# The Number Line

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**Draw a line from 0 to b.**

Mark a second point to the right of 0.

The distance between these points labelled as 0 and 1 is called unit distance. On this line, mark a point to the right of 1 and at unit distance from 1 and label it 2.

In this way go on labelling points at unit distances as 3, 4, 5,... on the line. You can go to any whole number on the right in this manner. For now do it up to 10.

**This is a number line for the whole numbers.**

**What is the distance between the points 2 and 4?**

Certainly, it is **2 units.** Can you tell the distance between the points 2 and 6, between 2 and 7?

On the number line you will see that the number 7 is on the right of 4.

The number 7 is greater than 4, i.e. 7 > 4. Similarly, the number 8 lies on the right of 6 thus, 8 > 6.

These observations help us to say that: **out of any two whole numbers, the number on the right of the other number is the greater number.**

In other words, we can also say that **the whole number on left is the smaller number.**

For example, 4 < 9; 4 is on the

Similarly, 12 > 5; 12 is to the

What can you say about 10 and 20?

**Test yourself by marking 30, 12, 18 on the number line.**

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Now, let's find out about **sucessor and predecessor.** Observe the numberline given above. It starts from the number-

**Instructions:** In the below given numberline, **click** on any number to choose the icon. Now, give the appropriate inputs in the popup box. First select the approrpriate operation that you want to perform. Say, to find the successor of 2: we need to add 2 and 1. Put "n1: 2" and "n2: 1" while keeping the **"Operation"** as **"Addition".** Click on **"Submit"** button.

Similarly, for predecessor of 5: we need to subtract 1 from 5.Put "n1: 5" and "n2: 1" while keeping the **"Operation"** as **"Subtraction".** Click on **"Submit"** button.

**Now, answer the following:** **What do we get sucessor of 2?**

**What do we get as predecessor of 5?**

**How many jumps do we need to make on the numberline when trying to find sucessor (or) predecessor?**

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Now, the addition of whole numbers can be shown on the number line. Let's see the addition of 3 and 4.

**Instructions:** In the below given numberline, **click** on any number to choose the icon. Now, give the appropriate inputs in the popup box. Say, to find addition of 2 and 6: put "n1: 2" and "n2: 6" while keeping the **"Operation"** as **"Addition".** Click on **"Submit"** button. Now, follow the same instructions to do 3 + 4.

**Note:** Since, addition is commutative, the **start value(n1)** and the **end value(n2)** are interchangeable when doing the operation of addtion.

For addition, we make jumps to the

Let the starting point for making the jumps be 3. Thus, the number of jumps we need to make is

The sum of 3 and 4 is

**Try these on numberline and answer:**

**Use the "Reset" Button to clear out arrows before starting the next question**

**(i) 4 + 5** =

**(ii) 2 + 6** =

**(iii) 3 + 5** =

**(iv) 1 + 6** =

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## Subtraction on the number line

Moving on to show the subtraction of two whole numbers on the number line.Say, we need to find 7 – 5.

**Note:** Always make sure that the **start value(n1)** is greater than the **end value(n2)** when doing the operation of subtraction.

**Instructions:** In the below given numberline, **click** on any number to choose the icon. Give the appropriate inputs in the popup box. Say we need to subtract 2 from 7 i.e. 7 – 2: Put "n1: 7" and "n2: 2" with **"Operation"** set to **"Subtraction".** Click on **"Submit"** button.

We see that the starting point for the jumps in this case is

Starting from 7, we move towards the left making a total of

We reach the number

Thus, 7 – 2 = 5.

**Try these on numberline and answer:**

**Use the "Reset" Button to clear out arrows before starting the next question**

**(i) 8 – 3** =

**(ii) 6 – 2** =

**(iii) 9 – 6** =

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## Multiplication on the number line

We will now see the multiplication of whole numbers on the number line. Let us find 2 x 4.

**Instructions:** In the below given numberline, **click** on any number to choose the icon. Give the appropriate inputs in the popup box. Say we need to multiply 2 and 4: Put "n1: 2" and "n2: 4" while keeping **"Operation"** set to **"Multiplication".** Click on **"Submit"** button.

**Note:** Since, we know that multiplication is commutative, the **start value (n1)** and **end value (n2)** are interchangeable when doing the operation of **"Multiplication".**

We take 0 as a starting point and move 2 units at a time to the

We make

**Where do we reach? You will reach**

**Thus, 2 x 4 = 8**

When representing multiplication on the numberline, the starting point to show the jumps is always zero.

**Try these on numberline and answer:**

**Use the "Reset" Button to clear out arrows before starting the next question**

(i) 2 × 6 =

(ii) 3 × 3 =

(iii) 4 × 2 =

(iv) 5 × 3 =

(iii) 7× 2 =