# How to Add Integers Using the Number Line

There are several methods that can be used in adding integers. One of this methods is to use the number line. If you can see the pattern in this method, it is easier to see the sign of the sum of two signed numbers even before you add them.

To be able to use this method to add integers, first we should think of numbers as movements on the number line. We can think of the positive numbers as movement to the right and the negative numbers as movement to the left. With these in mind, we can represent $^+3$ and $^-4$ as shown in the figure below.

In adding integers, the representation of the first movement should start from 0. The next movement should start from where the previous movement stopped.

#### Some Examples

Example 1: $^+ 3 + ^+4$

First, from 0, we move 3 units to the right and from where it stopped, we move another 4 units to the right.

It stopped at $^+7$. This is the same as moving 7 units  to the right of 0. This means that $^+3 + ^+4 = ^+7$.

Example 2: $^- 2 + ^- 5$

From 0, we move 2 units to the left and from where it stopped, we move another 5 units to the left.

It stlopped at $^-7$. This is the same as moving 7 units to the left. This means that $^-2 + ^-5 = ^-7$.

Example 3: $^+ 6 + ^-2$

From 0, we move 6 units to the right, and from where it stopped, we move 2 units to the left.

We stopped at $^+4$. Therefore, $^+6 + ^-2 = ^+4$.

Example 4: $^-5 + ^+4$

From 0, we move 4 units to the left and from where it stopped, we move 2 units the the right.

We stopped at $^-1$. Therefore, $^-5 + ^+4 = ^-1$.

Using this strategy, it is easy to see if the sum of an addition problem is positive or negative. For example, in the addition $^-8 + ^+5$, we move 8 units to the left of 0 and then 5 units to the right. After these movements, it is clear that we are still to the left of 0 since the distance of the movement to the left is greater than the distance of the movement to the right. Recall that this distance; that is, the distance from 0 to a number on the number line is also the absolute value of the number. So, the sign of the sum of two numbers is the same as the sign of the number with larger absolute value.

In adding numbers with more than two addends, it is sometimes easier to add the numbers with the same sign first, then perform the final addition using two addends. For example, if we have $^+ 3 + ^-3 + ^+2 + ^-8$, we add first $^+3 + ^+2 = ^+5$, then add $^-3 + ^-8 = ^-11$. Finally, we add $^+5 + ^-11 = ^-6$.