Page 24 - Maths Class 06

If we observe the number line, we derive the following important properties of whole numbers:
1. There is no whole number on the left of 0.
2. 0 is the smallest whole number.

3. There is no greatest whole number.
4. 1 is one more than 0, 2 is one more than 1, 3 is one more than 2; and so on.
1 is the succes sor of 0. Each whole number has one and only one succes sor. Also, 0 (zero) is not the
successor of any whole number.

5. In the reverse order, 0 is one less than 1, 1 is one less than 2, 2 is one less than 3 and so on. 0 is
called the predecessor of 1, 1 is the predecessor of 2; and so on.
Each whole number (except 0) has one and only one predecessor. 0 has no predecessor.
6. Every whole number on the number line is greater than every whole number on its left.

For exam ple, 12 6> , 8 5> , 3 2> .
7. Every whole number on the number line is less than every whole number on its right.
For exam ple, 8 12< , 2 5< , 17 20< .
NOTE
8. The number line displays the property of
‘0’ is the only whole number which is not a
betweenness. natural number.
For exam ple, 6 is between 3 and 8. ‘0’ does not have a predecessor whole number.

A. Addition of Whole Numbers on the Number Line

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

0 1 2 3 4 5 6 7 8 9

Method : Start from 3. Since we add 4 to this number, we make 4 jumps to the right, i e. ., from 3 to 4, 4 to
5, 5 to 6 and 6 to 7 as shown above. The tip of the rightmost arrow in the fourth jump is at 7.
Hence, sum of 3 and 4 is 7, i e. ., 3 + 4 = 7.

B. Subtraction of Whole Numbers on the Number Line
The subtraction of two whole numbers can also be shown on a number line.

Let us find 8 6- .

0 1 2 3 4 5 6 7 8

Method : Start from 8. Since 6 is being subtracted, move towards left with one jump of 1 unit. Make 6
jumps. We reach at the point 2.
Hence, 8 6- = 2.

C. Multiplication of Whole Numbers on the Number Line
After addition and subtraction of whole numbers on number line, let us see the multiplication of numbers
on number line.

Mathematics-6 24