maths class 8th ppt by Shaileja Sati

1. RATIONAL
NUMBERS
C L A S S - V I I I

2. SUBTOPICS:
1. What are Rational numbers?
2. Properties of Rational Numbers
• Closure Property
• Commutative Property
• Additive Identity
• Multiplicative Identity

3. C O U N T T H E N U M B E R S O F P E N C I L S O N
Y O U R S C R E E N

4. • Natural number : A natural number is a counting number. It starts from 1 onwards.
Examples : 1,2,3,4,5…….. infinity.
• Whole number : The numbers from zero to infinity.
Examples: 0,1,2,3,4,5………… infinity.
• Integers : Integers are the set of numbers containing whole numbers and their negatives.
Examples: ( -Infinity…….. -4,-3,-2,-1,0,1,2,3…….. Infinity)
• On solving equation 2x+5= 2, I m getting -3/2.
so what type of number is this?
Natural numbers + 0 = Whole
numbers
Whole numbers + negative
numbers= Integers
Good Question
Rahul. LET’S discuss
one more type of
numbers

5. RATIONAL NUMBERS
• A number which can be written in the form p/q, where p and q
are integers and q ≠ 0.
Examples:
−2
3
,
6
7
etc.
• A number is called a rational number if it satisfies three
conditions:
1. It should be in the form p/q.
2. p and q should be integers.
3. q≠ 0 ( denominator ≠ 0)
p= numerator
q= denominator

6. • A number is called a rational number
it satisfies three conditions:
1. It should be in the form p/q.
2. p and q should be integers.
3. q≠ 0 ( denominator ≠ 0)
Question: Is 5 a rational number?

7. ALL THE NATURAL NUMBERS, WHOLE
NUMBERS AND INTEGERS ARE
RATIONAL NUMBERS.
NATURAL NUMBERS
WHOLE NUMBERS
INTEGERS
RATIONAL NUMBERS
3
-2

8. PROPERTIES OF RATIONAL NUMBERS
•CLOSURE PROPERTY
•COMMUTATIVE PROPERTY
•ASSOCIATIVE PROPERTY
•DISTRIBUTIVE PROPERTY

9. CLOSURE PROPERTY
ACTIVITY-1
OPERATION EXAMPLE ( TAKE ANY
TWO RATIONAL
NUMBER)
YOUR RESULT
( IS IT A RATIONAL
NUMBER?)
CONCLUSION
ADDITION:
A+B= RATIONAL
NUMBER
½ +(- 1/5 )= _____ Yes RATIONAL NUMBERS
ARE CLOSED UNDER
ADDITION
SUBTRACTION:
A-B= RATIONAL
NUMBER
½ - ( - 1/5)=______ Yes RATIONAL NUMBERS
ARE CLOSED UNDER
SUBTRACTION
MULTIPLIACTION:
A X B= RATIONAL
NUMBER
3/5 X ½= ____ Yes RATIONAL NUMBERS
ARE CLOSED UNDER
MULTIPLICATION
DIVISION:
A÷B= RATIONAL
NUMBER
2/3 ÷ 0= ______ No RATIONAL NUMBERS
ARE NOT CLOSED
UNDER DIVISION

10. DEFINITION OF CLOSURE PROPERTY
•A set is closed under an operation if
performance of that operation on members of
the set always produces a member of that set.

11. • We commute when we go back and
forth from work to home.
Commutative
Property
A * B = B * A

12. COMMUTATIVE PROPERTY
• MARKS OF AMAN
MARKS IN MATHS = 45
MARKS IN SCIENCE= 40
• AMAN’S CALCULATION= M+S
= 45+40
=85
RITU’S CALCULATION=
S+M
=40+45
=85

13. COMMUTATIVE PROPERTY
ACTIVITY 2
OPERATION EXAMPLE YOUR RESULT CONCLUSION
ADDITION:
(A+B)=(B+A)
½ + ¼ = ¾
¼ + ½ = ¾
YES RATIONAL NUMBERS
ARE COMMUTATIVE
FOR ADDITION
SUBTRACTION:
(A-B)≠(B-A)
NO RATIONAL NUMBERS
ARE NOT
COMMUTATIVE FOR
SUBTRACTION
MULTIPLIACTION
(AXB) = (BXA)
YES RATIONAL NUMBERS
ARE COMMUTATIVE
FOR MULTIPLICATION
DIVISION:
(A÷ 𝐵) ≠ (𝐵 ÷ 𝐴)
2/3 ÷ 1/3 = 2/3 x3/1 = 2
1/3 ÷ 2/3 = 1/3 x 3/2 = 1/2
Hence, 2/3 ÷
NO RATIONAL NUMBERS
ARE NOT
COMMUTATIVE FOR
DIVISION

14. ADDITIVE IDENTITY
•
𝟐
𝟑
+ _____ =
𝟐
𝟑
• O is called the identity for addition of rational numbers.

15. MULTIPLICATIVE IDENTITY
•
𝟐
𝟑
X _____ =
𝟐
𝟑
• 1 is the multiplicative identity for rational numbers.

16. RECAPITULATION
• WHAT IS A RATIONAL NUMBER?
• PROPERTIES OF RATIONAL NUMBERS:- CLOSURE AND COMMUTATIVE PROPERTY
• CLOSURE PROPERTY IS CLOSED UNDER ADDITION, SUBTRACTION AND
MULTIPLICATION FOR RATIONAL NUMBERS.
• RATIONAL NUMBERS ARE COMMUTATIVE FOR ADDITION AND MULTIPLICATION.
• O is called the identity for addition of rational numbers.
• 1 is the multiplicative identity for rational numbers.

17. • IMPORTANT LINKS :-
https://www.youtube.com/watch?v=F0L2FENoJOo
https://www.youtube.com/watch?v=dPumqKzTLQ0
• HOME WORK :-
Do try these questions from page 13 and 14.
THANK YOU