What property do parenthesis represent? What operation is associated with this property?
Strictly speaking, parenthesis do not represent any property, but they serve to prioritize an operation. According to the order of operations agreement, the operation in parenthesis is always performed first. However, the property usually associated with parenthesis is distributive property. This property involves two operations: multiplication and addition or multiplication and subtraction.
For example, consider the following problem:
3 + 4*5
Here, according to the order of operations, multiplication needs to be performed first, so
3 + 4*5 = 23.
If one needs to calculate something where 3 needs to be added to 4, and the result multiplied by 5, one needs to put 3 + 4 in parenthesis:
(3 + 4)*5
Now addition is prioritized, since it is in parenthesis, and
(3 + 4)*5 = 7*5 = 35.