Contents

- Definition
- Overview
- Components of Number line
- Procedure for Sketching Number Line
- Addition of Positive Numbers on the Number Line
- Subtraction of Positive Numbers on the Number Line
- Addition of Negative Numbers on the Number Line
- Subtraction of Negative Numbers on the Number Line
- A Solved Example Using the Number Line

# Number Line|Definition & Meaning

**Definition**

As the name suggests, a **number line** is a **visual representation** of **numbers** on a **line** that can be **drawn** as an **x-axis or y-axis.** The** line compares numbers** that are equally **spaced** on an **infinite line** extending both **horizontally** and **vertically**, with equal intervals.Â

**Our abilit**y to **perform basic arithmetic** operations on **numbers** is **greatly enhanced** when we write them out **on a number line**.

**Overview **

Generally speaking, **zero** is taken as the **origin** or **starting point** of the **number line**. The **origin divides** the **number line** into **two portions** **left portion** and the **right portion**. The** left portion represents** the **numbers** that are **less than zero. **In other words, all the negative numbers. The **right portion** of the number line **represents** the **numbers** that are **greater than zero**, in other words, all the positive numbers.

Figure 1 – Components of Number Line

The **importance** of a number line **is** to **give a graphical representation** and **visualization** of numbers that help in various applications related to **probability**, **stochastic systems**, and other **statistical systems**.

**Components of Number line**

We can **divide** the **number line** from Figure 1 into **three parts: origin****, negative area**, and **positive area**. We will discuss them one by one.

**Origin**

The **midpoint** of the **number line **is known as the **origin** and it is denoted as “**o.**” Further, it **divides** the **number line** into **two equal parts.**

**Positive Area**

The **right portion** or right side of the origin is known as the **positive area**. All the **numbers** lying **in this region** are **positive**. The **range** of this portion is from natural numbers varying from **greater than zero to positive infinity**.

**Negative Area**

The **left portion** or left side of the origin is known as the **Negative area.** All the **numbers** lying **in this region** are **negative**. The **range** of this portion is from natural numbers varying from **less than zero to negative infinity**.

**Procedure for Sketching Number Line**

**Step 1**

**Draw** a** line,** either **horizontal** or **vertical,** according to the given specification. Often it’s **our choice** to draw a horizontal or vertical line that **best suits** the **given visualization**.

Figure 2 -Sketching Number Line First Step

**Step 2**

The second step is to** select** an **appropriate scale** according to the given problem. Suppose we want to **plot 3;** we can **select** a **scale of 1. **If we want to **plot **the number** 10,** we can select a **scale of 2,** and if we want to** plot** some **greater number,** then we will **increase** the **scale factor **accordingly**.** For example, to **plot the number 30,** we **can take a scale of 5**.

The **reason** for **selecting scale** is that **while plotting** numbers on the number line on a page or graph paper, there is **limited space,** so we have to** choose the scale** that **can best plot** in a given** limited space**.

Figure 3 – Sketching Number Line Second Step

**Step 3**

The third step is to **label** the **number line** according to the selected scale. For instance, if we want to **plot number 5** and we have **chosen** the **scale as 1,** then** starting from origin** 0, we will **label** the **number line after** every **1 unit space** as we will **mark the scale as 0, 1, 2, 3, 4, 5**.

Figure 4 – Sketching Number Line Third Step

**Step 4**

After sketching the number line, the **last step** is to **plot** the **number.** For plotting the number, **find the position** of that **number** on a number line and **highlight using** either a **dot** or a **cross**.

Figure 5 – Sketching Number Line Fourth Step

**Addition of Positive Numbers on the Number Line**

**Suppose** there are **two numbers, 5 and 3,** and we want to add them. **First**, we will **sketch** a **number line** with a **scale** of **1**. Then, from the **location of number 3 **on the number line, we will **move 5 steps** towards the **right side.** The** point where we stop** will be the **result** of the **addition** of these **two numbers**. This is shown in the illustration shown below.

Figure 6 – Addition of Positive Numbers on Number Line

**Subtraction of Positive Numbers on the Number Line**

Consider **two numbers 6 and 3** that we want to **subtract**. First of all **sketch** a **number line** with a **scale of 1. **Then, **from** the **location of 6** on the number line, **move 3** units **backward. **The **position** that **we get** after doing so will be the **result** of **subtraction**. This is shown in the illustration below.

Figure 7 – Subtraction of Positive Numbers on Number Line

**The Direction of Movement for Addition and Subtraction of Positive Numbers**

For the **addition** of **two numbers,** we will **move** toward the **right side** while **for** the **subtraction** of **two numbers,** we will **move** **toward the left** side. Keep in mind the fact that the number line** increases **as we move toward the **right side**, and **decreases** as we move toward the **left**.

**Addition of Negative Numbers on the Number Line**

The **concept** of **adding** a **negative number** is the **same** as that of a **positive number** but **with** the** change** that the **negative number** will be **dealt** in the **left side** of the **origin** i.e. in their domain.

Suppose we have to **add -5 and -3. **On the number line, we will **first plot -3** which would be **toward** the **left of the origin,** and **from -3,** we will **take 5 steps** towards the **left side. **The **position **we end up in will be the** result** of the **addition**.

Figure 8 – Addition of Negative Numbers on Number Line

**Subtraction of Negative Numbers on the Number Line**

For the **subtraction** of two numbers **-6 and -3**, we will **first plot the -6 number.** Then, **from** the **position** of **-6,** we will **take three steps** toward the **right side,** and this **position** will be the **result** of the **subtraction** of these two numbers.

Figure 9 – Subtraction of Negative Numbers on Number Line

**The Direction of Movement for Addition and Subtraction of Negative Numbers**

For the **addition** of two **negative numbers**, we will **move toward the left side,** while for the** subtraction** of **two negative numbers,** we will **move toward the right side. **The **interesting point** to be noted **here** is that the **direction** of **movement** for **negative numbers** is **opposite** to the direction of **positive numbers** that we dealt with earlier.

**A Solved Example Using the Number Line**

**Solve** the following **arithmetic problems** graphically.

- 3+2
- 5-2
- (-3)+(-2)
- (-5)-(-2)

**Solution**

Figure 10 – Example of Number Line

*All mathematical drawings and images were created with GeoGebra.*