Integers are a subset of the reals composed of numbers expressible without fractional or decimal components. Thus, 3 and -5 would both be classified as integers, whereas -2.4 and 1/2 would not. The addition or subtraction of any two integers returns an integer and is a very straightforward process for two positive values. However, special considerations must be made for finding the sum and difference of two integers that contain negative values.
Addition of Two Negative Integers
The sum of two negative integers is found in the same manner as the addition of two positive integers. The two values are summed and retain the sign of the added values. For example, the sum of -2 + -3 is -5, while the sum of 2 + 3 is 5.
Addition of a Positive and Negative Integer
The sum of a positive and negative integer can easily be found by following three simple steps: identify the integer with the largest absolute value (a number's value irrespective of sign), subtract the integer with the smaller absolute value from the integer with the larger absolute value and retain the sign of the larger. For example, the sum of -5 and +3 is -2. The absolute value of the two integers is 5 and 3, respectively, so -5 has the largest absolute value. The difference between the number with the larger absolute value and the number with the smaller absolute value (5 - 3) is 2. Applying the sign of the integer with the larger absolute value then gives a final answer of -2.
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Subtraction of Negative Integers
The procedure for finding the difference of two integers is the same for both two positive and two negative integers. Change the subtraction sign to an addition sign, reverse the sign of the integer being subtracted and then follow the addition rules for integers. For example, -3 - 5 is rewritten as -3 + -5. The values are then summed, and the sign of the two integers is retained, resulting in a difference of -8. Now take the opposite case. You would rewrite 3 - 5 as 3 + -5 and then use the directions in Section 2, subtracting the integer with the smaller absolute value from the integer with the larger absolute value (5 - 3 = 2) and then applying the sign of the integer with the larger absolute value, getting -2.
Follow the Rules
Subtraction of negative integers is the most difficult of the procedures to perform. However, if you follow the rules for addition in Sections 2 and 3, the process becomes very easy. Begin by transforming the problem from one of subtraction to one of addition as in Section 3. That is, transform the minus sign into a plus and then reverse the sign on the number being subtracted. For example, rewrite -3 - (-5) as -3 + (+5) or -3 + 5. Subtract the integer with the smaller absolute value from the integer with the larger absolute value (5 - 3 = 2) and then apply the sign of the integer with the larger absolute value, getting 2.