This document discusses rational numbers. It defines rational numbers as numbers that can be written as fractions p/q where p and q are integers and q is not equal to 0. Some key properties of rational numbers are discussed, including that they are closed under addition, subtraction, and multiplication. Rational numbers exhibit commutativity and associativity with addition and multiplication, as well as distributivity of multiplication over addition and subtraction. The document also shows the locations of different number types including rational numbers on the number line.

1. RATIONAL
NUMBER
By-Nandini Rai
Class-8th A
Roll No.-27

2. INDEX
- Introduction
- Properties
- Rational Numbers on the Number Line

3. INTRODUCTION
- Rational Number are closed under the
operations of Addition ,Subtraction ,
Multiplication.
- x+2=17
x=17-2
x=15 because this value of x satisfies the
given equation.The solution 15 is a
NATURAL NUMBER.

4. - x+5=5
x=5-5
x=0 the solution gives theWHOLE NUNBER
0 (zero).
- x+18=5
x=5-18
x=-13 which is not a whole number.This led
us to think of INTEGERS,(positive and
negative)
- 2x=3
x=3/2
- 5x+7= 0
- x= -7/5

5. PROPERTIES
 Commutivity
1) Whole numbers
2) Integers
3) Rational number
a) Addition is commutative for Rational
Numbers.
b) Subtraction is not commutative for
Rational Numbers.

6. - 3/2 and -7/5 this leads us to the collection of
RATIONAL NUMBER.
- A number which can be wrttten in the form
p/q where p and q are integers and q=0
cancel is called RATIONAL NUMBER.
- For example; -2/3, 6/7 are all rational
number.

7. c) Multiplication is commutative for RATIO-
-NAL NUMBERS.
d) Division is not commutative for
RATIONAL NUMBER.
 Associativity
1) Whole Numbers
2) Integers
3) Rational Number
a)Addition is Associative for Rational
Number.

8. c b) Subtraction is notAssociative for Rational
Numbers.
c) Multiplication is Associative for Rational
Numbers.
d) Division is not Associative for Rational
Numbers.
 Distributivity
- Distributivity of Multiplication over Addition
and Subtraction.
- For all rational numbers a,b and c.
- a(b+c) = ab+ac
a(b-c) = ab-ac

9.  Reciprocal
-We say that 21/8 is the Reciprocal of 8/21
and 7/-5 is the reciprocal of -5/7. 0(zero) has
no Reciprocal.
-We say that a Rational Number c/d is called
the Reciprocal or Multiplicative inverse of
another rational number a/b if a/b x c/d = 1

10. RATIONAL NUMBERS ON THE
NUMBER LINE
1) Natural Numbers
1 2 3 4 5 6 7
2) Whole Numbers
0 1 2 3 4 5

11. 3) Integers
-3 -2 -1 0 1 2 3
4) Rational Numbers
-1 -1/2 0 ½ 1

12. THANKYOU
The End