Operations on Rational Numbers

In mathematics, the real number system is introduced to describe the given set of numbers in a regular manner and it is represented as “R”. The number system which represents all the numbers in the number line is known as real numbers. It is classified into two categories namely rational and irrational number.

The numbers that can be written in the form of p/q, where p and q are integers with non-zero denominator “q” is known as rational numbers. It is denoted by the letter “Q”. These numbers are non-imaginary numbers. The numbers which cannot be written in the form of p/q is known as irrational numbers.

Some of the arithmetic operations of a rational number are addition, subtraction, multiplication and division. Before that, let us know about the two terms called “operand” and “operator”. Consider an example

                        (4/5) + (10/5)

Here the number 4/5 and 10/5 are called as the operand and the addition symbol “+” is called an operator. The operator will perform the operation with operands to produce the result.

Addition and Subtraction

If both the operand have the same denominator, then add or subtract the numerator and divide it by denominator. If the operands have different denominators, then take the LCM of denominators and make it as a common denominator. Finally, multiply each term by the least common denominator to perform addition or subtraction operation.

Multiplication and Division

When two numbers are multiplied, the result called “product” is obtained. Multiplication operation is simple. Multiply the numerator of the first operand with the second operand and multiply the denominator of the first operand with the second operand to get the product. But for division operation, it is quite different. The first operand is called dividend and the second operand is called divisor. In order to divide two terms, take the reciprocal of the divisor and perform the multiplication operation with the dividend. Finally, divide the obtained fractional number if possible. If both the numerator and denominator haveodd numbers or even numbers, then divide it and make it in a simplified form like n/1 or n/n. Or else let it be in a fractional form “p/q”.

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