Adding and Subtracting Positive and Negative Numbers

1. Adding Positive and Negative Numbers

The ability to work comfortably with negative numbers is essential to success in algebra. For this reason, we will do a quick review of adding and subtracting positive and negative integers. Integers are all the positive whole numbers, zero, and their opposites (negative numbers).

When adding integers, we have two cases to consider. The first case demonstrates a situation with matching signs: both integers are either positive, or both integers are negative. If the signs match, we will add the numbers together, and keep the sign. This is illustrated in the following examples:

	Same sign, add keep the negative
	Our Solution

	Same sign, add keep the negative
	Our Solution

The second case demonstrates a situation with signs that don't match (one integer is positive and one integer is negative). We will subtract the numbers (as if they were all positive), and then use the sign from the larger number. This means if the larger number is positive, the answer is positive; and if the larger number is negative, the answer is negative. This is shown in the following examples:

	Different signs, subtract use sign from bigger number, negative
	Our Solution

	Different signs, subtract use sign from bigger number, positive
	Our Solution

	Different signs, subtract use sign from bigger number, positive
	Our Solution

	Different signs, subtract use sign from bigger number, negative
	Our Solution

big idea

When adding two numbers with matching signs, add the two numbers (as if they are positive) and keep the sign. When adding two numbers with opposite signs, subtract the smaller number from the larger number (as if they are positive), and keep the sign of the larger number.

2. Subtracting Positive and Negative Numbers

For the subtraction of negative numbers, we will change the problem to an addition problem, which can then be solved using the above methods. The way we change subtraction to addition is to add the opposite of the number after the subtraction sign. Often this method is referred to as "adding the opposite." This is illustrated in the following examples:

	Add the opposite of
	Different signs, subtract use sign from bigger number, positive
	Our Solution

	Add the opposite of
	Same sign, add keep the negative
	Our Solution

	Add the opposite of
	Same sign, add keep the positive
	Our Solution

	Add the opposite of
	Different sign, subtract use sign from bigger number, negative
	Our Solution