Adding and Subtracting Positive and Negative Numbers using the Number Line
Adding numbers on a number line is a neat way to see how numbers are added using visual interpretations.
I. Steps on How to Add Numbers on the Number Line
As indicated in the diagram below:
- To add a positive number means that we move the point to the right of the number line.
- Similarly, to add a negative number implies that we move the point to the left of the number line.
Examples of Adding Numbers on the Number Line
Example 1: Simplify by adding the numbers, 2 + 4.
The first step is to locate the first number which is two (2) on the number line.
Adding four (4) means we have to move the point, four (4) units to the right.
After doing so, we end up at 6. Therefore, 2+4=6.
Example 2: Simplify by adding the numbers, 3 + (–5).
Locate the first point, 3, on the number line.
Now, we are going to add negative five (-5) which tells us to move the point 5 units going to the left.
We arrive at −2. That’s why 3 + (–5)=–2.
Example 3: Simplify by adding the numbers, –6 + 5.
Find where the first number, −6, is on the number line. To add five (5), the original point will be moved five (5) units to the right of the number line.
This gives us –6 + 5 = –1.
Example 4: Simplify by adding the numbers, –1 + (–6).
This time around, we are adding two negative numbers. To start, locate the first number which is −1. Then, add negative 6 to it which means moving the existing point 6 units to the left of the number line.
Therefore, we have –1 + (–6) = –7.
II. Steps on how to Subtract Numbers by Converting to Addition on the Number Line
The process of subtracting numbers is very similar to adding numbers with a very slight “twist”. The trick is to change the operation from subtraction to addition, then switch the sign of the number that follows it.
In other words, to “subtract” means to “add its opposite“.
Examples of Subtracting Numbers on the Number Line
Example 5: Simplify by subtracting the numbers, 5 − (+6).
As mentioned before, subtraction is just addition. After changing the operation from subtraction to addition, we must take the opposite sign of the number following it. That means, we can rewrite the problem as
5 − (+6) → 5 + (–6)
Since we already know how to add, this problem should be a breeze! We locate the first number which is 5 and then move it 6 units to the left.
This gives us the answer of 5 − (+6) = 5 + (–6) = –1.
Example 6: Simplify by subtracting the numbers, –4 − (–7).
This is an example where we subtract two negative numbers. Let’s transform this subtraction into an addition problem. Remember always add to its opposite.
–4 − (–7) → –4 + (+7)
Start by locating the first number, −4, and then move it 7 units to the right of the number line.
We arrive at 3. That’s why –4 − (–7) = –4 + (+7) = 3.