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\ 07-Nov-2024 Bharat Arora Proof-8 Reader’s Sign _______________________ Date __________

1. Fill in the blanks:

(a) The successor of the number 6745 is .......... and the predecessor of the number 2024 is
.......... .
(b) The smallest natural number is .......... and the smallest whole number is .......... .

(c) The aeroplane flies above the sea level but the submarine sails .......... the sea level.
2. State whether the following statements are True (T) or False (F).

(a) Natural number 1 has no predecessor.

(b) There are uncountable natural numbers.
3. Show the following numbers on the number lines:
(a) 10 + 12 (b) 20 + 4 + 3 (c) 9 – 5 (d) 8 – 3 – 2

4. Write the opposite of the given words:

(a) above (b) profit (c) increase (d) going up (e) positive
Need for a New Number System

Vivek: Do you mean all numbers which are less than ‘0’ are negative numbers? Please help me in
understanding this concept.
Lata: Yes. Negative numbers means less than 0 and positive numbers means more than 0. All these
numbers are known as integers. Let us know more about them.

We know that numbers are essential in our daily lives, whether we use them for counting items,
telling time, or assigning house numbers, etc. For counting objects, natural numbers are used
which start from 1 and continue forever, i.e., 1, 2, 3, … . These are also known as counting numbers.
When we include ‘0’ along with the collection of natural numbers, we get a new set of numbers,
i.e., 0, 1, 2, 3, 4, … which is called whole numbers.

We have also performed basic operations on the whole numbers. Let us try to find the difference
between any two whole numbers.
10 – 6 = 4, a whole number

23 – 11 = 12, a whole number
45 – 45 = 0, a whole number

But, 4 – 9 = ?
And, 17 – 20 = ?

We find that we can easily subtract a smaller number or the number itself from a larger whole
number, but we cannot subtract a larger whole number from a smaller one. This raises the question
of what kind of number will result from subtracting a larger whole number from a smaller one. In
order to address these issues, we must add a new class of numbers known as negative numbers
to the number system. These new numbers are represented by negative signs that are less than
zero, such as –1, –2, –3, –4,..., and are the reverse of natural numbers.

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