There are some properties or rules of rational number has been discussed below –
1) We would like to say that, the sum of two rational numbers is always a rational number.
a c ad + bc
--------- + -------- = ------------
b d bd
2) It's also has been observed that, two rational numbers can be added in any order.
a c c a
------- + ------- = ------- + -------
b d d b
3) While we adding three rational numbers, then they can be grouped in any order.
a c e a c e
------ + (------ + ------) = (------ + ------) + -------
b d f b d f
a e c
= ( ------- + ------- ) + -------
b f d
4) Zero ‘0’ is a rational number such that the sum of any rational number and Zero ‘0’ is the rational number itself.
a a a
------- + 0 = 0 + ------- = -------
b b b
5) For every rational number a/b, there is a rational number -a/b such that –
a -a a a
------- + ( ------- ) = -------- - ( -------- ) = 0
b b b b
6) The difference between two rational numbers is also a rational number -
a c ad - bc
--------- - --------- = --------------
b d bd
7) You would like to know that, the product of two rational number is always be a rational number
a c ac
--------- X --------- = ----------
b d bd
8) Two rational numbers can be multiplied in any order
a c c a
--------- X --------- = --------- X ---------
b d d b
9) While multiplying three (or more) rational numbers they can be grouped in any order
a c e a c e
(------ X ------) X ------ = ------ X (------ X ------)
b d f b d f
a e c
= (------- X -------) X -------
b f d
a
10) For any rational number -------, we have a
b
a a
rational number 1 such that ------- X 1 = 1 X ------- b b
a b
11) for any rational number ------, there is a rational ------
b a a b
such that ------- X ------- = 1
b a
a e
12) If ------- and ------- be two rational numbers such
b f
that ------- ≠ 0 then ------- ÷ ------- also would be a
f b f
rational number.
13) If a & b be two rational numbers such that, a < b then
a + b
--------- would be a rational number between a & b,
2
a + b
That is a < ---------- < b
2