# Adding and Subtracting Numbers using the Number Line

**Steps on How to Add Numbers on the Number Line**

Adding numbers on a number line is a neat way to see how numbers are added using some visual interpretations.

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**.

**Steps on How to Subtract Numbers on the Number Line**

To subtract numbers on the number line is very similar to what you have learned in adding numbers. 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, 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 add two negative numbers. Let’s transform this subtraction into an addition problem. Remember always to add 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**.