Rational Numbers and Their Simplification

There are various number systems in the modern mathematical world. They support the basic arithmetic operations. Simplification is the process of simplifying the terms in a mathematical expression or equation to its lowest terms. It helps in easy understanding of the concepts and also in the ease of calculations. The process of simplifying rational numbers can be explained with the help of examples and is very similar to other simplifications which are carried out in the mathematical world.  They can be in the form of a number which is like P/Q. Both P and Q are said to be integers but the condition is that the number or integer Q must not be equal to zero. This is because any number divided by the number zero gives a term called infinity which is not defined. The process to simplify rational numbers is quite simple and can be easily learnt. If they are to be added then their denominators must be made equal. After making the denominators equal the numerators are just added and the final result or the number is obtained. This number can be further simplified by dividing both the numerator and the denominator with a common number. This process can be continued till both the numerator and the denominator are not further divisible by a common number. It means the given expression has reached its lowest term and cannot be further simplified.

The question how to simplify rational numbers can be further clarified with the help of another example. If two such numbers are to be subtracted from another, then their denominators are to be made equal and the numerators are to be subtracted from one another. If the denominators are already equal then the task becomes easy. The denominators are made equal by taking the LCM of the two denominators. If there are more than two denominators, then the other denominator is also included in the process. For the process of multiplication both the numerators and the denominators are multiplied individually. There is no need to take LCM in this process. After multiplication the resultant is further simplified and made into its smallest form. This is the process of simplification. For the process of division the second number’s reciprocal is taken and multiplied with the first number and the same process is continued till the number in its smallest form is got. Once this is done, the process is complete.