Addition

Addition of Integers:

To add two Integers, a + b, we use the following rules:

	If the two numbers have the same sign, add the absolute values of the two numbers and keep the sign.
	If the two numbers have different signs, subtract the smaller absolute value from the larger absolute value and keep the sign of the number with the larger absolute value.
	If the two numbers have the same absolute value but opposite signs, the answer is zero.

Example:
Add the following numbers:

Question	Answer	Reason
6 + 8 =	14	Add and keep the sign. They have the same sign. (Same sign)
-6 + -4 =	-10	(6 + 4 = 10) keep the sign. They have the same sign. (Same sign)
-8 + 4 =	-4	(8 - 4 = 4) Subtract and keep the sign of the larger. (Different signs)
6 + -13 =	-7	(13 - 6 = 7) Subtract and keep the sign of the larger. (Different signs)
15 + -15 =	0	(15 - 15 = 0) Same number opposite signs. Rule #3

Opposites, or Additive Inverse:

The sum of any number and its opposite is always zero. The opposite of a number is also called the additive inverse. Finding the opposite of a number can, easily, be found by changing the sign of that number.

Example:

Find the opposite of each number.

Number	Its opposite
5	-5
-8	8
120	-120
-543	543

The opposite of the opposite of a number is the number itself.

Example:

Find the opposite.

Number	Its opposite	Reason
-8	-(-8) = 8	2 minus sign = positive sign
-14	-(-14) = 14	2 minus sign = positive sign
-7	-(-7) = 7	2 minus sign = positive sign
-0	-(-0) = 0	2 minus sign = positive sign
-55	-(-55) = 55	2 minus sign = positive sign