The document discusses properties of rational numbers. It defines a rational number as a number that can be expressed as p/q where p and q are integers and q is not equal to 0. It then lists properties of rational numbers under addition: 1) closure, 2) commutativity, 3) associativity, 4) existence of an additive identity element (0), and 5) existence of additive inverses. Examples are provided to illustrate each property.

1. Made by-
Madhvi
choudhary

2. 1. Rational numbers
2. Properties of addition
3. Closure property
4. Commutative property
5. Associative property
6. Existence of additive identity
7. Existence of additive inverse

3. A number which can be presented
in p/q form, where p and q are
integers q= 0 is called a Rational
Number.

4. 1. Closure property.
2. Associative property.
3. Commutative property.
4. Existence of additive identity.
5. Existence of additive inverse.

5. If p/q and r/s are two rational number,
then their sum will be also a rational
number .
For example- - 3 + 9 = -3 +9 =6
7 7 7 7

6. If p/q and r/s are two rational numbers, then
p/r + r/s = r/s+ p/q, where p , q , r , s are
integers and q , r are not equal to zero.
Example= -2/9 + 5/9 = -2+5 = 3
9 9

7. If p/q , r/s , t/u are three rational
number, then [p/q + r/s] + t/u = p/q +
[r/s + t/u ] , where p , q , r , s ,t , u are
integer and q , s , u are not equal to
zero.

8. If p/q is a rational number, then there exist a
rational number ‘0’, such that
p/q + 0 = p/q = 0+ p/q,
Where p and q are integer and q is not equal
to zero.
Additive identity is 0 (zero).

9. For a rational number p/q, there exist
another rational number (-p/q),such that
p/q + (-p/q) = 0 = (-p/q) + p/q
Where p and q are integers, and q is not
equal to zero.
p/q and –p/q are additive inverse of each
other.