Subtracting one integer from another is understood as adding its additive inverse: . This interpretation applies to all combinations of positive, negative, and zero integers, including subtracting a negative; on a number line, it represents moving in the direction opposite to the number subtracted, countering the misconception that subtraction always decreases a quantity. The scope is integer subtraction, not generalized operations with arbitrary rational or real expressions.
To subtract an integer, add its additive inverse:
The additive inverse is the number that is the same distance from zero but on the opposite side. For example, the additive inverse of is .
Example:
Step 1: Rewrite subtraction as addition.
Change the subtraction sign to addition and find the opposite of the number being subtracted:
Step 2: Add the integers.
Starting at on a number line, move units to the right because you are adding :
Therefore,
Subtracting does not always make a number smaller. Subtracting a negative means adding a positive, so the result can become greater.
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