NCERT Class VI Mathematics for Blind and Visually Impaired Students.

Draw a line. Mark a point on it. Label it 0. Mark a second point to the right of 0. Label it 1.

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.

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.
This number 7 is greater than 4, i.e. 7 > 4. The number 8 lies on the right of 6 and 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. We can also say that whole number on left is the smaller number.

For example, 4 < 9; 4 is on the left of 9. Similarly, 12 > 5; 12 is to the right of 5.

What can you say about 10 and 20?

Mark 30, 12, 18 on the number line. Which number is at the farthest left?

Can you say from 1005 and 9756, which number would be on the right relative to the other number.

Place the successor of 12 and the predecessor of 7 on the number line.

Addition on the number line

Addition of whole numbers can be shown on the number line. Let us see the addition of 3 and 4.

Start from 3. Since we add 4 to this number so we make 4 jumps to the right; from 3 to 4, 4 to 5, 5 to 6 and 6 to 7 as shown above. The tip of the last arrow in the fourth jump is at 7.

The sum of 3 and 4 is 7, i.e. 3 + 4 = 7.

Help yourself
Find
4 + 5;
2 + 6;
3 + 5 and
1+ 6
using the number line.

Subtraction on the number line

The subtraction of two whole numbers can also be shown on the number line.
Let us find 7 − 5.

Start from 7. Since 5 is being subtracted, so move towards left with 1 jump of 1 unit. Make 5 such jumps. We reach the point 2.
We get 7 − 5 = 2.

Help yourself
Find
8 − 3;
6 − 2; and
9 − 6
using the number line.

Multiplication on the number line

We now see the multiplication of whole numbers on the number line.

Let us find 4 × 3.

Start from 0, move 3 units at a time to the right, make such 4 moves. Where do you reach? You will reach 12.

So, we say, 3 × 4 = 12.

Help yourself
Find
2 × 6;
3 × 3; and
4 × 2
using the number line.

EXERCISE 2.1

Q1. Write the next three natural numbers after 10,999.

Q2. Write the three whole numbers occurring just before 10,001.

Q3. Which is the smallest whole number?

Q4. How many whole numbers are there between 32 and 53?

Q5. Write the successor of :
(a) 2,440,701
(b) 100199
(c) 1,099,999
(d) 2,345,670

Q6. Write the predecessor of :
(a) 94
(b) 10,000
(c) 208,090
(d) 7,654,321

Q7. In each of the following pairs of numbers, state which whole number is on the left of the other number on the number line. Also write them with the appropriate sign (>, <) between them.
(a) 530 and 503
(b) 370 and 307
(c) 98,765 and 56,789
(d) 9,830,415 and 10,023,001

Q8. Which of the following statements are true (T) and which are false (F) ?
(a) Zero is the smallest natural number.
(b) 400 is the predecessor of 399.
(c) Zero is the smallest whole number.
(d) 600 is the successor of 599.
(e) All natural numbers are whole numbers.
(f ) All whole numbers are natural numbers.
(g) The predecessor of a two digit number is never a single digit number.
(h) 1 is the smallest whole number.
(i) The natural number 1 has no predecessor.
(j) The whole number 1 has no predecessor.
(k) The whole number 13 lies between 11 and 12.
(l) The whole number 0 has no predecessor.
(m) The successor of a two digit number is always a two digit number.