Page 34 - Start Up Mathematics_6

2 Whole Numbers

We have already learnt about numbers, their place value, face value, estimation, Roman numbers,
etc. In this chapter, we will learn about numbers in detail and their properties. We will also learn
addition, subtraction and multiplication of numbers on a number line.

Natural Numbers

Answer the following questions before we proceed further.
1. How many footballs are required to play a soccer match?
2. How many eyes do we have?
3. How many months are there in a year?

To answer these questions, we need to count beginning from 1. The numbers 1, 2, 3, 4, ... are called
counting numbers. Counting of these numbers comes naturally to us. Therefore, mathematicians
also called these numbers natural numbers. Hence, the numbers 1, 2, 3, ..., 1,000, ..., 10,00,00,000,
..., etc. are called natural or counting numbers.

Successor and predecessor of natural numbers
On adding 1 to a natural number, we get the next natural number. This number is called the
successor of the given number. For example, the successor of 3 is 4. We can obtain successor of
any number by adding 1 to it. There is always a number next to the given number irrespective of
its value. Therefore, there is no last or greatest number. Similarly, the number 15 comes before
16, we say that on subtracting 1 from the given natural number, we get its predecessor.
The number 1 is the only natural number which has a successor but no predecessor because on
subtracting 1 from it, we get 0 which is not a natural number. All natural numbers except 1 have
both successor and predecessor.

Whole Numbers
In natural numbers, we have seen that there is no predecessor of 1. A collection of natural numbers
along with 0 are called whole numbers. Every natural number is a whole number but, on the other
hand there exists a whole number ‘0’ which is not a natural number.

Addition of Whole Numbers on a Number Line

Let’s add whole numbers 3 and 5. Do you know?
Step 1: Draw a number line as shown. The word zero originated
from the Hindu word sunya
0 1 2 3 4 5 6 7 8 9 10 which means ‘void’. Then
Step 2: First move three units to the right from ‘0’ to reach at 3. sunya was translated into
the Arabic sifr, which when

O translated to Latin gave
zero.
0 1 2 3 4 5 6 7 8 9 10