Question

Property of this equation

x + (y + 10) = (x + y) + 10​

Answer 1

The equation
`x + (y + 10) = (x + y) + 10` demonstrates the associative property of addition.

Explanation:

Addition is associative. In other words, when adding a finite list of numbers, the order in which the numbers are added to the sum does not matter.

In this question, the associative property of addition ensures that the following ways to calculate
`(x + y + 10)` are equivalent:

• 
  `((x + y) + 10)`: take the sum of
  `x` and
  `y` (the sum would be
  `(x + y)`) and then add
  `10`.
• 
  `(x + (y + 10))`: add
  `x` to
  `(y + 10)` (the sum of
  `y` and
  `10`.)

Notice that the relative order of the terms (
`x`,
`y`, and then
`10`) is the same. Only the grouping of the terms (the parentheses) was changed.

While this property ensures that the results would be equal, the actual calculations are different. For example,
`x` and
`y` are directly added to each other in
`((x + y) + 10)` but not in
`(x + (y + 10))`.