When we add a positive number, we move to the right on a number line. Conversely, adding a negative number involves movement to the left.
See solution.
Practice makes perfect
We want to explain how we can use a number line to find the sum of two integers. First, let's recall that integers are the set of whole numbers and their opposites. This means that the set includes have positive whole numbers, negative whole numbers, and 0, which is neither positive nor negative.
There are four types of sums of two integers that we can consider.
Adding two positive integers
Adding a negative integer to a positive integer
Adding a positive integer to a negative integer
Adding two negative integers
Let's describe the process of finding the sum of two integers using a number line for each type of sum, one at a time.
Adding Two Positive Integers
Let's imagine that we want to add the two positive integers 1 and 4. We can use the number line to find this sum. To do this, we first draw an arrow from 0 to 1.
Then we draw an arrow 4 units to the right to represent adding 4.
We can see that the sum of these two numbers is 5. Therefore, when we add a positive integer to a positive integer, we move to the right on the number line two times.
Adding a Negative Integer to a Positive Integer
Next, let's imagine that we want to add - 3 to 2. Again we will use the number line to find this sum. To do this, we first draw an arrow from 0 to 2.
Then we draw an arrow 3 units to the left to represent adding - 3. Notice that in the case of negative integers, the length of the arrow is the absolute value of the number we want to add.
These two numbers add up to - 1. When we add a negative integer to a positive integer, we first move to the right and then to the left on the number line.
Adding a Positive Integer to a Negative Integer
This time we will add - 2 and 4. Let's use the number line and draw an arrow from 0 to -2.
Now let's draw an arrow 4 units to the right to represent adding 4.
The sum of these two numbers is 2. When we add a positive integer to a negative integer, we first move to the left and then to the right on the number line.
Adding Two Negative Integers
Finally, let's imagine that we add the two negative integers - 5 and - 1 together. We can use the number line to find this sum just as before. Let's first draw an arrow from 0 to - 5. Remember that the length of this arrow is the absolute value of the number it represents.
Then we draw an arrow 1 unit to the left to represent adding - 1.
We can see that these two numbers add up to - 6. Therefore, when we add a negative integer to a negative integer, we move to the left on the number line two times.
