The Number Line
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.
Number line for 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.
Now, let's find out about sucessor and predecessor. Observe the numberline given above. It starts from the number-
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?
Moving on to show the addition of two whole numbers on the number line.Say, we need to find 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:
(i) 4 + 5 =
(ii) 2 + 6 =
(iii) 3 + 5 =
(iv) 1 + 6 =
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.
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 =
Try these on numberline and answer:
(i) 8 – 3 =
(ii) 6 – 2 =
(iii) 9 – 6 =
Multiplication on the number line
We will now see the multiplication of whole numbers on the number line. Let us find 2 x 4.
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 =
When representing multiplication on the numberline, the starting point to show the jumps is always zero.
Try these on numberline and answer:
(i) 2 × 6 =
(ii) 3 × 3 =
(iii) 4 × 2 =
(iv) 5 × 3 =
(iii) 7× 2 =