Answer to Question #190565 in Calculus for saji

Question

How to complete the rational numbers? Mention the processes.

Answer 1

There are three methods to find the rational number between two rational number

Method 1) It is generally used when it is desire to find one or two rational number between two numbers.

It is the average value of two minimum and maximum number. Say minimum value is 1/3 and max value is 1/2. Then the other rational number became 1/2+1/3=5/6

Method 2. It is generally used when we want to more rational number between two numbers.

Case 1) Having same denominator of minimum and maximum value.

Say 2/5 and 3/5. If we want two rational number in between these three numbers. Then we need to multiply and divide by 4 in both number. Thus number became 8/20 and 12/20 So the new rational number are 9/20, 10/20, 11/20

Case 2: If denominator are different, then make the denominator same by taking LCM, then do the process accordingly above.

Method 3: If we want n rational numbers in between 2 rational numbers. Then makes equal distance in between 2 rational numbers. d=(y-x)/(n+1)

where y-x is the length of two rational numbers.

first rational number becomes=x+d, second is x+2d and so on