Adding Integers

Integers: Negative + Negative

To add Integers, we will use a number line. The number line will help us organize our information and provide a positional strategy for dealing with numbers of this type. Here is the strategy.

When you add a negative number with a negative number, locate the first number on the number line. Next, move to the left of that number a number of spaces equal to the absolute value of the second number. The answer to the problem is the same value as the last number on which you land.

Dealing with positive and negative numbers requires knowledge of absolute value. Absolute value means distance from zero. So, the absolute value of 5 is 5 because 5 is 5 units from zero. The absolute value of -2 is 2, because -2 is 2 units from zero. The notation below says the exact same thing, but is written using mathematical symbols.

|5| = 5

|-2| = 2

Let us examine two examples that use this positional strategy. The number line below will assist you through the process.

Example #1: -1 + (-2)
The strategy says that you must start on the number line at -1. Next, the strategy says that you must move a number of spaces to the left equal to |-2|, which is 2. If you move to the left 2 spaces, you should go from -1 to -2 and from -2 to -3, for a total of 2 spaces. The last position is -3 and that is the answer to the problem. Therefore, -1 + (-2) = -3.
Example #2: -2 + (-6)
Following the same procedure as example above, start at -2. Next, move |-6| spaces to the left. After moving 6 spaces, the final position should be -8. Therefore, -2 + (-6) = -8.

To help you learn other skills with Integers, use the links below.

Positive + Positive
Positive + Negative
Negative + Positive

Go to Subtracting Integers.
Go to the Frontpage.
Go to MATHguide.

(Updated October 17th, 2004)