This is meant for age group 11 to 14 years. For Class VIII CBSE. Some viewers have requested me to send the file through mail. So I allowed everybody to download.My request is whenever you are using plz acknowledge me. Pratima Nayak ,Teacher,Kendriya Vidyalaya,Fort William,Kolkata pnpratima@gmail.com Based on Text book

1. Number
theory

2. Mathematics is the
‘Queen of Science’ and
Number theory is the
‘Queen of Mathematics’.

3. Introduction
Number theory as a fundamental body
of knowledge has played a pivotal role
in the development of Mathematics.
The Greek Mathematician Pythagoras
and his disciples believed that
“everything is number” .

4. History
The system of writing numerals was
developed some 10,000 years ago.
India was the main centre for the
development of the number system
which we use today. It took about 5000
years for the complete development of
the number system.

5. History
The Whole numbers are fountain head of all
Mathematics. The present system of writing numerals
is known as Hindu-Arabic numeral system.
In this system, we use the numbers 0, 1, 2, 3, 4, 5, 6,
7, 8, 9. It is also called the decimal system with base
10. The word ‘decimal’ comes from Latin word
‘Decem’ which means ‘Ten’.

6. Number System
 Natural numbers N = {1, 2, 3, g},
Whole numbers W = {0, 1, 2, g},
 Integers Z = {3, – 2, – 1, 0, 1, 2,3g}
 Rational numbers Q

8. The numbers of the form
where p and q are integers and q ≠ 0 are known
as rational numbers.
The collection of numbers of the form
, where q > 0 is denoted by Q.
q
p
q
p
Rational numbers include natural numbers, whole
numbers, integers and all negative and positive
fractions.
Rational numbers

10. Representation of Rational Numbers on the Number Line
To express rational numbers appropriately on the
number line, divide each unit length into as many
number of equal parts as the denominator of the
rational number and then mark the given number on
the number line.

11. Representation of Rational Numbers on the Number Line
Express on the number line.
7
4

12. Representation of Rational Numbers on the Number Line
Express on the number line.
5
17

13. Representation of Rational Numbers on the Number Line
Express on the number line.
3
2

14. To find rational numbers between two rational numbers

15. To find rational numbers between two rational numbers

16. To find rational numbers between two rational numbers

17. To find rational numbers between two rational numbers

18. To find rational numbers between two rational numbers

19. To find rational numbers between two rational numbers

20. So, unlike natural numbers
and integers, there are
countless rational numbers
between any two given
rational numbers.

21. Four Properties of
Rational Numbers

22. Addition

23. Addition

24. Addition

25. Addition