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Subtract integers symbolically

Subtracting one integer from another is understood as adding its additive inverse: ab=a+(b)a-b=a+(-b). 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.

Detailed Explanation: Subtract integers symbolically

To subtract an integer, add its additive inverse:

ab=a+(b)a-b=a+(-b)

The additive inverse is the number that is the same distance from zero but on the opposite side. For example, the additive inverse of 5-5 is 55.

Example:

3(5)-3-(-5)

Step 1: Rewrite subtraction as addition.
Change the subtraction sign to addition and find the opposite of the number being subtracted:

3(5)=3+5-3-(-5)=-3+5

Step 2: Add the integers.
Starting at 3-3 on a number line, move 55 units to the right because you are adding 55:

3+5=2-3+5=2

Therefore,

3(5)=2\boxed{-3-(-5)=2}

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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Negative Integer Subtraction


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