]

I am reading through a introductory algebra textbook and refreshing memory on this topic. In the matter of the Associative Properties, it is giving me the expression 3 + (8+x).

(I'm skipping the graphs section because I'm leaving that for my tutor Saturday. But I'm moving to algebra because I think I can refresh memory fairly quickly).

Now this is addition in this part of the book. However, I'm just a bit confused because I do remember some of my algebra where in this expression I would multiply 3 into 8 since it's part of (forgot the term) process to solve this equation which (in my memory) multiply 3 & 8 to get 24x. Anytime I deal with an expression (for example) 4 + (7x+10) would work out to 28x +10. Because it's in the ( ) I'm required to multiply the expression inside the ( ).

And it also states I need to change the order: 3 + (x +8). Not understanding this aspect.

Am I correct on this question or do I need to clarify more?

 

[squidsk]

Re: My FIrst Algebra Question

I am reading through a introductory algebra textbook and refreshing memory on this topic. In the matter of the Associative Properties, it is giving me the expression 3 + (8+x).

(I'm skipping the graphs section because I'm leaving that for my tutor Saturday. But I'm moving to algebra because I think I can refresh memory fairly quickly).

Now this is addition in this part of the book. However, I'm just a bit confused because I do remember some of my algebra where in this expression I would multiply 3 into 8 since it's part of (forgot the term) process to solve this equation which (in my memory) multiply 3 & 8 to get 24x. Anytime I deal with an expression (for example) 4 + (7x+10) would work out to 28x +10. Because it's in the ( ) I'm required to multiply the expression inside the ( ).

And it also states I need to change the order: 3 + (x +8). Not understanding this aspect.

Am I correct on this question or do I need to clarify more?

No you are missing the fact that the 3 is added to and not multiplied against the result of the bracket. The only way you'd multiply the three (3) from your first example or the four (4) from your second against the brackets is if the addition was replaced by a multiplication sign (*) or not present.

i.e. \(\displaystyle 3 + ( x + 8) \ne 3 * (x + 8) \) and \(\displaystyle 4 + (7x + 10) \ne 4 * (7x + 10)\)

Associative property of math means that the order in which the operations are done is not relevant. Addition is associative since the order you add numbers together does not affect the result. For example if you have 4 + 7 + 2 it doesn't matter if I force the addition to be (4 + 7) + 2 or 4 + (7 + 2) the result will be the same.