All of the underneath is utter ignorance. Communitive means "of or belonging to a community" and has no algebraic meaning whatsoever.
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The Communitive Property shows that a problem can have the same answer if you re-arrange the numbers
Communitive property
A+B= B+A
It will not matter in addition how you group your numbers.
Example: 5+3 + 6 =14
6+3+5 = 14
In abstract algebra, a binary operation * has the commutative property if
a*b = b*a.
For ordinary numbers, addition has the commutative property; for example 2+3 = 3+2.
Subtraction does not have the commutative property, because 2 - 3 does not equal 3 - 2.
Multiplication of ordinary numbers has the commutative property, as does multiplication of complex numbers.
Matrix multiplication does not have the commutative property in general; there are matrices A, B such that A*B does not equal B*A.
Also the vector cross product does not have the commutative property, as
i x j = k, but j x i = -k.
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Division Property of Equality
Its an algebra property(: ask someone else cause i got no idea!
properties are based on axioms
2x(3x-1) = 6x2-2x because of the distributive property.
in communitive prop., the problem does not change at all except for the order. In accociative prop. the grouping also changes. for example communitive prop. associative prop i forgot LOL x+1=154665 1+x=154665