Basic mathematical Operations on Rational numbers 
1.    Addition of rational numbers
    Suppose we have to add two given rational numbers. First convert each of them into a rational number with a positive denominator.

    Case I : When Denominators of Given Numbers are Equal :

Thus, in order to add two rational numbers with the same denominator, we simply add their numerators and divide the sum by the common denominator.

Case II : When Denominators of Given Numbers are Unequal :
    Step 1  Taken the LCM of the denominators of the given rational numbers.
    Step 2      Express each of the given rational numbers with the above LCM as the common denominator.
    Step 3.      Now, add the numbers as shown in above example.

2.    Subtraction of rational numbers
    Subtraction is the inverse process of addition, i.e. in subtraction we add the additive inverse of a number.
    Hence, additive inverse of a rational number is negative of that rational number.

4.    Division of rational numbers
    We know that division is the inverse of multiplication. So to divide a rational number by another rational number is the same as multiplying the first number by the multiplicative inverse (reciprocal) of the second number.