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Why are addition and subtraction considered inverse operations?
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arithmetic
A page from a first-grade workbook typical of “new math” might state: “Draw connecting lines from triangles in the first set to triangles in the second set. Are the two sets equivalent in number?”
Addition and subtraction are considered inverse operations because they effectively undo each other's effects. In mathematics, an inverse function is a procedure that reverses the action of another; applying one and then the other returns you to the original value.
For example, if you add a number to a value and then subtract that same number, you return to the starting point. This relationship is rooted in the concept of the additive inverse, where adding a number and its opposite (e.g., ) results in zero. Because subtraction is equivalent to adding an additive inverse, the two operations function as a pair that allows for the reversal of mathematical procedures, which is essential for solving equations.12