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**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.

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