What is the property illustrated in (2+g)+3 = 2+(g+3) ?
This is the associative property of addition, not the commutative property.
The commutative property only deals with 2 numbers not 3.
The order of the numbers or their groupings do not affect the result.
(2+1)+3 = 2+(1+3)
3+3 = 2+4 (eliminate parehtneses)
6 = 6
Instead of a variable, I have substituted real numbers to illustrate how this works. You of course would eliminate the parentheses first.
The same is true of multiplication as well.
(2*4)*5 = 2*(4*5)
8*5 = 2*20 (eliminate parentheses)
40 = 40
Again, you eliminate the parentheses first and then work out the problem the rest of the way.
This is the Associative Property of Addition. This property demonstrates the rule that 2 expressions are equal no matter how the numbers are grouped when all operations are addition. For example:
(3+10)+5 = 3+(10+5)
Each side of the equal sign is an expression. The expression on the left shows 3+10 as a group. The expression on the right shows 10+5 as a group.
(3+10)+5 = 18 Three plus ten equals 13. 13 plus five equals 18.
3+(10+5) = 18 Ten plus five equals 15. 15 plus three equals 18.
Rules state that any problem in parentheses must be solved first. You can see that regardless of how the numbers are grouped the expressions are equal.
associative property of addition
(2+g)+3=2+(g+3). This property is called associative property of the operation +, the addtion of numbers, in group theory of numbers. Or the addition of numbers is associative. Thus for any numbers a,b,c if =(a+b)+c=a+(b+c), the addtion of numbers is associative. The associative property of addtion has the use of has use of indepedence groupig while doing the operation.