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INTRODUCTION

We know that 1 is the smallest counting number in the number Remember
system. Counting numbers are also called natural numbers. Š 1 is the smallest natural
number.
Now, suppose Vihan has 5 candies which he wants to distribute Š 0 is the smallest whole
amongst his 5 friends. After distribution how many candies are number.
left with him? Result is 0. Š No largest natural
and whole number are
Hence, zero is in use for counting but this is not in the collection possible as there is no

of natural number. end of counting numbers.
So, no any predecessor of number 1 is possible as a natural number.
Thus, when we include 0 in the collection of natural number, the new collection is 0, 1,
2, 3, 4… known as whole number. If we talk about the number line, 0 is marked at the

extreme left position.
Left Right
0 1 2 3 4 5 6 7

Now, if we perform any fundamental operations on whole numbers (except division of
whole numbers by 0), then we get a whole number at least 0 as a result.
For example: 0 + 5 = 5, 5 – 5 = 0, 2 × 0 = 0, 0 ÷ 2 = 0, etc.

But, if we perform subtraction on whole numbers, it is not always true that we get a whole
number as a result.
Sometimes, if we subtract bigger numbers from the smaller numbers, we do not get a
whole number as the result. Such as

10 – 7 = 3 (whole number); 45 – 30 = 15 (whole number); 1 – 0 = 1 (whole number)
7 – 10 = ?; 30 – 45 = ? 0 – 1 = ?

There is a question arises, what come when we subtract bigger numbers from the smaller
numbers?
To answer of this question, we need to extend the number system with new kind of
numbers. These new numbers are represented as –1, –2, –3, –4, –5, … (whole numbers
together with – sign). These are opposite of counting numbers.

NEGATIVE NUMBERS
The numbers ..., – 3, – 2, –1, which are negatives of counting numbers 1, 2, 3, ... are called
negative numbers. These numbers are less than zero.
Negative numbers are shown left to zero on the number line.

–6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6
Negative numbers Positive numbers
Zero
Since, zero (0) is neither negative nor positive. So, 0 has no sign. If you observe the numbers
on number line, you will find that the negative numbers are the mirror image, considering
0 as the point of mirror, of corresponding to counting numbers.

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