CLASS-8IMPORTANT RULES OF RATIONAL NUMBERS

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.

--------- + -------- =  ------------

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 -

--------- - ---------  =   --------------

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

e                    a           e

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