cheeck this class 8 maths ppt in class 8 students or below can refer this ppt and make their mind map for maths. thank you and understant the table given in power point presentation give me like please

1. *
Numbers:- The systems of numbers expanded
with new needs.
*Natural numbers :- (Counting numbers)
1 , 2 ,3 ,4 , ………
*Whole numbers :-
0 , 1 , 2 , 3, 4 , …….

2. *
*Integers :- Positive & negative numbers & Zero
…., -2 , -1 , 0 , 1 , 2 , 3 , ……….
*Fractions :-
2
3
,
1
2
,
1
3
, etc.

3. *
*Need for rational numbers:
Do we have enough numbers to solve all simple
equations?
Lets us take 4𝑥 + 9 = 0
𝑥 =
−9
4
We need the number
−9
4
,which is neither a fraction
nor an integer, for solving the given equation.

4. *
*A number which can be written in the form
𝑝
𝑞
,
where p and q are integers and q ≠ 0 is called a
rational number.
Eg. 2 , 0 , -3 ,
2
3
,
−5
7
*Note:- Every natural number ,whole number
integer and fraction is also a rational number.

5. *Properties of Rational
numbers
How do rational numbers behave when they are
added , subtracted ,multiplied or divided with each
other?

6. *1) Closure Property:
Operation Example Rational
number?
Remarks
Addition 2 +
1
2
=
5
2
Yes
Rational numbers
are closed under
addition
Subtraction
5
8
-
3
4
=
5−6
8
=
−1
8
yes
R.Nos are closed
under subtraction
Multiplicatio
n
−4
5
X
5
8
=
−1
2
yes
R.Nos are closed
under
multiplication
Division
2
7
÷
5
3
=
2
7
X
3
5
=
6
35
3
5
÷ 0 is not defined
Not always
Note:- For any rational number a , a ÷ 0 is not defined .Rational numbers are not
closed under division.

7. *2) Commutativity:
Operation Example Remarks
Addition 1 +
1
2
=
1
2
+ 1 =
3
2
Addition is commutative for
Rational numbers
Subtraction
6
3
-
4
3
≠
4
3
-
6
3
Subtraction is not
commutative for Rational
numbers
multiplicatio
n -
7
3
x
6
5
=
6
5
x -
7
3
Multiplication is
commutative for Rational
numbers
Division -
5
4
÷
1
4
≠
1
4
÷ -
5
4
Division is not commutative
for
Rational numbers

8. *3) Associativity:
*Addition and Multiplication are associative for
rational numbers.
*For any three rational numbers a, b and c,
a + (b + c) = ( a + b) + c
Also, a x(b x c) = ( a x b) x c
Note: Subtraction and Division are not
associative for Rational numbers.

9. 5) The Role of
ONE:
*For any rational number ‘a’,
a + 0 = 0 + a = a
Zero is called the identity for the addition of Rational
numbers.
● For any rational number ‘a’,
a x 1 = 1 x a = a
One is the multiplicative identity for Rational numbers.

10. *
Additive Inverse and Multiplicative
Inverse
6) Negative of a number (Additive Inverse):
- 𝑎
𝑏
is the additive inverse of
𝑎
𝑏
since,
𝑎
𝑏
+ (-
𝑎
𝑏
) = 0
7) Reciprocal ( Multiplicative Inverse):
Eg:
2
3
x
3
2
= 1 Also, -
5
4
x -
4
5
= 1
𝑎
𝑏
and
𝑐
𝑑
are the reciprocals of each other if
𝑎
𝑏
x
𝑐
𝑑
= 1

11. *8) Distributivity of
Mutiplication over
Addition and
Subtraction:
For all rational numbers a , b and c
a( b + c) = ab + ac
a( b – c) = ab - ac

12. *Find the no./nos. in each case:
1)The rational number that does not have a reciprocal
Ans) Zero
2) The rational nos. that are equal to their reciprocals
Ans) 1 and -1
3) The rational number that is equal to its negative
Ans) Zero
4) The reciprocal of -5
Ans) -
1
5
5) The negative of -
1
4
Ans)
1
4

13. *Fill in the blanks:
1) The reciprocal of
1
𝑥
where x ≠ 0 is ---x------.
2) The product of two R.nos is always a –R.NOS----.
3) The reciprocal of a positive R.no is ----Possitive-
-----.

14. *Rational numbers
between two rational
numbers
Eg: Finding rational numbers between -2 and 0
-2 = -
2
1
= -
20
10
0 =
0
1
=
0
10
Ans) Rational nos. between -2 and 0 are:
-
19
10
, -
18
10
, ------------ , -
1
10

15. THANKYOU