Rational numbers can be written as a ratio of two integers. They can be expressed as decimals that either terminate or repeat. Examples of rational numbers include integers like 16, 1/2, 8, and decimals like 1.33. Rational numbers have properties when added, subtracted, multiplied, and divided, such as closure, commutativity, associativity, and others. Every rational number has a reciprocal, and the reciprocal of a rational number a/b is b/a.

1. Rational Numbers
Name : Nishant Rohatgi
Class : VIII A
Roll No. : 25

2. Rational Numbers
 A rational number is a real number that can
be written as a ratio of two integers.
 A rational number written in decimal form is
or repeating.

3. Examples of Rational Numbers
• 16
• 1/2
• 8
• 1.33

5. What are integers?
• Integers are the whole numbers and their negatives
• Examples of integers are
6
-12
0
186
-934
Integers are rational numbers because they can be
written as fraction with 1 as the denominator.

6. PROPERTIES OF ADDITION OF RATIONAL NUMBERS
1) CLOSURE PROPERTY:
The sum of two rational no. is always a rational number. for eg: if a/b
and c/d are any 2 rational numbers then a/b+c/d is also a rational
number
2) Commutative property:
If , a and b are two integers , then , a+ b =b + a
3) Associative property:
If a , b and c are any three integers then a+(b + c)=(a + b)+c.
4) Re-arrangement property:
The sum of three or more rational numbers remains the same , whatever
may be the order of their addition.
5) Property of zero:
If we add zero to any integer , its value does not change. If x is any
integer then , x+ 0=0+x.

7. PROPERTIES OF SUBSTRACTION OF RATIONAL
NUMBERS
1. The difference of two rational numbers is a rational
number .
For exmple if a/ b and c/d are any two rational
numbers a/b-c/d is a rational number
2. If a/b is a rational number ,
then a/b – 0 = a/b

8. PROPERTIES OF MULTIPLICATION OF RATIONAL
NUMBERS
1. Commutative property:
If x and y are two integers , then x * y = y * x
2. Associative property:
If x , y , z are any three integers, then x*(y*z)=(x*y)*z
3. Distributive property of multiplication over addition :
If x , y , z are any three integers, then
x* ( y + z ) = x * y + x * z and x* ( y - z ) = x * y - x * z
4. Multiplication by 1 :
The value of rational number remains unchanged by multiplying it by 1. for
ex -4/7 * 1 = -4/7
5. Multiplication by 0 :
If we multiply fraction by zero or vice-versa , the product is zero.
For ex -4/7*0= 0.

9. RECIPROCAL OF A RATIONAL NUMBER
1. A rational number b/a is called a reciprocal or
multiplicative inverse of a rational number a/b.
a/b * b/a = b/a * a/b = 1.
2. 1 and -1 are the only rational numbers which are their
own reciprocals.

10. PROPERTIES OF DIVISION OF RATIONAL
NUMBERS
1. If p/q and q/r are any two rational numbers and
q/r ≠ 0 , then
p/q ÷ q/r is always a rational number.
2. For any rational number p/q ,
p/q÷1 =p/q ; p/q÷(-1) = -p/q
3. For every non rational number p/q
p/q ÷ p/q = 1 ;
p/q ÷ {-p/q} = -1 ;
{-p/q} ÷ { p/q } = -1

11. Thank You